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17.9125 8.46625C18.6138 9.23625 19.04 10.2125 19.04 11.4225C19.04 15.6437 16.4688 16.5787 14.0213 16.8537C14.42 17.1975 14.7638 17.8575 14.7638 18.8887C14.7638 20.36 14.75 21.5425 14.75 21.9137C14.75 22.2025 14.9563 22.5462 15.5063 22.4362C19.8513 20.9787 23 16.8537 23 12C23 5.9225 18.0775 1 12 1Z"></path> </svg> </a> <div class="flex-1 flex-order-2 text-right"> <a href="/login?return_to=https%3A%2F%2Fgithub.com%2Fethz-adrl%2Fcontrol-toolbox" class="HeaderMenu-link HeaderMenu-button d-inline-flex d-lg-none flex-order-1 f5 no-underline border color-border-default rounded-2 px-2 py-1 color-fg-inherit js-prevent-focus-on-mobile-nav" data-hydro-click="{"event_type":"authentication.click","payload":{"location_in_page":"site header menu","repository_id":null,"auth_type":"SIGN_UP","originating_url":"https://github.com/ethz-adrl/control-toolbox","user_id":null}}" data-hydro-click-hmac="b29fd0ed3b822cd9c8a98d960c003f495838098276691f88c394007c09041ff4" data-analytics-event="{"category":"Marketing nav","action":"click to Sign in","label":"ref_page:Marketing;ref_cta:Sign in;ref_loc:Header"}" > Sign in </a> </div> </div> <div class="HeaderMenu js-header-menu height-fit position-lg-relative d-lg-flex flex-column flex-auto top-0"> <div class="HeaderMenu-wrapper d-flex flex-column flex-self-start flex-lg-row flex-auto rounded rounded-lg-0"> <nav class="HeaderMenu-nav" aria-label="Global"> <ul class="d-lg-flex list-style-none"> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Product <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"github_copilot","context":"product","tag":"link","label":"github_copilot_link_product_navbar"}" href="https://github.com/features/copilot"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-copilot color-fg-subtle mr-3"> <path d="M23.922 16.992c-.861 1.495-5.859 5.023-11.922 5.023-6.063 0-11.061-3.528-11.922-5.023A.641.641 0 0 1 0 16.736v-2.869a.841.841 0 0 1 .053-.22c.372-.935 1.347-2.292 2.605-2.656.167-.429.414-1.055.644-1.517a10.195 10.195 0 0 1-.052-1.086c0-1.331.282-2.499 1.132-3.368.397-.406.89-.717 1.474-.952 1.399-1.136 3.392-2.093 6.122-2.093 2.731 0 4.767.957 6.166 2.093.584.235 1.077.546 1.474.952.85.869 1.132 2.037 1.132 3.368 0 .368-.014.733-.052 1.086.23.462.477 1.088.644 1.517 1.258.364 2.233 1.721 2.605 2.656a.832.832 0 0 1 .053.22v2.869a.641.641 0 0 1-.078.256ZM12.172 11h-.344a4.323 4.323 0 0 1-.355.508C10.703 12.455 9.555 13 7.965 13c-1.725 0-2.989-.359-3.782-1.259a2.005 2.005 0 0 1-.085-.104L4 11.741v6.585c1.435.779 4.514 2.179 8 2.179 3.486 0 6.565-1.4 8-2.179v-6.585l-.098-.104s-.033.045-.085.104c-.793.9-2.057 1.259-3.782 1.259-1.59 0-2.738-.545-3.508-1.492a4.323 4.323 0 0 1-.355-.508h-.016.016Zm.641-2.935c.136 1.057.403 1.913.878 2.497.442.544 1.134.938 2.344.938 1.573 0 2.292-.337 2.657-.751.384-.435.558-1.15.558-2.361 0-1.14-.243-1.847-.705-2.319-.477-.488-1.319-.862-2.824-1.025-1.487-.161-2.192.138-2.533.529-.269.307-.437.808-.438 1.578v.021c0 .265.021.562.063.893Zm-1.626 0c.042-.331.063-.628.063-.894v-.02c-.001-.77-.169-1.271-.438-1.578-.341-.391-1.046-.69-2.533-.529-1.505.163-2.347.537-2.824 1.025-.462.472-.705 1.179-.705 2.319 0 1.211.175 1.926.558 2.361.365.414 1.084.751 2.657.751 1.21 0 1.902-.394 2.344-.938.475-.584.742-1.44.878-2.497Z"></path><path d="M14.5 14.25a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Zm-5 0a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Z"></path> </svg> <div> <div class="color-fg-default h4">GitHub Copilot</div> Write better code with AI </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"security","context":"product","tag":"link","label":"security_link_product_navbar"}" href="https://github.com/features/security"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-shield-check color-fg-subtle mr-3"> <path d="M16.53 9.78a.75.75 0 0 0-1.06-1.06L11 13.19l-1.97-1.97a.75.75 0 0 0-1.06 1.06l2.5 2.5a.75.75 0 0 0 1.06 0l5-5Z"></path><path d="m12.54.637 8.25 2.675A1.75 1.75 0 0 1 22 4.976V10c0 6.19-3.771 10.704-9.401 12.83a1.704 1.704 0 0 1-1.198 0C5.77 20.705 2 16.19 2 10V4.976c0-.758.489-1.43 1.21-1.664L11.46.637a1.748 1.748 0 0 1 1.08 0Zm-.617 1.426-8.25 2.676a.249.249 0 0 0-.173.237V10c0 5.46 3.28 9.483 8.43 11.426a.199.199 0 0 0 .14 0C17.22 19.483 20.5 15.461 20.5 10V4.976a.25.25 0 0 0-.173-.237l-8.25-2.676a.253.253 0 0 0-.154 0Z"></path> </svg> <div> <div class="color-fg-default h4">Security</div> Find and fix vulnerabilities </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"actions","context":"product","tag":"link","label":"actions_link_product_navbar"}" href="https://github.com/features/actions"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-workflow color-fg-subtle mr-3"> <path d="M1 3a2 2 0 0 1 2-2h6.5a2 2 0 0 1 2 2v6.5a2 2 0 0 1-2 2H7v4.063C7 16.355 7.644 17 8.438 17H12.5v-2.5a2 2 0 0 1 2-2H21a2 2 0 0 1 2 2V21a2 2 0 0 1-2 2h-6.5a2 2 0 0 1-2-2v-2.5H8.437A2.939 2.939 0 0 1 5.5 15.562V11.5H3a2 2 0 0 1-2-2Zm2-.5a.5.5 0 0 0-.5.5v6.5a.5.5 0 0 0 .5.5h6.5a.5.5 0 0 0 .5-.5V3a.5.5 0 0 0-.5-.5ZM14.5 14a.5.5 0 0 0-.5.5V21a.5.5 0 0 0 .5.5H21a.5.5 0 0 0 .5-.5v-6.5a.5.5 0 0 0-.5-.5Z"></path> </svg> <div> <div class="color-fg-default h4">Actions</div> Automate any workflow </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"codespaces","context":"product","tag":"link","label":"codespaces_link_product_navbar"}" href="https://github.com/features/codespaces"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-codespaces color-fg-subtle mr-3"> <path d="M3.5 3.75C3.5 2.784 4.284 2 5.25 2h13.5c.966 0 1.75.784 1.75 1.75v7.5A1.75 1.75 0 0 1 18.75 13H5.25a1.75 1.75 0 0 1-1.75-1.75Zm-2 12c0-.966.784-1.75 1.75-1.75h17.5c.966 0 1.75.784 1.75 1.75v4a1.75 1.75 0 0 1-1.75 1.75H3.25a1.75 1.75 0 0 1-1.75-1.75ZM5.25 3.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h13.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Zm-2 12a.25.25 0 0 0-.25.25v4c0 .138.112.25.25.25h17.5a.25.25 0 0 0 .25-.25v-4a.25.25 0 0 0-.25-.25Z"></path><path d="M10 17.75a.75.75 0 0 1 .75-.75h6.5a.75.75 0 0 1 0 1.5h-6.5a.75.75 0 0 1-.75-.75Zm-4 0a.75.75 0 0 1 .75-.75h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1-.75-.75Z"></path> </svg> <div> <div class="color-fg-default h4">Codespaces</div> Instant dev environments </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"issues","context":"product","tag":"link","label":"issues_link_product_navbar"}" href="https://github.com/features/issues"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-issue-opened color-fg-subtle mr-3"> <path d="M12 1c6.075 0 11 4.925 11 11s-4.925 11-11 11S1 18.075 1 12 5.925 1 12 1ZM2.5 12a9.5 9.5 0 0 0 9.5 9.5 9.5 9.5 0 0 0 9.5-9.5A9.5 9.5 0 0 0 12 2.5 9.5 9.5 0 0 0 2.5 12Zm9.5 2a2 2 0 1 1-.001-3.999A2 2 0 0 1 12 14Z"></path> </svg> <div> <div class="color-fg-default h4">Issues</div> Plan and track work </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"code_review","context":"product","tag":"link","label":"code_review_link_product_navbar"}" href="https://github.com/features/code-review"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-code-review color-fg-subtle mr-3"> <path d="M10.3 6.74a.75.75 0 0 1-.04 1.06l-2.908 2.7 2.908 2.7a.75.75 0 1 1-1.02 1.1l-3.5-3.25a.75.75 0 0 1 0-1.1l3.5-3.25a.75.75 0 0 1 1.06.04Zm3.44 1.06a.75.75 0 1 1 1.02-1.1l3.5 3.25a.75.75 0 0 1 0 1.1l-3.5 3.25a.75.75 0 1 1-1.02-1.1l2.908-2.7-2.908-2.7Z"></path><path d="M1.5 4.25c0-.966.784-1.75 1.75-1.75h17.5c.966 0 1.75.784 1.75 1.75v12.5a1.75 1.75 0 0 1-1.75 1.75h-9.69l-3.573 3.573A1.458 1.458 0 0 1 5 21.043V18.5H3.25a1.75 1.75 0 0 1-1.75-1.75ZM3.25 4a.25.25 0 0 0-.25.25v12.5c0 .138.112.25.25.25h2.5a.75.75 0 0 1 .75.75v3.19l3.72-3.72a.749.749 0 0 1 .53-.22h10a.25.25 0 0 0 .25-.25V4.25a.25.25 0 0 0-.25-.25Z"></path> </svg> <div> <div class="color-fg-default h4">Code Review</div> Manage code changes </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"discussions","context":"product","tag":"link","label":"discussions_link_product_navbar"}" href="https://github.com/features/discussions"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-comment-discussion color-fg-subtle mr-3"> <path d="M1.75 1h12.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 14.25 14H8.061l-2.574 2.573A1.458 1.458 0 0 1 3 15.543V14H1.75A1.75 1.75 0 0 1 0 12.25v-9.5C0 1.784.784 1 1.75 1ZM1.5 2.75v9.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h6.5a.25.25 0 0 0 .25-.25v-9.5a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Z"></path><path d="M22.5 8.75a.25.25 0 0 0-.25-.25h-3.5a.75.75 0 0 1 0-1.5h3.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 22.25 20H21v1.543a1.457 1.457 0 0 1-2.487 1.03L15.939 20H10.75A1.75 1.75 0 0 1 9 18.25v-1.465a.75.75 0 0 1 1.5 0v1.465c0 .138.112.25.25.25h5.5a.75.75 0 0 1 .53.22l2.72 2.72v-2.19a.75.75 0 0 1 .75-.75h2a.25.25 0 0 0 .25-.25v-9.5Z"></path> </svg> <div> <div class="color-fg-default h4">Discussions</div> Collaborate outside of code </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"code_search","context":"product","tag":"link","label":"code_search_link_product_navbar"}" href="https://github.com/features/code-search"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-code-square color-fg-subtle mr-3"> <path d="M10.3 8.24a.75.75 0 0 1-.04 1.06L7.352 12l2.908 2.7a.75.75 0 1 1-1.02 1.1l-3.5-3.25a.75.75 0 0 1 0-1.1l3.5-3.25a.75.75 0 0 1 1.06.04Zm3.44 1.06a.75.75 0 1 1 1.02-1.1l3.5 3.25a.75.75 0 0 1 0 1.1l-3.5 3.25a.75.75 0 1 1-1.02-1.1l2.908-2.7-2.908-2.7Z"></path><path d="M2 3.75C2 2.784 2.784 2 3.75 2h16.5c.966 0 1.75.784 1.75 1.75v16.5A1.75 1.75 0 0 1 20.25 22H3.75A1.75 1.75 0 0 1 2 20.25Zm1.75-.25a.25.25 0 0 0-.25.25v16.5c0 .138.112.25.25.25h16.5a.25.25 0 0 0 .25-.25V3.75a.25.25 0 0 0-.25-.25Z"></path> </svg> <div> <div class="color-fg-default h4">Code Search</div> Find more, search less </div> </a></li> </ul> </div> </div> <div class="HeaderMenu-column px-lg-4"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="product-explore-heading">Explore</span> <ul class="list-style-none f5" aria-labelledby="product-explore-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"all_features","context":"product","tag":"link","label":"all_features_link_product_navbar"}" href="https://github.com/features"> All features </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"documentation","context":"product","tag":"link","label":"documentation_link_product_navbar"}" href="https://docs.github.com"> Documentation <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 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12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Solutions <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 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Link--secondary" data-analytics-event="{"location":"navbar","action":"view_all_industries","context":"solutions","tag":"link","label":"view_all_industries_link_solutions_navbar"}" href="/solutions/industry"> View all industries </a></li> </ul> </div> </div> <div class="HeaderMenu-trailing-link rounded-bottom-2 flex-shrink-0 mt-lg-4 px-lg-4 py-4 py-lg-3 f5 text-semibold"> <a href="/solutions"> View all solutions <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-right HeaderMenu-trailing-link-icon"> <path d="M6.22 3.22a.75.75 0 0 1 1.06 0l4.25 4.25a.75.75 0 0 1 0 1.06l-4.25 4.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L9.94 8 6.22 4.28a.75.75 0 0 1 0-1.06Z"></path> </svg> </a> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Resources <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="resources-topics-heading">Topics</span> <ul 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data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"executive_insights","context":"resources","tag":"link","label":"executive_insights_link_resources_navbar"}" href="https://github.com/solutions/executive-insights"> Executive Insights </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Open Source <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4"> <div class="HeaderMenu-column"> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"github_sponsors","context":"open_source","tag":"link","label":"github_sponsors_link_open_source_navbar"}" href="/sponsors"> <div> <div class="color-fg-default h4">GitHub Sponsors</div> Fund open source developers </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"the_readme_project","context":"open_source","tag":"link","label":"the_readme_project_link_open_source_navbar"}" href="https://github.com/readme"> <div> <div class="color-fg-default h4">The ReadME Project</div> GitHub community articles </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="open-source-repositories-heading">Repositories</span> <ul class="list-style-none f5" aria-labelledby="open-source-repositories-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"topics","context":"open_source","tag":"link","label":"topics_link_open_source_navbar"}" href="https://github.com/topics"> Topics </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"trending","context":"open_source","tag":"link","label":"trending_link_open_source_navbar"}" href="https://github.com/trending"> Trending </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" 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1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg></button> </div> </div> </div> <scrollable-region data-labelled-by="custom-scopes-dialog-title"> <div data-view-component="true" class="Overlay-body"> <div data-target="custom-scopes.customScopesModalDialogFlash"></div> <div hidden class="create-custom-scope-form" data-target="custom-scopes.createCustomScopeForm"> </option></form><form id="custom-scopes-dialog-form" data-turbo="false" action="/search/custom_scopes" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="u65OqVVX5dL+VIMvULmWXONeNWX2zsVvWcpB/20VByIYPQXT9g25ZAavRXHyn9VbfktdA5TzmYxGMTnTFTg+5Q==" /> <div data-target="custom-scopes.customScopesModalDialogFlash"></div> <input type="hidden" id="custom_scope_id" name="custom_scope_id" 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dir=\"auto\"\u003eControl Toolbox\u003c/h1\u003e\u003ca id=\"user-content-control-toolbox\" class=\"anchor\" aria-label=\"Permalink: Control Toolbox\" href=\"#control-toolbox\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://camo.githubusercontent.com/489c66c07cabfd2a9a7afe919534bb48506a6737a3f5d4277fdd7dd2b8a885b8/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c616e6775616765732f746f702f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/489c66c07cabfd2a9a7afe919534bb48506a6737a3f5d4277fdd7dd2b8a885b8/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c616e6775616765732f746f702f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c\" alt=\"GitHub top language\" data-canonical-src=\"https://img.shields.io/github/languages/top/ethz-adrl/control-toolbox.svg?style=social\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://camo.githubusercontent.com/2d66165213d48ca4291cb199718ba47966f4b60d25b832d91a3c2dd0aa44f3c3/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c6963656e73652f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/2d66165213d48ca4291cb199718ba47966f4b60d25b832d91a3c2dd0aa44f3c3/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c6963656e73652f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c\" alt=\"GitHub\" data-canonical-src=\"https://img.shields.io/github/license/ethz-adrl/control-toolbox.svg?style=social\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-diff notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"- Important note (July 2021): this library is currently only scarcely maintained,\n- it may take a while until we respond to bugs or feature requests.\"\u003e\u003cpre\u003e\u003cspan class=\"pl-md\"\u003e\u003cspan class=\"pl-md\"\u003e-\u003c/span\u003e Important note (July 2021): this library is currently only scarcely maintained,\u003c/span\u003e\n\u003cspan class=\"pl-md\"\u003e\u003cspan class=\"pl-md\"\u003e-\u003c/span\u003e it may take a while until we respond to bugs or feature requests.\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis is the Control Toolbox, an efficient C++ library for control, estimation, optimization and motion planning in robotics.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eLink to the wiki, \u003ca href=\"https://github.com/ethz-adrl/control-toolbox/wiki/Quickstart\"\u003equickstart!\u003c/a\u003e \u003cbr\u003e\nFind the detailed documentation \u003ca href=\"https://ethz-adrl.github.io/ct/\" rel=\"nofollow\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eOverview\u003c/h2\u003e\u003ca id=\"user-content-overview\" class=\"anchor\" aria-label=\"Permalink: Overview\" href=\"#overview\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis is the ADRL Control Toolbox ('CT'), an open-source C++ library for efficient modelling, control,\nestimation, trajectory optimization and model predictive control. The CT is applicable to a broad class of dynamic systems, but features additional modelling tools specially designed for robotics. This page outlines its general concept, its major building blocks and highlights selected application examples.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems.\nThe CT was designed with the following features in mind:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eSystems and dynamics\u003c/strong\u003e:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eintuitive modelling of systems governed by ordinary differential or difference equations.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eTrajectory optimization, optimal control and (nonlinear) model predictive control\u003c/strong\u003e:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eintuitive modelling of cost functions and constraints\u003c/li\u003e\n\u003cli\u003ecommon interfaces for optimal control solvers and nonlinear model predictive control\u003c/li\u003e\n\u003cli\u003ecurrently supported algorithms:\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eClassical Single Shooting\u003c/li\u003e\n\u003cli\u003eiLQR / iLQG (iterative Linear Quadratic Optimal Control)\u003c/li\u003e\n\u003cli\u003eMultiple-shooting iLQR\u003c/li\u003e\n\u003cli\u003eGauss-Newton-Multiple-Shooting (GNMS)\u003c/li\u003e\n\u003cli\u003eClassical Direct Multiple Shooting (DMS)\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003estandardized interfaces for the solvers\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eIPOPT (first and second order)\u003c/li\u003e\n\u003cli\u003eSNOPT\u003c/li\u003e\n\u003cli\u003eHPIPM\u003c/li\u003e\n\u003cli\u003ecustom Riccati-solver\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003ePerformance\u003c/strong\u003e:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003esolve large scale optimal control problems in MPC fashion.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eRobot Modelling, Rigid Body Kinematics and Dynamics\u003c/strong\u003e:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003estraight-forward interface to the state-of the art rigid body dynamics modelling tool \u003ca href=\"https://robcogenteam.bitbucket.io/\" rel=\"nofollow\"\u003eRobCoGen\u003c/a\u003e.\u003c/li\u003e\n\u003cli\u003eimplementation of a basic nonlinear-programming inverse kinematics solver for fix-base robots.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eAutomatic Differentiation\u003c/strong\u003e:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003efirst and second order automatic differentiation of arbitrary vector-valued functions including cost functions and constraints\u003c/li\u003e\n\u003cli\u003eautomatic differentiation and code generation of rigid body dynamics\u003c/li\u003e\n\u003cli\u003ederivative code generation for maximum efficiency\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRobot Application Examples\u003c/h2\u003e\u003ca id=\"user-content-robot-application-examples\" class=\"anchor\" aria-label=\"Permalink: Robot Application Examples\" href=\"#robot-application-examples\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe Control Toolbox has been used for Hardware and Simulation control tasks on flying, walking and ground robots.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://www.youtube.com/watch?feature=player_embedded\u0026amp;v=Y7-1CBqs4x4\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/ccfefa38effcf388c4c63d9c0a881a937003f6414d88af7bce86088c2477f42e/687474703a2f2f696d672e796f75747562652e636f6d2f76692f59372d31434271733478342f302e6a7067\" alt=\"Control Toolbox example video\" width=\"360\" height=\"270\" border=\"10\" data-canonical-src=\"http://img.youtube.com/vi/Y7-1CBqs4x4/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003ca href=\"http://www.youtube.com/watch?feature=player_embedded\u0026amp;v=vuCSKtP67E4\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/9d917540ebd1bdc47f7d5212f6519991d2f4c5af190516e2453763bf0e6d9f61/687474703a2f2f696d672e796f75747562652e636f6d2f76692f767543534b7450363745342f302e6a7067\" alt=\"Control Toolbox example video\" width=\"360\" height=\"270\" border=\"10\" data-canonical-src=\"http://img.youtube.com/vi/vuCSKtP67E4/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://www.youtube.com/watch?feature=player_embedded\u0026amp;v=rWmw-ERGyz4\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/8145c8e48bbb7dc313e6570989b3b17ed3be15d31513167dd78f507cd909e605/687474703a2f2f696d672e796f75747562652e636f6d2f76692f72576d772d455247797a342f302e6a7067\" alt=\"Control Toolbox example video\" width=\"360\" height=\"270\" border=\"10\" data-canonical-src=\"http://img.youtube.com/vi/rWmw-ERGyz4/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\n\u003ca href=\"http://www.youtube.com/watch?feature=player_embedded\u0026amp;v=rVu1L_tPCoM\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/0e662a73ff860e1ad7bef5d1ff7db1acc8064e40960cc31d72479ab102ad53f3/687474703a2f2f696d672e796f75747562652e636f6d2f76692f725675314c5f7450436f4d2f302e6a7067\" alt=\"Control Toolbox example video\" width=\"360\" height=\"270\" border=\"10\" data-canonical-src=\"http://img.youtube.com/vi/rVu1L_tPCoM/0.jpg\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSlightly more complex optimization examples, including gait optimization for a quadruped, are availabe in \u003ca href=\"https://github.com/ethz-adrl/ct_ros\"\u003ect_ros\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWhat is the CT?\u003c/h2\u003e\u003ca id=\"user-content-what-is-the-ct\" class=\"anchor\" aria-label=\"Permalink: What is the CT?\" href=\"#what-is-the-ct\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eA common tasks for researchers and practitioners in both the control and the robotics communities\nis to model systems, implement equations of motion and design model-based controllers, estimators,\nplanning algorithms, etc.\nSooner or later, one is confronted with questions of efficient implementation, computing derivative\ninformation, formulating cost functions and constraints or running controllers in model-predictive\ncontrol fashion.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe Control Toolbox is specifically designed for these tasks. It is written entirely in C++ and has\na strong focus on highly efficient code that can be run online (in the loop) on robots or other\nactuated hardware. A major contribution of the CT is its implementations of optimal control\nalgorithms, spanning a range from simple LQR reference implementations to constrained model predictive\ncontrol. The CT supports Automatic Differentiation (Auto-Diff) and allows to generate derivative code\nfor arbitrary scalar and vector-valued functions.\nWe designed the toolbox with usability in mind, allowing users to apply advanced concepts such as\nnonlinear model predictive control (NMPC) or numerical optimal control easily and with minimal effort.\nWhile we provide an interface to a state-of-the art Auto-Diff compatible robot modelling software, all\nother modules are independent of the a particular modelling framework, allowing the code to be interfaced\nwith existing C/C++ code or libraries.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe CT has been successfully used in a variety of different projects, including a large number of\nhardware experiments, demonstrations and academic publications.\nExample hardware applications are online trajectory optimization with collision\navoidance \\cite giftthaler2017autodiff, trajectory optimization for Quadrupeds \\cite neunert:2017:ral\nand mobile manipulators \\cite giftthaler2017efficient as well as NMPC on ground robots \\cite neunert2017mpc\nand UAVs \\cite neunert16hexrotor. The project originated from research conducted at the Agile \u0026amp; Dexterous\nRobotics Lab at ETH Zurich, but is continuously extended to cover more fields of applications and algorithms.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eScope of the CT\u003c/h2\u003e\u003ca id=\"user-content-scope-of-the-ct\" class=\"anchor\" aria-label=\"Permalink: Scope of the CT\" href=\"#scope-of-the-ct\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eSoftware is one of the key building blocks for robotic systems and there is a great effort\nin creating software tools and libraries for robotics.\nHowever, when it comes to control and especially Numerical Optimal Control, there are not\nmany open source tools available that are both easy to use for fast development as well as\nefficient enough for online usage.\nWhile there exist mature toolboxes for Numerical Optimal Control and Trajectory Optimization,\nthey are highly specialized, standalone tools that due not provide sufficient flexibility\nfor other applications. Here is where the CT steps in. The CT has been designed from ground\nup to provide the tools needed for fast development and evaluation of control methods while\nbeing optimized for efficiency allowing for online operation. While the emphasis lies on control,\nthe tools provided can also be used for simulation, estimation or optimization applications.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn contrast to other robotic software, CT is not a rigid integrated application but can be\nseen quite literal as a toolbox: It offers a variety of tools which can be used and combined\nto solve a task at hand. While ease-of-use has been a major criteria during the design and\napplication examples are provided, using CT still requires programming and control knowledge.\nHowever, it frees the users from implementing standard methods that require in-depth experience\nwith linear algebra or numerical methods. Furthermore, by using common definitions and types,\na seamless integration between different components such as systems, controllers or integrators\nis provided, enabling fast prototyping.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDesign and Implementation\u003c/h2\u003e\u003ca id=\"user-content-design-and-implementation\" class=\"anchor\" aria-label=\"Permalink: Design and Implementation\" href=\"#design-and-implementation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe main focus of CT is efficiency, which is why it is fully implemented in C++.\nSince CT is designed as a toolbox rather than an integrated application, we tried to provide\nmaximum flexibility to the users. Therefore, it is not tied to a specific middleware such as\nROS and dependencies are kept at a minimum. The two essential dependencies for CT are\n\u003ca href=\"http://eigen.tuxfamily.org\" rel=\"nofollow\"\u003eEigen\u003c/a\u003e and\n\u003ca href=\"http://github.com/ethz-asl/kindr\"\u003eKindr\u003c/a\u003e\n(which is based on Eigen). This Eigen dependency is intentional since Eigen\nis a defacto standard for linear algebra in C++, as it provides highly efficient implementations\nof standard matrix operations as well as more advanced linear algebra methods.\nKindr is a header only Kinematics library which builds on top of it and provides data types\nfor different rotation representations such as Quaternions, Euler angles or rotation matrices.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eStructure and Modules of the CT\u003c/h2\u003e\u003ca id=\"user-content-structure-and-modules-of-the-ct\" class=\"anchor\" aria-label=\"Permalink: Structure and Modules of the CT\" href=\"#structure-and-modules-of-the-ct\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe Control Toolbox consists of three main modules. The Core (\u003ccode\u003ect_core\u003c/code\u003e) module, the Optimal\nControl (\u003ccode\u003ect_optcon\u003c/code\u003e) module and the Rigid Body Dynamics (\u003ccode\u003ect_rbd\u003c/code\u003e) module.\nThere is a clear hierarchy between the modules.\nThat means, the modules depend on each other in this order, e.g. you can use the core module\nwithout the optcon or rbd module.\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eThe Core (\u003ccode\u003ect_core\u003c/code\u003e) module provides general type definitions and mathematical tools.\nFor example, it contains most data type definitions, definitions for systems and controllers,\nas well as basic functionality such as numerical integrators for differential equations.\u003c/li\u003e\n\u003cli\u003eThe Optimal Control (\u003ccode\u003ect_optcon\u003c/code\u003e) module builds on top of the Core module and adds\ninfrastructure for defining and solving Optimal Control Problems. It contains the functionality\nfor defining cost functions, constraints, solver backends and a general MPC wrapper.\u003c/li\u003e\n\u003cli\u003eThe Rigid Body Dynamics (\u003ccode\u003ect_rbd\u003c/code\u003e) module provides tools for modelling Rigid Body Dynamics\nsystems and interfaces with \u003ccode\u003ect_core\u003c/code\u003e and \u003ccode\u003ect_optcon\u003c/code\u003e data types.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eFor testing as well as examples, we also provide the models module (\u003ccode\u003ect_models\u003c/code\u003e) which contains\nvarious robot models including a quadruped, a robotic arm, a normal quadrotor and a quadrotor\nwith slung load.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe four different main modules are detailed in the following.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ect_core (Core)\u003c/h3\u003e\u003ca id=\"user-content-ct_core-core\" class=\"anchor\" aria-label=\"Permalink: ct_core (Core)\" href=\"#ct_core-core\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eDefinitions of fundamental types for \u003cstrong\u003econtrol\u003c/strong\u003e and simulation, such as dynamic systems\n(ct::core::System), states (ct::core::StateVector), controls (ct::core::Controller), or trajectories\n(ct::core::DiscreteTrajectoryBase).\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eNumeric integration\u003c/strong\u003e (ct::core::Integrator) with various ODE solvers including fixed step\n(ct::core::IntegratorEuler, ct::core::IntegratorRK4) and variable step (ct::core::IntegratorRK5Variable,\nct::core::ODE45) integrators, as well as symplectic (semi-implicit) integrators.\u003c/li\u003e\n\u003cli\u003eNumerical approximation of Trajectory \u003cstrong\u003eSensitivities\u003c/strong\u003e (ct::core::Sensitivity , e.g. by forward-integrating\nvariational differential equations)\u003c/li\u003e\n\u003cli\u003eCommon \u003cstrong\u003efeedback controllers\u003c/strong\u003e (e.g. ct::core::PIDController)\u003c/li\u003e\n\u003cli\u003eDerivatives/Jacobians of general functions using \u003cstrong\u003eNumerical Differentiation\u003c/strong\u003e (ct::core::DerivativesNumDiff)\nor \u003cstrong\u003eAutomatic-Differentiation\u003c/strong\u003e with code-generation (ct::core::DerivativesCppadCG) and just-in-time (JIT)\ncompilation (ct::core::DerivativesCppadJIT)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ect_optcon (Optimal Control)\u003c/h3\u003e\u003ca id=\"user-content-ct_optcon-optimal-control\" class=\"anchor\" aria-label=\"Permalink: ct_optcon (Optimal Control)\" href=\"#ct_optcon-optimal-control\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eDefinitions for \u003cstrong\u003eOptimal Control Problems\u003c/strong\u003e (ct::optcon::OptConProblem) and \u003cstrong\u003eOptimal Control Solvers\u003c/strong\u003e (ct::optcon::OptConSolver)\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eCostFunction toolbox\u003c/strong\u003e allowing to construct cost functions from file and providing first-order and \u003cstrong\u003esecond-order approximations\u003c/strong\u003e, see ct::optcon::CostFunction.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eConstraint toolbox\u003c/strong\u003e for formulating constraints of Optimal Control Problems, as well as automatically computing their Jacobians.\u003c/li\u003e\n\u003cli\u003ereference C++ implementations of the \u003cstrong\u003eLinear Quadratic Regulator\u003c/strong\u003e, infinite-horizon LQR and time-varying LQR (ct::optcon::LQR, ct::optcon::TVLQR)\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eRiccati-solver\u003c/strong\u003e (ct::optcon::GNRiccatiSolver) for unconstrained linear-quadratic optimal control problems, interface to high-performance\n\u003ca href=\"https://github.com/giaf/hpipm\"\u003e third-party Riccati-solvers\u003c/a\u003e for constrained linear-quadratic optimal control problems\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eiterative non-linear Optimal Control\u003c/strong\u003e solvers, i.e. Gauss-Newton solvers such as iLQR (ct::optcon::iLQR) and\nGauss-Newton Multiple Shooting(ct::optcon::GNMS), constrained direct multiple-shooting (ct::optcon::DmsSolver)\u003c/li\u003e\n\u003cli\u003eNon-Linear \u003cstrong\u003eModel Predictive Control\u003c/strong\u003e (ct::optcon::MPC)\u003c/li\u003e\n\u003cli\u003eDefinitions for Nonlinear Programming Problems (\u003cstrong\u003eNLPs\u003c/strong\u003e, ct::optcon::Nlp) and interfaces to third-party \u003cstrong\u003eNLP Solvers\u003c/strong\u003e\n(ct::optcon::SnoptSolver and ct::optcon::IpoptSolver)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ect_rbd (Rigid Body Dynamics)\u003c/h3\u003e\u003ca id=\"user-content-ct_rbd-rigid-body-dynamics\" class=\"anchor\" aria-label=\"Permalink: ct_rbd (Rigid Body Dynamics)\" href=\"#ct_rbd-rigid-body-dynamics\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eStandard models for Rigid Body Dynamics\u003c/li\u003e\n\u003cli\u003eDefinitions for the state of a Rigid Body System expressed as general coordinates (ct::rbd::RBDState)\u003c/li\u003e\n\u003cli\u003eRoutines for different flavors of \u003cstrong\u003eForward\u003c/strong\u003e and \u003cstrong\u003eInverse Dynamics\u003c/strong\u003e (ct::rbd::Dynamics)\u003c/li\u003e\n\u003cli\u003eRigid body and end-effector \u003cstrong\u003ekinematics\u003c/strong\u003e (ct::rbd::Kinematics)\u003c/li\u003e\n\u003cli\u003eOperational Space Controllers\u003c/li\u003e\n\u003cli\u003eBasic soft \u003cstrong\u003eauto-differentiable contact model\u003c/strong\u003e for arbitrary frames (ct::rbd::EEContactModel)\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eActuator dynamics\u003c/strong\u003e (ct::rbd::ActuatorDynamics)\u003c/li\u003e\n\u003cli\u003eBackend uses \u003ca href=\"https://robcogenteam.bitbucket.io/\" rel=\"nofollow\"\u003eRobCoGen\u003c/a\u003e,\na highly efficient Rigid Body Dynamics library\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ect_models\u003c/h3\u003e\u003ca id=\"user-content-ct_models\" class=\"anchor\" aria-label=\"Permalink: ct_models\" href=\"#ct_models\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eVarious standard models for testing and evaluation including UAVs (ct::models::Quadrotor), ground robots,\nlegged robots (ct::models::HyQ), robot arms (ct::models::HyA), inverted pendulums etc.\u003c/li\u003e\n\u003cli\u003eMeans of creating linear approximation of these models\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eHow to get started\u003c/h2\u003e\u003ca id=\"user-content-how-to-get-started\" class=\"anchor\" aria-label=\"Permalink: How to get started\" href=\"#how-to-get-started\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo get started with the control toolbox, please build the repository documentation with doxygen and follow the \"Getting Started\" tutorial.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSupport\u003c/h2\u003e\u003ca id=\"user-content-support\" class=\"anchor\" aria-label=\"Permalink: Support\" href=\"#support\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003econtact the devs: \u003ca href=\"mailto:control-toolbox-dev@googlegroups.com\"\u003econtrol-toolbox-dev@googlegroups.com\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAcknowledgements\u003c/h2\u003e\u003ca id=\"user-content-acknowledgements\" class=\"anchor\" aria-label=\"Permalink: Acknowledgements\" href=\"#acknowledgements\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eContributors\u003c/h3\u003e\u003ca id=\"user-content-contributors\" class=\"anchor\" aria-label=\"Permalink: Contributors\" href=\"#contributors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eMarkus Giftthaler, markusgft (at) gmail (dot) com\u003c/li\u003e\n\u003cli\u003eMichael Neunert\u003c/li\u003e\n\u003cli\u003eMarkus Stäuble\u003c/li\u003e\n\u003cli\u003eFarbod Farshidian\u003c/li\u003e\n\u003cli\u003eDiego Pardo\u003c/li\u003e\n\u003cli\u003eTimothy Sandy\u003c/li\u003e\n\u003cli\u003eJan Carius\u003c/li\u003e\n\u003cli\u003eRuben Grandia\u003c/li\u003e\n\u003cli\u003eHamza Merzic\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFunding\u003c/h3\u003e\u003ca id=\"user-content-funding\" class=\"anchor\" aria-label=\"Permalink: Funding\" href=\"#funding\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis software has been developed at the \u003ca href=\"http://www.adrl.ethz.ch\" rel=\"nofollow\"\u003eAgile \u0026amp; Dexterous Robotics Lab\u003c/a\u003e\nat \u003ca href=\"http://www.ethz.ch/en\" rel=\"nofollow\"\u003eETH Zurich\u003c/a\u003e, Switzerland between 2014 and 2018.\nDuring that time, development has been made possible through financial support from the \u003ca href=\"http://www.snf.ch/en/\" rel=\"nofollow\"\u003eSwiss National Science Foundation (SNF)\u003c/a\u003e\nthrough a SNF Professorship award to Jonas Buchli and the National Competence Centers in Research (NCCR)\n\u003ca href=\"https://www.nccr-robotics.ch/\" rel=\"nofollow\"\u003eRobotics\u003c/a\u003e and \u003ca href=\"http://www.dfab.ch/en/\" rel=\"nofollow\"\u003eDigital Fabrication\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eLicence Information\u003c/h2\u003e\u003ca id=\"user-content-licence-information\" class=\"anchor\" aria-label=\"Permalink: Licence Information\" href=\"#licence-information\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe Control Toolbox is released under the\n\u003ca href=\"https://choosealicense.com/licenses/bsd-2-clause/\" rel=\"nofollow\"\u003eBSD-2 clause license\u003c/a\u003e.\nPlease see LICENCE.txt and NOTICE.txt\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eHow to cite the CT\u003c/h2\u003e\u003ca id=\"user-content-how-to-cite-the-ct\" class=\"anchor\" aria-label=\"Permalink: How to cite the CT\" href=\"#how-to-cite-the-ct\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"@article{adrlCT,\n title={The control toolbox — An open-source C++ library for robotics, optimal and model predictive control},\n author={Markus Giftthaler and Michael Neunert and Markus St{\\\u0026quot;a}uble and Jonas Buchli},\n journal={2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)},\n year={2018},\n pages={123-129}\n}\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e@article{adrlCT,\n title={The control toolbox — An open-source C++ library for robotics, optimal and model predictive control},\n author={Markus Giftthaler and Michael Neunert and Markus St{\\\"a}uble and Jonas Buchli},\n journal={2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)},\n year={2018},\n pages={123-129}\n}\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eEarlier Versions\u003c/h2\u003e\u003ca id=\"user-content-earlier-versions\" class=\"anchor\" aria-label=\"Permalink: Earlier Versions\" href=\"#earlier-versions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eEarlier versions up to v2.3 are hosted on bitbucket, they can be found at \u003ca href=\"https://bitbucket.org/adrlab/ct/wiki/Home\" rel=\"nofollow\"\u003ehttps://bitbucket.org/adrlab/ct/wiki/Home\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRelated Publications\u003c/h2\u003e\u003ca id=\"user-content-related-publications\" class=\"anchor\" aria-label=\"Permalink: Related Publications\" href=\"#related-publications\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis toolbox has been used in, or has helped to realize the following academic publications:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler, Michael Neunert, Markus Stäuble and Jonas Buchli.\n“The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control”.\nIEEE Simpar 2018 (Best Student Paper Award).\n\u003ca href=\"https://arxiv.org/abs/1801.04290\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl.\n“A Family of iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control”.\nIROS 2018.\n\u003ca href=\"https://arxiv.org/abs/1711.11006\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eJan Carius, René Ranftl, Vladlen Koltun and Marco Hutter.\n\"Trajectory Optimization with Implicit Hard Contacts.\"\nIEEE Robotics and Automation Letters 3, no. 4 (2018): 3316-3323.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMichael Neunert, Markus Stäuble, Markus Giftthaler, Dario Bellicoso, Jan Carius, Christian Gehring,\nMarco Hutter and Jonas Buchli.\n“Whole Body Model Predictive Control Through Contacts For Quadrupeds”.\nIEEE Robotics and Automation Letters, 2017.\n\u003ca href=\"https://arxiv.org/abs/1712.02889\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler and Jonas Buchli.\n“A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control”.\n2017 IEEE-RAS International Conference on Humanoid Robots, November 15-17, Birmingham, UK.\n\u003ca href=\"http://ieeexplore.ieee.org/document/8239538/\" rel=\"nofollow\"\u003eIEEE Xplore\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler, Michael Neunert, Markus Stäuble, Marco Frigerio, Claudio Semini and Jonas Buchli.\n“Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation”,\nAdvanced Robotics, SIMPAR special issue. November 2017.\n\u003ca href=\"https://arxiv.org/abs/1709.03799\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMichael Neunert, Markus Giftthaler, Marco Frigerio, Claudio Semini and Jonas Buchli.\n“Fast Derivatives of Rigid Body Dynamics for Control, Optimization and Estimation”,\n2016 IEEE International Conference on Simulation, Modelling, and Programming for Autonomous Robots,\nSan Francisco. (Best Paper Award).\n\u003ca href=\"http://ieeexplore.ieee.org/document/7862380/\" rel=\"nofollow\"\u003eIEEE Xplore\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMichael Neunert, Farbod Farshidian, Alexander W. Winkler, Jonas Buchli\n\"Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds\",\nIEEE Robotics and Automation Letters,\n\u003ca href=\"http://ieeexplore.ieee.org/document/7845678/\" rel=\"nofollow\"\u003eIEEE Xplore\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMichael Neunert, Cédric de Crousaz, Fadri Furrer, Mina Kamel, Farbod Farshidian, Roland Siegwart, Jonas Buchli.\n\"Fast nonlinear model predictive control for unified trajectory optimization and tracking\",\n2016 IEEE International Conference on Robotics and Automation (ICRA),\n\u003ca href=\"http://ieeexplore.ieee.org/document/7487274/\" rel=\"nofollow\"\u003eIEEE Xplore\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler, Farbod Farshidian, Timothy Sandy, Lukas Stadelmann and Jonas Buchli.\n“Efficient Kinematic Planning for Mobile Manipulators with Non-holonomic Constraints Using Optimal Control”,\nIEEE International Conference on Robotics and Automation, 2017, Singapore.\n\u003ca href=\"https://arxiv.org/abs/1701.08051\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMarkus Giftthaler, Timothy Sandy, Kathrin Dörfler, Ian Brooks, Mark Buckingham, Gonzalo Rey,\nMatthias Kohler, Fabio Gramazio and Jonas Buchli.\n“Mobile Robotic Fabrication at 1:1 scale: the In situ Fabricator”. Construction Robotics, Springer Journal no. 41693\n\u003ca href=\"https://arxiv.org/abs/1701.03573\" rel=\"nofollow\"\u003earXiv preprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eTimothy Sandy, Markus Giftthaler, Kathrin Dörfler, Matthias Kohler and Jonas Buchli.\n“Autonomous Repositioning and Localization of an In situ Fabricator”,\nIEEE International Conference on Robotics and Automation 2016, Stockholm, Sweden.\n\u003ca href=\"http://ieeexplore.ieee.org/document/7487449/\" rel=\"nofollow\"\u003eIEEE Xplore\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eMichael Neunert, Farbod Farshidian, Jonas Buchli (2014). Adaptive Real-time Nonlinear Model Predictive Motion Control.\nIn IROS 2014 Workshop on Machine Learning in Planning and Control of Robot Motion\n\u003ca href=\"http://www.adrl.ethz.ch/archive/p_14_mlpc_mpc_rezero.pdf\" rel=\"nofollow\"\u003epreprint\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Control Toolbox","anchor":"control-toolbox","htmlText":"Control Toolbox"},{"level":2,"text":"Overview","anchor":"overview","htmlText":"Overview"},{"level":2,"text":"Robot Application Examples","anchor":"robot-application-examples","htmlText":"Robot Application Examples"},{"level":2,"text":"What is the CT?","anchor":"what-is-the-ct","htmlText":"What is the CT?"},{"level":2,"text":"Scope of the CT","anchor":"scope-of-the-ct","htmlText":"Scope of the CT"},{"level":2,"text":"Design and Implementation","anchor":"design-and-implementation","htmlText":"Design and Implementation"},{"level":2,"text":"Structure and Modules of the CT","anchor":"structure-and-modules-of-the-ct","htmlText":"Structure and Modules of the CT"},{"level":3,"text":"ct_core (Core)","anchor":"ct_core-core","htmlText":"ct_core (Core)"},{"level":3,"text":"ct_optcon (Optimal Control)","anchor":"ct_optcon-optimal-control","htmlText":"ct_optcon (Optimal Control)"},{"level":3,"text":"ct_rbd (Rigid Body Dynamics)","anchor":"ct_rbd-rigid-body-dynamics","htmlText":"ct_rbd (Rigid Body Dynamics)"},{"level":3,"text":"ct_models","anchor":"ct_models","htmlText":"ct_models"},{"level":2,"text":"How to get started","anchor":"how-to-get-started","htmlText":"How to get started"},{"level":2,"text":"Support","anchor":"support","htmlText":"Support"},{"level":2,"text":"Acknowledgements","anchor":"acknowledgements","htmlText":"Acknowledgements"},{"level":3,"text":"Contributors","anchor":"contributors","htmlText":"Contributors"},{"level":3,"text":"Funding","anchor":"funding","htmlText":"Funding"},{"level":2,"text":"Licence Information","anchor":"licence-information","htmlText":"Licence Information"},{"level":2,"text":"How to cite the CT","anchor":"how-to-cite-the-ct","htmlText":"How to cite the CT"},{"level":2,"text":"Earlier Versions","anchor":"earlier-versions","htmlText":"Earlier Versions"},{"level":2,"text":"Related Publications","anchor":"related-publications","htmlText":"Related Publications"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Fethz-adrl%2Fcontrol-toolbox"}},{"displayName":"LICENCE.txt","repoName":"control-toolbox","refName":"v3.0.2","path":"LICENCE.txt","preferredFileType":"license","tabName":"BSD-2-Clause","richText":null,"loaded":false,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":null,"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Fethz-adrl%2Fcontrol-toolbox"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-7d7eb7c71814.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-96e76d5fdb2c.js","githubDevUrl":null,"enabled_features":{"copilot_workspace":null,"code_nav_ui_events":false,"overview_shared_code_dropdown_button":false,"react_blob_overlay":false,"accessible_code_button":true,"github_models_repo_integration":false}}}}</script> <div data-target="react-partial.reactRoot"><style 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0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a target="_blank" rel="noopener noreferrer nofollow" href="https://camo.githubusercontent.com/489c66c07cabfd2a9a7afe919534bb48506a6737a3f5d4277fdd7dd2b8a885b8/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c616e6775616765732f746f702f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c"><img src="https://camo.githubusercontent.com/489c66c07cabfd2a9a7afe919534bb48506a6737a3f5d4277fdd7dd2b8a885b8/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c616e6775616765732f746f702f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c" alt="GitHub top language" data-canonical-src="https://img.shields.io/github/languages/top/ethz-adrl/control-toolbox.svg?style=social" style="max-width: 100%;"></a> <a target="_blank" rel="noopener noreferrer nofollow" href="https://camo.githubusercontent.com/2d66165213d48ca4291cb199718ba47966f4b60d25b832d91a3c2dd0aa44f3c3/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c6963656e73652f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c"><img src="https://camo.githubusercontent.com/2d66165213d48ca4291cb199718ba47966f4b60d25b832d91a3c2dd0aa44f3c3/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f6c6963656e73652f6574687a2d6164726c2f636f6e74726f6c2d746f6f6c626f782e7376673f7374796c653d736f6369616c" alt="GitHub" data-canonical-src="https://img.shields.io/github/license/ethz-adrl/control-toolbox.svg?style=social" style="max-width: 100%;"></a></p> <div class="highlight highlight-source-diff notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="- Important note (July 2021): this library is currently only scarcely maintained, - it may take a while until we respond to bugs or feature requests."><pre><span class="pl-md"><span class="pl-md">-</span> Important note (July 2021): this library is currently only scarcely maintained,</span> <span class="pl-md"><span class="pl-md">-</span> it may take a while until we respond to bugs or feature requests.</span></pre></div> <p dir="auto">This is the Control Toolbox, an efficient C++ library for control, estimation, optimization and motion planning in robotics.</p> <p dir="auto">Link to the wiki, <a href="https://github.com/ethz-adrl/control-toolbox/wiki/Quickstart">quickstart!</a> <br> Find the detailed documentation <a href="https://ethz-adrl.github.io/ct/" rel="nofollow">here</a>.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Overview</h2><a id="user-content-overview" class="anchor" aria-label="Permalink: Overview" href="#overview"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This is the ADRL Control Toolbox ('CT'), an open-source C++ library for efficient modelling, control, estimation, trajectory optimization and model predictive control. The CT is applicable to a broad class of dynamic systems, but features additional modelling tools specially designed for robotics. This page outlines its general concept, its major building blocks and highlights selected application examples.</p> <p dir="auto">The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems. The CT was designed with the following features in mind:</p> <ul dir="auto"> <li> <p dir="auto"><strong>Systems and dynamics</strong>:</p> <ul dir="auto"> <li>intuitive modelling of systems governed by ordinary differential or difference equations.</li> </ul> </li> <li> <p dir="auto"><strong>Trajectory optimization, optimal control and (nonlinear) model predictive control</strong>:</p> <ul dir="auto"> <li>intuitive modelling of cost functions and constraints</li> <li>common interfaces for optimal control solvers and nonlinear model predictive control</li> <li>currently supported algorithms: <ul dir="auto"> <li>Classical Single Shooting</li> <li>iLQR / iLQG (iterative Linear Quadratic Optimal Control)</li> <li>Multiple-shooting iLQR</li> <li>Gauss-Newton-Multiple-Shooting (GNMS)</li> <li>Classical Direct Multiple Shooting (DMS)</li> </ul> </li> <li>standardized interfaces for the solvers <ul dir="auto"> <li>IPOPT (first and second order)</li> <li>SNOPT</li> <li>HPIPM</li> <li>custom Riccati-solver</li> </ul> </li> </ul> </li> <li> <p dir="auto"><strong>Performance</strong>:</p> <ul dir="auto"> <li>solve large scale optimal control problems in MPC fashion.</li> </ul> </li> <li> <p dir="auto"><strong>Robot Modelling, Rigid Body Kinematics and Dynamics</strong>:</p> <ul dir="auto"> <li>straight-forward interface to the state-of the art rigid body dynamics modelling tool <a href="https://robcogenteam.bitbucket.io/" rel="nofollow">RobCoGen</a>.</li> <li>implementation of a basic nonlinear-programming inverse kinematics solver for fix-base robots.</li> </ul> </li> <li> <p dir="auto"><strong>Automatic Differentiation</strong>:</p> <ul dir="auto"> <li>first and second order automatic differentiation of arbitrary vector-valued functions including cost functions and constraints</li> <li>automatic differentiation and code generation of rigid body dynamics</li> <li>derivative code generation for maximum efficiency</li> </ul> </li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Robot Application Examples</h2><a id="user-content-robot-application-examples" class="anchor" aria-label="Permalink: Robot Application Examples" href="#robot-application-examples"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The Control Toolbox has been used for Hardware and Simulation control tasks on flying, walking and ground robots.</p> <p dir="auto"><a href="http://www.youtube.com/watch?feature=player_embedded&v=Y7-1CBqs4x4" rel="nofollow"><img src="https://camo.githubusercontent.com/ccfefa38effcf388c4c63d9c0a881a937003f6414d88af7bce86088c2477f42e/687474703a2f2f696d672e796f75747562652e636f6d2f76692f59372d31434271733478342f302e6a7067" alt="Control Toolbox example video" width="360" height="270" border="10" data-canonical-src="http://img.youtube.com/vi/Y7-1CBqs4x4/0.jpg" style="max-width: 100%;"></a> <a href="http://www.youtube.com/watch?feature=player_embedded&v=vuCSKtP67E4" rel="nofollow"><img src="https://camo.githubusercontent.com/9d917540ebd1bdc47f7d5212f6519991d2f4c5af190516e2453763bf0e6d9f61/687474703a2f2f696d672e796f75747562652e636f6d2f76692f767543534b7450363745342f302e6a7067" alt="Control Toolbox example video" width="360" height="270" border="10" data-canonical-src="http://img.youtube.com/vi/vuCSKtP67E4/0.jpg" style="max-width: 100%;"></a></p> <p dir="auto"><a href="http://www.youtube.com/watch?feature=player_embedded&v=rWmw-ERGyz4" rel="nofollow"><img src="https://camo.githubusercontent.com/8145c8e48bbb7dc313e6570989b3b17ed3be15d31513167dd78f507cd909e605/687474703a2f2f696d672e796f75747562652e636f6d2f76692f72576d772d455247797a342f302e6a7067" alt="Control Toolbox example video" width="360" height="270" border="10" data-canonical-src="http://img.youtube.com/vi/rWmw-ERGyz4/0.jpg" style="max-width: 100%;"></a> <a href="http://www.youtube.com/watch?feature=player_embedded&v=rVu1L_tPCoM" rel="nofollow"><img src="https://camo.githubusercontent.com/0e662a73ff860e1ad7bef5d1ff7db1acc8064e40960cc31d72479ab102ad53f3/687474703a2f2f696d672e796f75747562652e636f6d2f76692f725675314c5f7450436f4d2f302e6a7067" alt="Control Toolbox example video" width="360" height="270" border="10" data-canonical-src="http://img.youtube.com/vi/rVu1L_tPCoM/0.jpg" style="max-width: 100%;"></a></p> <p dir="auto">Slightly more complex optimization examples, including gait optimization for a quadruped, are availabe in <a href="https://github.com/ethz-adrl/ct_ros">ct_ros</a>.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">What is the CT?</h2><a id="user-content-what-is-the-ct" class="anchor" aria-label="Permalink: What is the CT?" href="#what-is-the-ct"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">A common tasks for researchers and practitioners in both the control and the robotics communities is to model systems, implement equations of motion and design model-based controllers, estimators, planning algorithms, etc. Sooner or later, one is confronted with questions of efficient implementation, computing derivative information, formulating cost functions and constraints or running controllers in model-predictive control fashion.</p> <p dir="auto">The Control Toolbox is specifically designed for these tasks. It is written entirely in C++ and has a strong focus on highly efficient code that can be run online (in the loop) on robots or other actuated hardware. A major contribution of the CT is its implementations of optimal control algorithms, spanning a range from simple LQR reference implementations to constrained model predictive control. The CT supports Automatic Differentiation (Auto-Diff) and allows to generate derivative code for arbitrary scalar and vector-valued functions. We designed the toolbox with usability in mind, allowing users to apply advanced concepts such as nonlinear model predictive control (NMPC) or numerical optimal control easily and with minimal effort. While we provide an interface to a state-of-the art Auto-Diff compatible robot modelling software, all other modules are independent of the a particular modelling framework, allowing the code to be interfaced with existing C/C++ code or libraries.</p> <p dir="auto">The CT has been successfully used in a variety of different projects, including a large number of hardware experiments, demonstrations and academic publications. Example hardware applications are online trajectory optimization with collision avoidance \cite giftthaler2017autodiff, trajectory optimization for Quadrupeds \cite neunert:2017:ral and mobile manipulators \cite giftthaler2017efficient as well as NMPC on ground robots \cite neunert2017mpc and UAVs \cite neunert16hexrotor. The project originated from research conducted at the Agile & Dexterous Robotics Lab at ETH Zurich, but is continuously extended to cover more fields of applications and algorithms.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Scope of the CT</h2><a id="user-content-scope-of-the-ct" class="anchor" aria-label="Permalink: Scope of the CT" href="#scope-of-the-ct"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Software is one of the key building blocks for robotic systems and there is a great effort in creating software tools and libraries for robotics. However, when it comes to control and especially Numerical Optimal Control, there are not many open source tools available that are both easy to use for fast development as well as efficient enough for online usage. While there exist mature toolboxes for Numerical Optimal Control and Trajectory Optimization, they are highly specialized, standalone tools that due not provide sufficient flexibility for other applications. Here is where the CT steps in. The CT has been designed from ground up to provide the tools needed for fast development and evaluation of control methods while being optimized for efficiency allowing for online operation. While the emphasis lies on control, the tools provided can also be used for simulation, estimation or optimization applications.</p> <p dir="auto">In contrast to other robotic software, CT is not a rigid integrated application but can be seen quite literal as a toolbox: It offers a variety of tools which can be used and combined to solve a task at hand. While ease-of-use has been a major criteria during the design and application examples are provided, using CT still requires programming and control knowledge. However, it frees the users from implementing standard methods that require in-depth experience with linear algebra or numerical methods. Furthermore, by using common definitions and types, a seamless integration between different components such as systems, controllers or integrators is provided, enabling fast prototyping.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Design and Implementation</h2><a id="user-content-design-and-implementation" class="anchor" aria-label="Permalink: Design and Implementation" href="#design-and-implementation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The main focus of CT is efficiency, which is why it is fully implemented in C++. Since CT is designed as a toolbox rather than an integrated application, we tried to provide maximum flexibility to the users. Therefore, it is not tied to a specific middleware such as ROS and dependencies are kept at a minimum. The two essential dependencies for CT are <a href="http://eigen.tuxfamily.org" rel="nofollow">Eigen</a> and <a href="http://github.com/ethz-asl/kindr">Kindr</a> (which is based on Eigen). This Eigen dependency is intentional since Eigen is a defacto standard for linear algebra in C++, as it provides highly efficient implementations of standard matrix operations as well as more advanced linear algebra methods. Kindr is a header only Kinematics library which builds on top of it and provides data types for different rotation representations such as Quaternions, Euler angles or rotation matrices.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Structure and Modules of the CT</h2><a id="user-content-structure-and-modules-of-the-ct" class="anchor" aria-label="Permalink: Structure and Modules of the CT" href="#structure-and-modules-of-the-ct"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The Control Toolbox consists of three main modules. The Core (<code>ct_core</code>) module, the Optimal Control (<code>ct_optcon</code>) module and the Rigid Body Dynamics (<code>ct_rbd</code>) module. There is a clear hierarchy between the modules. That means, the modules depend on each other in this order, e.g. you can use the core module without the optcon or rbd module.</p> <ul dir="auto"> <li>The Core (<code>ct_core</code>) module provides general type definitions and mathematical tools. For example, it contains most data type definitions, definitions for systems and controllers, as well as basic functionality such as numerical integrators for differential equations.</li> <li>The Optimal Control (<code>ct_optcon</code>) module builds on top of the Core module and adds infrastructure for defining and solving Optimal Control Problems. It contains the functionality for defining cost functions, constraints, solver backends and a general MPC wrapper.</li> <li>The Rigid Body Dynamics (<code>ct_rbd</code>) module provides tools for modelling Rigid Body Dynamics systems and interfaces with <code>ct_core</code> and <code>ct_optcon</code> data types.</li> </ul> <p dir="auto">For testing as well as examples, we also provide the models module (<code>ct_models</code>) which contains various robot models including a quadruped, a robotic arm, a normal quadrotor and a quadrotor with slung load.</p> <p dir="auto">The four different main modules are detailed in the following.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">ct_core (Core)</h3><a id="user-content-ct_core-core" class="anchor" aria-label="Permalink: ct_core (Core)" href="#ct_core-core"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Definitions of fundamental types for <strong>control</strong> and simulation, such as dynamic systems (ct::core::System), states (ct::core::StateVector), controls (ct::core::Controller), or trajectories (ct::core::DiscreteTrajectoryBase).</li> <li><strong>Numeric integration</strong> (ct::core::Integrator) with various ODE solvers including fixed step (ct::core::IntegratorEuler, ct::core::IntegratorRK4) and variable step (ct::core::IntegratorRK5Variable, ct::core::ODE45) integrators, as well as symplectic (semi-implicit) integrators.</li> <li>Numerical approximation of Trajectory <strong>Sensitivities</strong> (ct::core::Sensitivity , e.g. by forward-integrating variational differential equations)</li> <li>Common <strong>feedback controllers</strong> (e.g. ct::core::PIDController)</li> <li>Derivatives/Jacobians of general functions using <strong>Numerical Differentiation</strong> (ct::core::DerivativesNumDiff) or <strong>Automatic-Differentiation</strong> with code-generation (ct::core::DerivativesCppadCG) and just-in-time (JIT) compilation (ct::core::DerivativesCppadJIT)</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">ct_optcon (Optimal Control)</h3><a id="user-content-ct_optcon-optimal-control" class="anchor" aria-label="Permalink: ct_optcon (Optimal Control)" href="#ct_optcon-optimal-control"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Definitions for <strong>Optimal Control Problems</strong> (ct::optcon::OptConProblem) and <strong>Optimal Control Solvers</strong> (ct::optcon::OptConSolver)</li> <li><strong>CostFunction toolbox</strong> allowing to construct cost functions from file and providing first-order and <strong>second-order approximations</strong>, see ct::optcon::CostFunction.</li> <li><strong>Constraint toolbox</strong> for formulating constraints of Optimal Control Problems, as well as automatically computing their Jacobians.</li> <li>reference C++ implementations of the <strong>Linear Quadratic Regulator</strong>, infinite-horizon LQR and time-varying LQR (ct::optcon::LQR, ct::optcon::TVLQR)</li> <li><strong>Riccati-solver</strong> (ct::optcon::GNRiccatiSolver) for unconstrained linear-quadratic optimal control problems, interface to high-performance <a href="https://github.com/giaf/hpipm"> third-party Riccati-solvers</a> for constrained linear-quadratic optimal control problems</li> <li><strong>iterative non-linear Optimal Control</strong> solvers, i.e. Gauss-Newton solvers such as iLQR (ct::optcon::iLQR) and Gauss-Newton Multiple Shooting(ct::optcon::GNMS), constrained direct multiple-shooting (ct::optcon::DmsSolver)</li> <li>Non-Linear <strong>Model Predictive Control</strong> (ct::optcon::MPC)</li> <li>Definitions for Nonlinear Programming Problems (<strong>NLPs</strong>, ct::optcon::Nlp) and interfaces to third-party <strong>NLP Solvers</strong> (ct::optcon::SnoptSolver and ct::optcon::IpoptSolver)</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">ct_rbd (Rigid Body Dynamics)</h3><a id="user-content-ct_rbd-rigid-body-dynamics" class="anchor" aria-label="Permalink: ct_rbd (Rigid Body Dynamics)" href="#ct_rbd-rigid-body-dynamics"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Standard models for Rigid Body Dynamics</li> <li>Definitions for the state of a Rigid Body System expressed as general coordinates (ct::rbd::RBDState)</li> <li>Routines for different flavors of <strong>Forward</strong> and <strong>Inverse Dynamics</strong> (ct::rbd::Dynamics)</li> <li>Rigid body and end-effector <strong>kinematics</strong> (ct::rbd::Kinematics)</li> <li>Operational Space Controllers</li> <li>Basic soft <strong>auto-differentiable contact model</strong> for arbitrary frames (ct::rbd::EEContactModel)</li> <li><strong>Actuator dynamics</strong> (ct::rbd::ActuatorDynamics)</li> <li>Backend uses <a href="https://robcogenteam.bitbucket.io/" rel="nofollow">RobCoGen</a>, a highly efficient Rigid Body Dynamics library</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">ct_models</h3><a id="user-content-ct_models" class="anchor" aria-label="Permalink: ct_models" href="#ct_models"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Various standard models for testing and evaluation including UAVs (ct::models::Quadrotor), ground robots, legged robots (ct::models::HyQ), robot arms (ct::models::HyA), inverted pendulums etc.</li> <li>Means of creating linear approximation of these models</li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">How to get started</h2><a id="user-content-how-to-get-started" class="anchor" aria-label="Permalink: How to get started" href="#how-to-get-started"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To get started with the control toolbox, please build the repository documentation with doxygen and follow the "Getting Started" tutorial.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Support</h2><a id="user-content-support" class="anchor" aria-label="Permalink: Support" href="#support"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>contact the devs: <a href="mailto:control-toolbox-dev@googlegroups.com">control-toolbox-dev@googlegroups.com</a></li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Acknowledgements</h2><a id="user-content-acknowledgements" class="anchor" aria-label="Permalink: Acknowledgements" href="#acknowledgements"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Contributors</h3><a id="user-content-contributors" class="anchor" aria-label="Permalink: Contributors" href="#contributors"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Markus Giftthaler, markusgft (at) gmail (dot) com</li> <li>Michael Neunert</li> <li>Markus Stäuble</li> <li>Farbod Farshidian</li> <li>Diego Pardo</li> <li>Timothy Sandy</li> <li>Jan Carius</li> <li>Ruben Grandia</li> <li>Hamza Merzic</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Funding</h3><a id="user-content-funding" class="anchor" aria-label="Permalink: Funding" href="#funding"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This software has been developed at the <a href="http://www.adrl.ethz.ch" rel="nofollow">Agile & Dexterous Robotics Lab</a> at <a href="http://www.ethz.ch/en" rel="nofollow">ETH Zurich</a>, Switzerland between 2014 and 2018. During that time, development has been made possible through financial support from the <a href="http://www.snf.ch/en/" rel="nofollow">Swiss National Science Foundation (SNF)</a> through a SNF Professorship award to Jonas Buchli and the National Competence Centers in Research (NCCR) <a href="https://www.nccr-robotics.ch/" rel="nofollow">Robotics</a> and <a href="http://www.dfab.ch/en/" rel="nofollow">Digital Fabrication</a>.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Licence Information</h2><a id="user-content-licence-information" class="anchor" aria-label="Permalink: Licence Information" href="#licence-information"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The Control Toolbox is released under the <a href="https://choosealicense.com/licenses/bsd-2-clause/" rel="nofollow">BSD-2 clause license</a>. Please see LICENCE.txt and NOTICE.txt</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">How to cite the CT</h2><a id="user-content-how-to-cite-the-ct" class="anchor" aria-label="Permalink: How to cite the CT" href="#how-to-cite-the-ct"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="@article{adrlCT, title={The control toolbox — An open-source C++ library for robotics, optimal and model predictive control}, author={Markus Giftthaler and Michael Neunert and Markus St{\"a}uble and Jonas Buchli}, journal={2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)}, year={2018}, pages={123-129} }"><pre class="notranslate"><code>@article{adrlCT, title={The control toolbox — An open-source C++ library for robotics, optimal and model predictive control}, author={Markus Giftthaler and Michael Neunert and Markus St{\"a}uble and Jonas Buchli}, journal={2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)}, year={2018}, pages={123-129} } </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Earlier Versions</h2><a id="user-content-earlier-versions" class="anchor" aria-label="Permalink: Earlier Versions" href="#earlier-versions"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Earlier versions up to v2.3 are hosted on bitbucket, they can be found at <a href="https://bitbucket.org/adrlab/ct/wiki/Home" rel="nofollow">https://bitbucket.org/adrlab/ct/wiki/Home</a></p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Related Publications</h2><a id="user-content-related-publications" class="anchor" aria-label="Permalink: Related Publications" href="#related-publications"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This toolbox has been used in, or has helped to realize the following academic publications:</p> <ul dir="auto"> <li> <p dir="auto">Markus Giftthaler, Michael Neunert, Markus Stäuble and Jonas Buchli. “The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control”. IEEE Simpar 2018 (Best Student Paper Award). <a href="https://arxiv.org/abs/1801.04290" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl. “A Family of iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control”. IROS 2018. <a href="https://arxiv.org/abs/1711.11006" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Jan Carius, René Ranftl, Vladlen Koltun and Marco Hutter. "Trajectory Optimization with Implicit Hard Contacts." IEEE Robotics and Automation Letters 3, no. 4 (2018): 3316-3323.</p> </li> <li> <p dir="auto">Michael Neunert, Markus Stäuble, Markus Giftthaler, Dario Bellicoso, Jan Carius, Christian Gehring, Marco Hutter and Jonas Buchli. “Whole Body Model Predictive Control Through Contacts For Quadrupeds”. IEEE Robotics and Automation Letters, 2017. <a href="https://arxiv.org/abs/1712.02889" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Markus Giftthaler and Jonas Buchli. “A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control”. 2017 IEEE-RAS International Conference on Humanoid Robots, November 15-17, Birmingham, UK. <a href="http://ieeexplore.ieee.org/document/8239538/" rel="nofollow">IEEE Xplore</a></p> </li> <li> <p dir="auto">Markus Giftthaler, Michael Neunert, Markus Stäuble, Marco Frigerio, Claudio Semini and Jonas Buchli. “Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation”, Advanced Robotics, SIMPAR special issue. November 2017. <a href="https://arxiv.org/abs/1709.03799" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Michael Neunert, Markus Giftthaler, Marco Frigerio, Claudio Semini and Jonas Buchli. “Fast Derivatives of Rigid Body Dynamics for Control, Optimization and Estimation”, 2016 IEEE International Conference on Simulation, Modelling, and Programming for Autonomous Robots, San Francisco. (Best Paper Award). <a href="http://ieeexplore.ieee.org/document/7862380/" rel="nofollow">IEEE Xplore</a></p> </li> <li> <p dir="auto">Michael Neunert, Farbod Farshidian, Alexander W. Winkler, Jonas Buchli "Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds", IEEE Robotics and Automation Letters, <a href="http://ieeexplore.ieee.org/document/7845678/" rel="nofollow">IEEE Xplore</a></p> </li> <li> <p dir="auto">Michael Neunert, Cédric de Crousaz, Fadri Furrer, Mina Kamel, Farbod Farshidian, Roland Siegwart, Jonas Buchli. "Fast nonlinear model predictive control for unified trajectory optimization and tracking", 2016 IEEE International Conference on Robotics and Automation (ICRA), <a href="http://ieeexplore.ieee.org/document/7487274/" rel="nofollow">IEEE Xplore</a></p> </li> <li> <p dir="auto">Markus Giftthaler, Farbod Farshidian, Timothy Sandy, Lukas Stadelmann and Jonas Buchli. “Efficient Kinematic Planning for Mobile Manipulators with Non-holonomic Constraints Using Optimal Control”, IEEE International Conference on Robotics and Automation, 2017, Singapore. <a href="https://arxiv.org/abs/1701.08051" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Markus Giftthaler, Timothy Sandy, Kathrin Dörfler, Ian Brooks, Mark Buckingham, Gonzalo Rey, Matthias Kohler, Fabio Gramazio and Jonas Buchli. “Mobile Robotic Fabrication at 1:1 scale: the In situ Fabricator”. Construction Robotics, Springer Journal no. 41693 <a href="https://arxiv.org/abs/1701.03573" rel="nofollow">arXiv preprint</a></p> </li> <li> <p dir="auto">Timothy Sandy, Markus Giftthaler, Kathrin Dörfler, Matthias Kohler and Jonas Buchli. “Autonomous Repositioning and Localization of an In situ Fabricator”, IEEE International Conference on Robotics and Automation 2016, Stockholm, Sweden. <a href="http://ieeexplore.ieee.org/document/7487449/" rel="nofollow">IEEE Xplore</a></p> </li> <li> <p dir="auto">Michael Neunert, Farbod Farshidian, Jonas Buchli (2014). Adaptive Real-time Nonlinear Model Predictive Motion Control. In IROS 2014 Workshop on Machine Learning in Planning and Control of Robot Motion <a href="http://www.adrl.ethz.ch/archive/p_14_mlpc_mpc_rezero.pdf" rel="nofollow">preprint</a></p> </li> </ul> </article></div></div></div></div></div>   <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" value="hXBe8fuhTRm11tvJqYf6APiJf+oLSI4yKqjNcZnCHFXVhdB3K6qH6XSCe+guPFleS83BcgcBVMMEYGbI75C1+A==" /> </div> <div data-view-component="true" class="Layout-sidebar"> <div class="BorderGrid about-margin" data-pjax> <div class="BorderGrid-row"> <div class="BorderGrid-cell"> <div class="hide-sm hide-md"> <h2 class="mb-3 h4">About</h2> <p class="f4 my-3"> The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control </p> <h3 class="sr-only">Topics</h3> <div class="my-3"> <div class="f6"> <a href="/topics/cpp" title="Topic: cpp" data-view-component="true" class="topic-tag topic-tag-link"> cpp </a> <a href="/topics/robotics" title="Topic: robotics" data-view-component="true" class="topic-tag topic-tag-link"> robotics </a> <a href="/topics/automatic-differentiation" title="Topic: automatic-differentiation" data-view-component="true" class="topic-tag topic-tag-link"> automatic-differentiation </a> <a href="/topics/control-systems" title="Topic: control-systems" data-view-component="true" class="topic-tag topic-tag-link"> control-systems </a> <a href="/topics/trajectory-optimization" title="Topic: trajectory-optimization" data-view-component="true" class="topic-tag topic-tag-link"> trajectory-optimization </a> <a href="/topics/optimal-control" title="Topic: optimal-control" data-view-component="true" class="topic-tag topic-tag-link"> optimal-control </a> <a href="/topics/model-predictive-control" title="Topic: model-predictive-control" data-view-component="true" class="topic-tag topic-tag-link"> model-predictive-control </a> <a href="/topics/rigid-body-dynamics" title="Topic: rigid-body-dynamics" data-view-component="true" class="topic-tag topic-tag-link"> rigid-body-dynamics </a> <a href="/topics/lqr-controller" title="Topic: lqr-controller" data-view-component="true" class="topic-tag topic-tag-link"> lqr-controller </a> <a href="/topics/extended-kalman-filter" title="Topic: extended-kalman-filter" data-view-component="true" class="topic-tag topic-tag-link"> extended-kalman-filter </a> <a href="/topics/ilqg" title="Topic: ilqg" data-view-component="true" class="topic-tag topic-tag-link"> ilqg </a> <a href="/topics/ilqr" title="Topic: ilqr" data-view-component="true" class="topic-tag topic-tag-link"> ilqr </a> <a href="/topics/disturbance-observer" title="Topic: disturbance-observer" data-view-component="true" class="topic-tag topic-tag-link"> disturbance-observer </a> <a href="/topics/multiple-shooting" title="Topic: multiple-shooting" data-view-component="true" class="topic-tag topic-tag-link"> 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href="/ethz-adrl/control-toolbox/watchers" data-view-component="true" class="Link Link--muted"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-eye mr-2"> <path d="M8 2c1.981 0 3.671.992 4.933 2.078 1.27 1.091 2.187 2.345 2.637 3.023a1.62 1.62 0 0 1 0 1.798c-.45.678-1.367 1.932-2.637 3.023C11.67 13.008 9.981 14 8 14c-1.981 0-3.671-.992-4.933-2.078C1.797 10.83.88 9.576.43 8.898a1.62 1.62 0 0 1 0-1.798c.45-.677 1.367-1.931 2.637-3.022C4.33 2.992 6.019 2 8 2ZM1.679 7.932a.12.12 0 0 0 0 .136c.411.622 1.241 1.75 2.366 2.717C5.176 11.758 6.527 12.5 8 12.5c1.473 0 2.825-.742 3.955-1.715 1.124-.967 1.954-2.096 2.366-2.717a.12.12 0 0 0 0-.136c-.412-.621-1.242-1.75-2.366-2.717C10.824 4.242 9.473 3.5 8 3.5c-1.473 0-2.825.742-3.955 1.715-1.124.967-1.954 2.096-2.366 2.717ZM8 10a2 2 0 1 1-.001-3.999A2 2 0 0 1 8 10Z"></path> </svg> <strong>45</strong> watching</a> </div> <h3 class="sr-only">Forks</h3> <div class="mt-2"> <a href="/ethz-adrl/control-toolbox/forks" data-view-component="true" class="Link Link--muted"><svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-repo-forked mr-2"> <path d="M5 5.372v.878c0 .414.336.75.75.75h4.5a.75.75 0 0 0 .75-.75v-.878a2.25 2.25 0 1 1 1.5 0v.878a2.25 2.25 0 0 1-2.25 2.25h-1.5v2.128a2.251 2.251 0 1 1-1.5 0V8.5h-1.5A2.25 2.25 0 0 1 3.5 6.25v-.878a2.25 2.25 0 1 1 1.5 0ZM5 3.25a.75.75 0 1 0-1.5 0 .75.75 0 0 0 1.5 0Zm6.75.75a.75.75 0 1 0 0-1.5.75.75 0 0 0 0 1.5Zm-3 8.75a.75.75 0 1 0-1.5 0 .75.75 0 0 0 1.5 0Z"></path> </svg> <strong>326</strong> forks</a> </div> <div class="mt-2"> <a class="Link--muted" href="/contact/report-content?content_url=https%3A%2F%2Fgithub.com%2Fethz-adrl%2Fcontrol-toolbox&report=ethz-adrl+%28user%29"> Report repository </a> </div> </div> </div> </div> <div class="BorderGrid-row"> <div class="BorderGrid-cell"> <h2 class="h4 mb-3" 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