The 2007 Darpa Urban Challenge called for a kinematic vehicle path planning method that could navigate and park in an obstacle-filled environment with realistic vehicle constraints. Key capabilities include minimum-time trajectories with both forward and reverse segments, and obstacle avoidance. An algorithm which generalizes the collocation method is developed and used to optimally control a differentially flat parameterization of the kinematic car. The singularity inherent in the differentially flat formulation is addressed without any constraints imposed on the state space. Experimental data is presented showing this algorithm running on Alice, the Caltech autonomous vehicle. The flexibility of the algorithm developed in this paper allows it to be applied to a large group of practical optimal control problems.
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