# Real Time Trajectory Generation for Differentially Flat Systems

### Michiel J. van Nieuwstadt and Richard M. Murray

*Int'l. J. Robust & Nonlinear Control* 8:(11) 995-1020

This paper considers the problem of real time trajectory generation and tracking for nonlinear control systems. We employ a two degree of freedom approach that separates the nonlinear tracking problem into real time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included.

- CDS Technical

report (preprint): http://www.cds.caltech.edu/~murray/preprints/nm96-ijrnc.pdf

- Project(s): Template:HTDB funding::NSF, Template:HTDB funding::AFOSR