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Gabriel Robles-De-La-Torre-Research-Haptic perception

<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <head><script type="text/javascript" src="/_static/js/bundle-playback.js?v=HxkREWBo" charset="utf-8"></script> <script type="text/javascript" src="/_static/js/wombat.js?v=txqj7nKC" charset="utf-8"></script> <script>window.RufflePlayer=window.RufflePlayer||{};window.RufflePlayer.config={"autoplay":"on","unmuteOverlay":"hidden"};</script> <script type="text/javascript" src="/_static/js/ruffle/ruffle.js"></script> <script type="text/javascript"> __wm.init("https://web.archive.org/web"); __wm.wombat("http://www.roblesdelatorre.com:80/gabriel/haptics.htm","20130819061043","https://web.archive.org/","web","/_static/", "1376892643"); </script> <link rel="stylesheet" type="text/css" href="/_static/css/banner-styles.css?v=S1zqJCYt" /> <link rel="stylesheet" type="text/css" href="/_static/css/iconochive.css?v=3PDvdIFv" /> <!-- End Wayback Rewrite JS Include --> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="Author" content="Gabriel Robles-De-La-Torre"> <meta name="GENERATOR" content="Mozilla/4.61 [en] (Win95; I) [Netscape]"> <title>Gabriel Robles-De-La-Torre-Research-Haptic perception</title> </head> <body text="#000000" bgcolor="#FFFFFF" link="#FFFF99" vlink="#FFCC00" alink="#FFFF99" background="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/fondo.gif"> &nbsp; <table width="100%"> <tr align="LEFT" valign="TOP"> <td valign="TOP" width="80%"></td> </tr> <tr> <td><!-- AddThis Bookmark Button BEGIN --><a href="https://web.archive.org/web/20130819061043/http://www.addthis.com/bookmark.php" onclick="addthis_url = location.href; addthis_title = document.title; return addthis_click(this);" target="_blank"><img src="https://web.archive.org/web/20130819061043im_/http://s9.addthis.com/button2-bm.png" alt="AddThis Social Bookmark Button" nosave border="0" height="24" width="160"></a><script type="text/javascript">var addthis_pub = 'robles_gabriel';</script> <script type="text/javascript" src="https://web.archive.org/web/20130819061043js_/http://s9.addthis.com/js/widget.php?v=10"></script> <!-- AddThis Bookmark Button END --> <br><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+3">Haptic Perception of Shape:</font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+3">touch illusions, forces and the geometry of objects</font></font></font></b> <br>&nbsp; <br>&nbsp; <table cols="2" width="100%"> <tr> <td align="LEFT" valign="TOP"><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2"><a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/portada2.htm">Gabriel Robles-De-La-Torre, PhD</a></font></font></font></b> <br>&nbsp; <p><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+2"><a href="https://web.archive.org/web/20130819061043/http://roblesdelatorre.blogspot.com/2007/04/dr-robles-de-la-torre-speaks-about.html">Meet Dr. Robles-De-La-Torre in New York next April 14th, 2007.</a></font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+2"><a href="https://web.archive.org/web/20130819061043/http://roblesdelatorre.blogspot.com/2007/04/dr-robles-de-la-torre-speaks-about.html">He will speak about this work at the New York Academy of Sciences</a></font></font></font></b> <br>&nbsp; <p><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+1">This ongoing research has been featured at:</font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFCC"><font size="+1"><a href="https://web.archive.org/web/20130819061043/http://www.economist.com/science/tq/displaystory.cfm?story_id=8766116">The Economist</a></font></font></font></b> <br><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1"><b><a href="https://web.archive.org/web/20130819061043/http://www.technologyreview.com/read_article.aspx?id=17363&amp;ch=biotech&amp;sc=&amp;pg=1">MIT Technology Review</a></b>&nbsp; (read here the <a href="https://web.archive.org/web/20130819061043/http://www.heise.de/tr/artikel/77771">German version</a>)</font></font></font> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1"><a href="https://web.archive.org/web/20130819061043/http://www.nature.com/search/executeSearch?sp-a=sp1001702d&amp;sp-sfvl-field=subject|ujournal&amp;sp-q=robles-de-la-torre&amp;sp-p=phrase&amp;sp-d=custom&amp;sp-start-day=01&amp;sp-end-day=31&amp;sp-s=date&amp;sp-c=10">Nature</a></font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1"><a href="https://web.archive.org/web/20130819061043/http://www.highbeam.com/Search.aspx?q=gabriel+robles-de-la-torre&amp;st=NL&amp;nml=True&amp;t=&amp;a=&amp;src=NEWS&amp;count=10&amp;offset=0&amp;sort=T2&amp;sortdir=A&amp;pst=INCLUDE_ALL&amp;cn=&amp;storage=ALL&amp;display=ALL">The Washington Post</a></font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1"><a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/pls.html">Scientific American France (Pour la Science)</a></font></font></font></b> <p><a name="intro"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">Introduction</font></font></font></b> <p><font face="Arial,Helvetica"><font size="+1"><font color="#FFFFFF">Touch and related capabilities are commonly underrated. Yet, these capabilities are essential for normal human functioning, as demonstrated by the catastrophic consequences that follow after losing them (</font><b><font color="#000000"><a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/GR-IEEE-MM-2006.pdf">Robles-De-La-Torre 2006</a></font></b><font color="#FFFFFF">). Also, we perhaps tend to think that touch is somehow more veridical than the other senses. Perhaps this is because we&nbsp; know that there are many visual illusions, but we rarely hear about touch illusions.&nbsp;</font></font></font> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">As we will see, there <i>are </i>compelling touch illusions of shape. In such illusions, persons touch objects that have a certain shape, but they perceive touching a&nbsp; <b><i>radically different </i></b>shape (Figure 1).&nbsp; This document will&nbsp; help you understand how such illusions are created. In particular, a <a href="vsdemo.html">simple demo</a> is provided in Section 4 below to give you an idea of how some illusory shapes feel like. I would recommend reading the document first and then watch the demo.&nbsp; Alternatively, you can watch the demo after reading about impossible, paradoxical haptic objects in section 3.2 below. Keep in mind, however, that the demo is only a <b>very rough</b> <b>approximation</b>.&nbsp;</font></font></font> <br>&nbsp;</td> <td align="LEFT" valign="TOP" width="30%"> <br>&nbsp; <br>&nbsp; <br>&nbsp; <div align="right"><img src="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/figure2e.jpg" height="350" width="556" align="TEXTTOP"> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><b>Figure 1</b>. A person explores&nbsp; a paradoxical object that combines the geometry of a real hole (gray bar) with an illusory bump (red dotted line) created through computer-controlled forces alone. These forces are generated by a <a href="ch.html">haptic interface</a> (blue machine). Surprisingly, when exploring this paradoxical object, persons perceive that they touch a bumpy object, and not an object with a hole.&nbsp;</font></font> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF">See the text for details</font></font></b></div> </td> </tr> </table> <font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">A second demo provides the basics of <a href="ch.html">computer haptics</a>, which is the technology used to create illusory and other haptic virtual objects.</font></font></font> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">Your feedback is always welcome at:</font></font></font> <p><img src="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/roble.gif" height="21" width="221"> <br>&nbsp; <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">Table of Contents</font></font></font> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">1. <a href="#Howdoweperceive">How do we haptically perceive the shape of objects?</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">2. <a href="#force_or_geom">Haptic perception of shape: force or geometry?</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3. <a href="#using_vo">Using virtual objects to understand haptic perception of shape</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.1 <a href="#Real_world">The normal, real-world scenario: forces and geometrical information vary together in a natural way</a></font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.2 <a href="#paradoxical">The paradoxical object scenario: forces and geometry vary in an "impossible" manner.</a></font></font></font></b> <br><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.3 <a href="#key_finding">The key finding: force information can overcome geometrical information to determine haptic perception of shape</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">4. <a href="#try_illusion">Experience how illusory objects feel like.</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">5. <a href="#future">Future work</a></font></font></font></b> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">6. <a href="#applying">Applying haptic perception research:&nbsp; illusory haptic objects for perception-based rendering of sharp objects</a></font></font></font></b> <br>&nbsp; <p><a name="Howdoweperceive"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">1. How do we haptically perceive the shape of objects?</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">I investigate how humans perceive the shape of objects when actively exploring them through touch (which is commonly called active or <a href="https://web.archive.org/web/20130819061043/http://www.isfh.org/haptics.html"><i>haptic </i>touch</a>). I use computer haptics to create virtual haptic objects for this research (<a href="ch.html">see a demo of computer haptics and virtual objects here</a>).&nbsp; When a person haptically explores an object, he/she has access to several sources of information ("cues") about its shape.&nbsp; A major shape cue is the geometry of the object. Consider the following case. When we slide a fingertip along the surface of an object, the geometry of the surface determines the way our finger will move. For example, if the object has a bump on it, our finger will ascend into the bump and then descend from it.&nbsp;</font></font></font> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">Until very recently, it was assumed that we used such geometrical information to perceive the shape of an object. However, there are other sources of shape information that are also experienced when touching an object. These are the <b>forces </b>that we experience when exploring the object.&nbsp; For example, when sliding the fingertip along a surface with a small bump, the bump will resist the movement of the fingertip.&nbsp; Such resistance forces are largely determined by the local geometry of an object and by how much force we apply when exploring the object.&nbsp;</font></font></font> <p><a name="force_or_geom"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">2. Haptic perception of shape: force or geometry?</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">Note how force and geometrical information are experienced together&nbsp; when exploring objects. Because of this, we cannot be sure that object geometry is <i>the information</i> that is used for haptic shape perception.&nbsp; In other words, what is the relative contribution of geometry and force to haptic shape perception? When considering two extreme cases, is it enough to experience geometry, or is enough to experience force? How do these related sources of haptic shape interact with each other? (<a href="publications.htm">Robles-De-La-Torre &amp; Hayward, 2000</a>) . In the experiments discussed here, only touch information about objects was provided. Visual and auditory information were not provided.</font></font></font> <br>&nbsp; <p><a name="using_vo"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">3. Using virtual objects to understand haptic perception of shape</font></font></font></b> <br>&nbsp; <table cols="2" width="100%"> <tr align="LEFT" valign="TOP"> <td><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">In collaboration with <a href="https://web.archive.org/web/20130819061043/http://www.cim.mcgill.ca/~hayward/">Vincent Hayward</a>, we used <a href="ch.html">haptic virtual shapes</a> to tackle these questions (<a href="publications.htm">Robles-De-La-Torre &amp; Hayward, 2000, 2001</a>). Our virtual shapes are force fields that are generated by using a <a href="ch.html">haptic interface</a> (the blue machine in Figure 1, <b>the figure is shown here again for your convenience</b>). The interface we used (<a href="pencat.htm">PenCAT/Pro&reg;</a>) is a robot that generates computer-controlled forces to create virtual objects. The interface has a small plate that can be held by a person's fingertip (Fig. 1).&nbsp; The plate is attached to a wheeled tool that rests on top of a hard plastic object (the gray bar in Fig. 1, just ignore the red dotted line for the time being).&nbsp; The tool is mechanically constrained, so it is always in a vertical position relative to the surface of the object.&nbsp; The person can freely explore the plastic object by rolling the wheeled tool on top of it, as shown in Fig. 1. Note that the person's fingertip moves downwards when entering the plastic object's hole, and upwards when exiting it.&nbsp;</font></font></font> <p><a name="Real_world"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.1 The normal, real-world scenario: forces and geometrical information vary together in a natural way&nbsp;</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">When the haptic interface is turned off, the person only experiences the forces that arise naturally from the tool-surface interaction. For example, when exiting the hole (Fig. 1), the person experiences some resistance forces. These forces depend on the of the hole's slope, and also on how hard the person pushes down to hold the tool. So far, there is nothing extraordinary going on here: the person experiences forces and geometrical information that vary together in a natural way.&nbsp;</font></font></font> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">&nbsp;</font></font></font></td> <td width="30%"> <br>&nbsp; <br>&nbsp; <div align="right"><img src="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/figure2e.jpg" height="350" width="556"></div> &nbsp; <div align="right"> <br><font face="Arial,Helvetica"><font color="#FFFFFF"><b>Figure 1</b>. This figure and its legend are shown again here for your convenience. A person explores&nbsp; a paradoxical object that combines the geometry of a real hole (gray bar) with an illusory bump (red dotted line) created through computer-controlled forces alone. These forces are generated by a <a href="ch.html">haptic interface</a> (blue machine). Surprisingly, when exploring this paradoxical object, persons perceive that they touch a bumpy object, and not an object with a hole.&nbsp;</font></font></div> </td> </tr> </table> <a name="paradoxical"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.2 The paradoxical object scenario: forces and geometry vary in an "impossible" manner.</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">When the haptic interface is powered on, it generates computer-controlled forces. Such forces are added to the forces that arise naturally from the normal tool-surface interaction. In this manner, it is feasible to <b>create </b>normally <b><i>impossible, paradoxical objects </i></b>in which geometrical information conflicts with force information. Figure 1 presents one of these impossible objects. Here, a person is exploring and object with a real, physical hole object (Figure 1, gray bar). Normally, the person would simultaneously experience forces that are related to the geometry of the hole, as in the normal case described before. However,&nbsp; in this impossible object, the haptic interface modifies such forces, so that the person experiences forces that are normally associated with an object that has a bump on it (Figure 1, red dotted line).&nbsp; Here the bump is purely virtual: it is created with forces, and has no geometrical information of its own. That is, when exploring this object, the person's fingertip still follows the hole trajectory given by the plastic surface (gray bar in Figure 1). The end result is that the person experiences the geometrical information of a hole, together with the force information of a bump.</font></font></font> <p><a name="key_finding"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">3.3 The key finding: force information can overcome geometrical information to determine haptic perception of shape</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">Which information is used by a person in such a situation to perceive the shape of the object?&nbsp; We found (<a href="publications.htm#nat">Robles-De-La-Torre &amp; Hayward, 2001</a>) that, surprisingly, people's perception depended on the <i>forces </i>they experienced, and not on the geometrical information they simultaneously received. That is, in the case shown in Figure 1, subjects typically perceived a surface with a haptic bump (created through forces alone), and not a surface with a haptic hole, even though there was a <b><i>real physical hole present</i></b>. This can be considered as a <b>touch illusion,</b> in which a conflict between sources of information is resolved in favor of force cues, perhaps by weighing each source of information differently (<a href="publications.htm#nat">Robles-De-La-Torre &amp; Hayward, 2001</a>). It can be also considered that&nbsp; the virtual object <b><i>masked</i></b> or&nbsp; perceptually hid the real object.</font></font></font> <p><a name="try_illusion"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">4. Experience how illusory objects feel like.</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">We tested other paradoxical objects, too (<a href="publications.htm#nat">Robles-De-La-Torre &amp; Hayward, 2001</a>). For example, if you replace the plastic object (Fig. 1, gray bar) with a totally flat object, and the haptic interface produces the forces of a hole (or bump), you will still experience exploring an object with a hole (or bump, depending on the case), even though your fingertip will move along a totally flat surface. <a href="vsdemo.html">Here you can find a simple demo to approximately experience how these virtual, illusory objects feel like</a>.</font></font></font> <p><a name="future"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">5. Future work&nbsp;</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">These results indicate that force can overcome geometrical information in haptic shape perception. Again, how do geometric and force information interact with each other? What is the relative&nbsp; contribution of each one to haptic shape perception? I am currently exploring these and other, related questions.</font></font></font> <p><a name="applying"></a><b><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+2">6. Applying haptic perception research:&nbsp; illusory haptic objects for perception-based rendering of sharp objects</font></font></font></b> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">The important role of&nbsp; force in haptic shape perception provides the scientific basis for simple <a href="ch.html">haptic rendering</a> algorithms to generate illusory, force-based haptic shapes (<a href="publications.htm">Robles-De-La-Torre &amp; Hayward, 2000</a>).&nbsp;</font></font></font> <table width="100%"> <tr> <td align="LEFT" valign="TOP" width="60%"> <br><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">In this regard, as part of an ongoing collaboration with <a href="https://web.archive.org/web/20130819061043/http://www.percro.org/index.php?pageId=People">Carlo Alberto Avizzano</a> , <a href="https://web.archive.org/web/20130819061043/http://www.otniel.p-ortillo.com/">Otniel Portillo-Rodr&iacute;guez</a>&nbsp; and <a href="https://web.archive.org/web/20130819061043/http://www.percro.org/index.php?pageId=People">Massimo Bergamasco</a> (<a href="https://web.archive.org/web/20130819061043/http://www.percro.org/">PERCRO</a>, Italy), we used the <a href="https://web.archive.org/web/20130819061043/http://www.percro.org/index.php?pageId=GRAB">GRAB haptic interface</a> to apply illusory objects in the solution of a difficult problem in <a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/ch.html">haptic rendering</a>: how to produce realistic virtual objects with features such as sharp edges (<a href="roman.html">Portillo-Rodr&iacute;guez, Avizzano, Bergamasco, Robles-De-La-Torre 2006</a>; <a href="https://web.archive.org/web/20130819061043/http://www.technologyreview.com/read_article.aspx?id=17363&amp;ch=biotech&amp;sc=&amp;pg=1">Graham-Rowe. The Cutting Edge of Haptics, MIT Technology Review 2006</a>). This is a difficult problem for several reasons. In particular, sudden force changes are common when using other rendering approaches to generate virtual objects with sharp edges. This is due to the spatial discontinuity at a sharp edge: forces vary greatly in their direction from one side of the edge to the other. As a result, an user's hand tends to be unnaturally pushed away from the virtual object when touching the vicinity of an edge. This decreases the realism of the virtual object.</font></font></font></td> <td align="LEFT" valign="TOP"> <br><img src="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/sharp.jpg" height="343" width="688"> <br>&nbsp; <div align="right"><font face="Arial,Helvetica"><font color="#FFFFFF"><b>Figure 2</b>. Using haptic illusions to render challenging virtual objects with sharp edges. An user wears a thimble-like tool&nbsp; (in blue, both panels) to explore a virtual object (gray surface, both panels). The tool is connected to a haptic interface (not shown). Although the user's hand actually travels along a smooth trajectory&nbsp; (<b>a</b>), the user perceives touching a surface with a sharp edge, which is illusory (<b>b</b>). The illusory edge is created through lateral forces. Unlike the case depicted in Fig. 1, here the virtual object does not involve a real object such as the gray plastic bar in Figure 1.</font></font> <br><font face="Arial,Helvetica"><font color="#FFFFFF">I thank <a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/lorena/">Lorena Robles-De-La-Torre</a> for designing this figure.&nbsp;</font></font></div> </td> </tr> </table> &nbsp;<font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">Such undesirable artifacts can be avoided by rendering illusory, sharp edges instead (<a href="roman.html">Portillo-Rodr&iacute;guez, Avizzano, Bergamasco, Robles-De-La-Torre 2006</a>; <a href="https://web.archive.org/web/20130819061043/http://www.technologyreview.com/read_article.aspx?id=17363&amp;ch=biotech&amp;sc=&amp;pg=1">Graham-Rowe. The Cutting Edge of Haptics, MIT Technology Review 2006</a>).&nbsp; In this approach, when exploring&nbsp; a virtual object, an user's hand travels along a smooth trajectory without geometrical sharp edges (Fig. 2a), and lateral forces are used to render illusory sharp edges (Fig. 2b). Our experiments indicate that this approach allows for a more natural rendering of such challenging objects. This is an example of <b><i>perception-based haptic rendering, </i></b>in which the characteristics of human haptic perception allow to overcome limitations in the engineering of haptic technology.</font></font></font> <p><font face="Arial,Helvetica"><font color="#FFFFFF"><font size="+1">More generally, this research illustrates the many opportunities for combining basic and applied research in this exciting, rapidly developing field.&nbsp;</font></font></font></td> </tr> </table> <center> <p><a href="research.htm#top"><img src="/web/20130819061043im_/http://www.roblesdelatorre.com/gabriel/back.gif" border="0" height="19" width="58"></a> <p><b><font face="Arial,Helvetica"><font color="#FFFFFF">&copy; <a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/portada2.htm">Gabriel Robles-De-La-Torre</a>, 2000-2007</font></font></b> <br><b><font face="Arial, Helvetica, sans-serif"><font size="+1"><a href="https://web.archive.org/web/20130819061043/http://www.roblesdelatorre.com/gabriel/hapticsl/legal.html">Legal notice</a></font></font></b></center> <p><br> </body> </html> <!-- FILE ARCHIVED ON 06:10:43 Aug 19, 2013 AND RETRIEVED FROM THE INTERNET ARCHIVE ON 23:25:19 Nov 26, 2024. 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