View source for NCS: Real-Time Trajectory Generation

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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 ==
* [[Media:L3-1_ntg.pdf|Lecture: Nonlinear Trajectory Generation]]

== 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>

== Additional Resources ==
* <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>