Trajectory Generation for Nonlinear Control Systems

Michiel van Nieuwstadt, CDS/ME, California Institute of Technology

Two degree of freedom design is a control paradigm where we calculate a nominal trajectory to deal with nonlinearities, and use linear control theory to design a stabilizing controller around this trajectory and deal with uncertainty. Calculation of the nominal trajectory is a hard problem in general since it requires solution of two point boundary value problems. For certain classes of systems it is easy. In particular, for differentially flat systems, there is a 1-1 mapping from curves in the output space to curves in state space. Some properties of differentially flat systems will be discussed and several interesting trajectory generation problems for this class will be presented. Two algorithms are proposed that solve real time trajectory generation for differentially flat systems by computing the feed forward term on line. Non-flat systems can be dealt with by using flat approximations, and various approaches to deal with the perturbations terms are discussed. Outer flatness is defined as a two layered structure where one layer is flat. This concept is compared with backstepping and dynamic inversion. The talk will focus on computational issues and experimental validation. The various algorithms will be validated in experiment on the first and second generation ducted fan, and the Caltech helicopter.