NCS: Real-Time Trajectory Generation - Revision history

Murray: /* Reading */

2006-04-08T23:03:14Z

Reading

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	== Reading ==		== Reading ==
	* <p>[http://www.cds.caltech.edu/~milam/publications/mmm00-cdc.pdf A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems], M. B. Milam, K. Mushambi and R. M. Murray. Conference on Decision and Control, 2000. This is one of the earliest papers on NTG, written by a Caltech PhD student (Milam) and a Caltech undergradaute (Mushambi). This is a good overview paper for the setup that NTG uses.</p>		* <p>[http://www.cds.caltech.edu/~milam/publications/mmm00-cdc.pdf A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems], M. B. Milam, K. Mushambi and R. M. Murray. Conference on Decision and Control, 2000. This is one of the earliest papers on NTG, written by a Caltech PhD student (Milam) and a Caltech undergradaute (Mushambi). This is a good overview paper for the setup that NTG uses.</p>
	* <p>[http://www.cds.caltech.edu/~murray/papers/2000k_pmm01-nolcos.html Inversion Based Constrained Trajectory Optimization], N. Petit, M. B. Milam and R. M. Murray. IFAC Symposium on Nonlinear Control Systems Design (NOLCOS), 2001.		* <p>[http://www.cds.caltech.edu/~murray/papers/2000k_pmm01-nolcos.html Inversion Based Constrained Trajectory Optimization], N. Petit, M. B. Milam and R. M. Murray. IFAC Symposium on Nonlinear Control Systems Design (NOLCOS), 2001. This paper talks about some of the computational tradeoffs regarding defect (non-flatness) of a system. </p>

	== Additional Resources ==		== Additional Resources ==

Murray: /* Reading */

2006-04-08T22:59:18Z

Reading

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	== Reading ==		== Reading ==
	* <p>[http://www.cds.caltech.edu/~milam/publications/mmm00-cdc.pdf A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems], M. B. Milam, K. Mushambi and R. M. Murray. Conference on Decision and Control, 2000. This is one of the earliest papers on NTG, written by a Caltech PhD student (Milam) and a Caltech undergradaute (Mushambi). This is a good overview paper for the setup that NTG uses.</p>		* <p>[http://www.cds.caltech.edu/~milam/publications/mmm00-cdc.pdf A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems], M. B. Milam, K. Mushambi and R. M. Murray. Conference on Decision and Control, 2000. This is one of the earliest papers on NTG, written by a Caltech PhD student (Milam) and a Caltech undergradaute (Mushambi). This is a good overview paper for the setup that NTG uses.</p>
			* <p>[http://www.cds.caltech.edu/~murray/papers/2000k_pmm01-nolcos.html Inversion Based Constrained Trajectory Optimization], N. Petit, M. B. Milam and R. M. Murray. IFAC Symposium on Nonlinear Control Systems Design (NOLCOS), 2001.

	== Additional Resources ==		== Additional Resources ==

Murray: /* Additional Resources */

2006-04-08T22:57:16Z

Additional Resources

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	* <p>[http://www.cds.caltech.edu/~murray/papers/2003_milam03-phd.html Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>		* <p>[http://www.cds.caltech.edu/~murray/papers/2003_milam03-phd.html Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>
	* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>		* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>
			* <p>[http://aero.tamu.edu/people/raktim/sw.html Optragen], version 1.0, 2006. This is a new MATLAB toolbox for optimal trajectory generation written by Raktim Bhattacharya, a former postdoc at Caltech. This version does not run in real-time, but has a much more user-friendly interface than NTG.</p>

Murray at 00:47, 8 April 2006

2006-04-08T00:47:22Z

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	== Additional Resources ==		== Additional Resources ==
	* <p>[http://www.cds.caltech.edu/~murray/papers/2003_milam03-phd.html Real-Time Optimal Trajectory Generation for		* <p>[http://www.cds.caltech.edu/~murray/papers/2003_milam03-phd.html Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>
	Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>
	* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>		* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>

Murray: /* Additional Resources */

2006-04-08T00:46:29Z

Additional Resources

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	== Additional Resources ==		== Additional Resources ==
	* <p>[~~ftp~~://~~avalon~~.caltech.edu/~~pub/~~murray/~~preprints~~/~~milam03~~-phd.~~pdf~~ Real-Time Optimal ~~Tra jectory~~ Generation for		* <p>[http://www.cds.caltech.edu/~murray/papers/2003_milam03-phd.html Real-Time Optimal Trajectory Generation for
	Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>		Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>
	* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>		* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>

Murray: /* Additional Resources */

2006-04-07T23:29:46Z

Additional Resources

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	== Additional Resources ==		== Additional Resources ==
	<!-- ~~Links to additional information~~. ~~If there are good sources of additional information for students interested in exploring this topic further~~, ~~these should go at~~ the ~~bottom~~ of the ~~page~~. -->		* <p>[ftp://avalon.caltech.edu/pub/murray/preprints/milam03-phd.pdf Real-Time Optimal Tra jectory Generation for
			Constrained Dynamical Systems], M. Milam. PhD Thesis, 2003.</p>
			* <p>[http://www.cds.caltech.edu/~murray/software/2002a_ntg.html NTG software], version 2.2a, 2002. This is the last publically released version of [[NTG]]. The documentation is a bit sparse, but the examples are heavily commented.</p>

Murray: /* Reading */

2006-04-07T23:26:35Z

Reading

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	== Reading ==		== Reading ==
	<!-- ~~A reading list~~ for ~~the lecture~~. This ~~will typically be 3-5 articles or book chapters that are particularly relevant to~~ the ~~material being presented~~. ~~The reading list should be annotated to explain how the articles fit into the topic~~ for the ~~lecture~~. -->		* <p>[http://www.cds.caltech.edu/~milam/publications/mmm00-cdc.pdf A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems], M. B. Milam, K. Mushambi and R. M. Murray. Conference on Decision and Control, 2000. This is one of the earliest papers on NTG, written by a Caltech PhD student (Milam) and a Caltech undergradaute (Mushambi). This is a good overview paper for the setup that NTG uses.</p>

	== Additional Resources ==		== Additional Resources ==
	<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. -->		<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. -->

Murray at 23:21, 7 April 2006

2006-04-07T23:21:43Z

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	{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page -->		{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page -->

	<!-~~- Enter a 1 paragraph description~~ of the ~~contents~~ of ~~the lecture~~. ~~Make sure~~ to ~~include any key concepts, so~~ that the ~~wiki search feature will pick them up -->~~		In this lecture we provide an overview of real-time trajectory generation for nonlinear control systems. Using the concept of differential flatness, we show how to convert the trajectory generation problem from one in optimal control to one of optimization. Efficient numerical methods can then be used to find trajectories that satify the system dynamics and constraints, as well as minimizing a cost function. We concentrate on methods for real-time trajectory generation, and in particular the [[NTG]] software package.
	~~This is the template for CDS 270 lectures~~. ~~If you edit this page~~, ~~you will see comments describing what goes~~ in ~~each section. '''Do not edit this template.''' See~~ [[~~CDS 270: Information for Lecturers~~]] ~~for more information on how to create a wiki page corresponding to a lecture~~.

	== Lecture Materials ==		== Lecture Materials ==
	<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful -->		* [[Media:L3-1_ntg.pdf\|Lecture: Nonlinear Trajectory Generation]]
	~~<!-- Sample lecture link:~~ * [[Media:L1-~~1_Intro~~.pdf\|Lecture: ~~Networked Control Systems: Course Overview~~]] ~~-->~~

	== Reading ==		== Reading ==

Murray at 05:33, 6 April 2006

2006-04-06T05:33:23Z

New page

{{cds270-2 header}} 


This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture.

== Lecture Materials ==



== Reading ==


== Additional Resources ==