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	<id>https://murray.cds.caltech.edu/index.php?action=history&amp;feed=atom&amp;title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades</id>
	<title>Bootstrapping bilinear models of robotic sensorimotor cascades - Revision history</title>
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	<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades&amp;action=history"/>
	<updated>2026-09-09T17:17:59Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades&amp;diff=19771&amp;oldid=prev</id>
		<title>Murray: htdb2wiki: creating page for 2010g_cm10-wafr.html</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades&amp;diff=19771&amp;oldid=prev"/>
		<updated>2016-05-15T06:16:18Z</updated>

		<summary type="html">&lt;p&gt;htdb2wiki: creating page for 2010g_cm10-wafr.html&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 06:16, 15 May 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{HTDB paper&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{HTDB paper&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| authors = Andrea Censi &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and &lt;/del&gt;Richard M&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. &lt;/del&gt;Murray&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| authors = Andrea Censi&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, &lt;/ins&gt;Richard M Murray&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| title = Bootstrapping bilinear models of robotic sensorimotor cascades&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| title = Bootstrapping bilinear models of robotic sensorimotor cascades&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| source = &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2011 International Conference &lt;/del&gt;on Robotics &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and Automation &lt;/del&gt;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ICRA&lt;/del&gt;)&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| source = &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Workshop &lt;/ins&gt;on &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the Algorithmic Foundations of &lt;/ins&gt;Robotics (&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;WAFR), 2010 (Submitted&lt;/ins&gt;)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| year = 2010&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| year = 2010&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| type = &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Conference Paper&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| type = &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Preprint&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| funding = &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;NSF CPS&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| funding =  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| url = http://www.cds.caltech.edu/~murray/preprints/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cm11&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;icra&lt;/del&gt;.pdf&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| url = http://www.cds.caltech.edu/~murray/preprints/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cm10&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wafr_s&lt;/ins&gt;.pdf&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| abstract =  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| abstract = We consider the bootstrapping problem, which &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;consists &lt;/ins&gt;in learning a model of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;agent&#039;s &lt;/ins&gt;sensors and actuators starting from zero prior &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;informa- tion&lt;/ins&gt;, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;simple &lt;/ins&gt;bioplausible control strategy. The convergence &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;proper- ties &lt;/ins&gt;of learning and control are demonstrated with extensive simulations and by analytical arguments.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;We consider the bootstrapping problem, which &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;con- sists &lt;/del&gt;in learning a model of the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;agentâs &lt;/del&gt;sensors and actuators starting from zero prior &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;information&lt;/del&gt;, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range- finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sim- ple &lt;/del&gt;bioplausible control strategy. The convergence &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;properties &lt;/del&gt;of learning and control are demonstrated with extensive simulations and by analytical arguments.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| flags =  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| flags =  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| id = &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2010o&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| id = &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2010g&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>Murray</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades&amp;diff=19763&amp;oldid=prev</id>
		<title>Murray: htdb2wiki: creating page for 2010o_cm11-icra.html</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Bootstrapping_bilinear_models_of_robotic_sensorimotor_cascades&amp;diff=19763&amp;oldid=prev"/>
		<updated>2016-05-15T06:16:11Z</updated>

		<summary type="html">&lt;p&gt;htdb2wiki: creating page for 2010o_cm11-icra.html&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{HTDB paper&lt;br /&gt;
| authors = Andrea Censi and Richard M. Murray&lt;br /&gt;
| title = Bootstrapping bilinear models of robotic sensorimotor cascades&lt;br /&gt;
| source = 2011 International Conference on Robotics and Automation (ICRA)&lt;br /&gt;
| year = 2010&lt;br /&gt;
| type = Conference Paper&lt;br /&gt;
| funding = NSF CPS&lt;br /&gt;
| url = http://www.cds.caltech.edu/~murray/preprints/cm11-icra.pdf&lt;br /&gt;
| abstract = &lt;br /&gt;
We consider the bootstrapping problem, which con- sists in learning a model of the agentâs sensors and actuators starting from zero prior information, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range- finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a sim- ple bioplausible control strategy. The convergence properties of learning and control are demonstrated with extensive simulations and by analytical arguments.&lt;br /&gt;
| flags = &lt;br /&gt;
| tag = cm11-icra&lt;br /&gt;
| id = 2010o&lt;br /&gt;
}}&lt;/div&gt;</summary>
		<author><name>Murray</name></author>
	</entry>
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