Approximate Trajectory Generation for Di erentially Flat Systems with Zero DynamicsMichiel

This paper describes algorithms to generate trajec-tories for diierentially at systems with zero dynamics. Zero dynamics in at systems occur when the at outputs are not the tracking outputs. This means that the output trajectories can be fully parametrized by the at outputs, but that there is some additional freedom left. This freedom can be exploited to minimize a cost criterion. We parametrize the diierentially at outputs by basis functions, and solve for the parameters so as to track a prescribed trajectory approximately while minimizing a cost function. We give examples of such systems , and present simulations and experimental data. We focus on implementation issues and point out the computational cost involved in the various problems.