# Approximate Trajectory Generation for Differentially Flat Systems with Zero Dynamics

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### M. van Nieuwstadt, R. M. Murray

1995 Conference on Decision and Control

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

- Conference paper: http://www.cds.caltech.edu/~murray/preprints/nm95-cdc.pdf
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