NCS: RealTime Trajectory Generation
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In this lecture we provide an overview of realtime 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 realtime trajectory generation, and in particular the NTG software package.
Lecture Materials
Reading

A New Computational Approach to RealTime 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.

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 (nonflatness) of a system.
Additional Resources

RealTime 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 realtime, but has a much more userfriendly interface than NTG.