NCS: Real-Time Trajectory Generation: Difference between revisions

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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 ==
<!-- 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>
* <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 ==
<!-- 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>[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://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>

Latest revision as of 23:03, 8 April 2006

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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.

Lecture Materials

Reading

Additional Resources

  • Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems, M. Milam. PhD Thesis, 2003.

  • 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.

  • 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.

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