EECI08: Trajectory Generation and Differential Flatness
| Prev: Embedded Systems | Course home | Next: 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 notes: Chapter 1 - Trajectory Generation and Tracking
Reading
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.
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.
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
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.
