EECI08: Trajectory Generation and Differential Flatness - Revision history

Murray: EECI: Trajectory Generation and Differential Flatness moved to EECI08: Trajectory Generation and Differential Flatness

2009-03-01T20:13:41Z

EECI: Trajectory Generation and Differential Flatness moved to EECI08: Trajectory Generation and Differential Flatness

← Older revision	Revision as of 20:13, 1 March 2009
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Murray at 01:00, 29 March 2008

2008-03-29T01:00:32Z

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	{{eeci-sp08 header\|prev=[[~~NCS~~: Embedded Systems Programming\|Embedded Systems]]\|next=[[~~NCS~~: Optimization-Based Control\|Optimization-Based Control]]}}		{{eeci-sp08 header\|prev=[[EECI: Embedded Systems Programming\|Embedded Systems]]\|next=[[EECI: Optimization-Based Control\|Optimization-Based Control]]}}

	{{righttoc}}		{{righttoc}}

Murray: /* Reading */

2008-03-29T00:21:04Z

Reading

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	== Reading ==		== Reading ==
			* <p>[http://www.cds.caltech.edu/~murray/papers/2003d_mmr03-cds.html Flat systems, equivalence and trajectory generation], Phillipe Martin, Richard Murray, Pierre Rouchon. CDS Technical Report, 2003. This is a long survey article on differential flatness, giving multiple formulations and many examples.</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/~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. This paper talks about some of the computational tradeoffs regarding defect (non-flatness) of a system. </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. This paper talks about some of the computational tradeoffs regarding defect (non-flatness) of a system. </p>

Murray at 00:18, 29 March 2008

2008-03-29T00:18:44Z

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			{{righttoc}}
	In this lecture we provide an overview of trajectory generation and tracking 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.		In this lecture we provide an overview of trajectory generation and tracking 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.

Murray: NCS: Trajectory Generation and Differential Flatness moved to EECI: Trajectory Generation and Differential Flatness

2008-03-28T15:19:08Z

NCS: Trajectory Generation and Differential Flatness moved to EECI: Trajectory Generation and Differential Flatness

← Older revision	Revision as of 15:19, 28 March 2008
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Murray: /* Lecture Materials */

2008-03-17T14:55:53Z

Lecture Materials

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	== Lecture Materials ==		== Lecture Materials ==
	* Lecture notes: {{eeci-sp08 pdf\|L4_flatness.pdf\|Trajectory Generation and Differential Flatness}} (handwritten)
	* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}		* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}

Murray: /* Lecture Materials */

2008-03-16T21:38:16Z

Lecture Materials

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	== Lecture Materials ==		== Lecture Materials ==
	* Lecture ~~slides~~: {{eeci-sp08 pdf ~~placeholder~~\|~~L4_flagness~~.pdf\|Trajectory Generation and Differential Flatness}} (handwritten)		* Lecture notes: {{eeci-sp08 pdf\|L4_flatness.pdf\|Trajectory Generation and Differential Flatness}} (handwritten)
	* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}		* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}

Murray: /* Lecture Materials */

2008-03-16T20:20:48Z

Lecture Materials

← Older revision		Revision as of 20:20, 16 March 2008
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	== Lecture Materials ==		== Lecture Materials ==
	* Lecture slides: {{eeci-sp08 pdf placeholder\|L4_flagness.pdf\|Trajectory Generation and Differential Flatness}}		* Lecture slides: {{eeci-sp08 pdf placeholder\|L4_flagness.pdf\|Trajectory Generation and Differential Flatness}} (handwritten)
	* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}		* Lecture notes: {{obc08\|Chapter 1 - Trajectory Generation and Tracking}}

Murray at 20:20, 16 March 2008

2008-03-16T20:20:33Z

New page

{{eeci-sp08 header|prev=[[NCS: Embedded Systems Programming|Embedded Systems]]|next=[[NCS: Optimization-Based Control|Optimization-Based Control]]}}

In this lecture we provide an overview of trajectory generation and tracking 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.

== Lecture Materials ==
* Lecture slides: {{eeci-sp08 pdf placeholder|L4_flagness.pdf|Trajectory Generation and Differential Flatness}}
* Lecture notes: {{obc08|Chapter 1 - Trajectory Generation and Tracking}}

== Reading ==

* [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.
* [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. 

== Additional Resources ==
* [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.
* [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.
* [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.