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Time-optimal parking and flying: Solving path following problems efficiently

Path following deals with the problem of following a geometric path without any preassigned timing information and constitutes an important step in solving the general motion planning problem. The current paper considers path following for differentially flat systems. In this case the dynamics of the system can be projected along the path to a single input system, resulting in a free end-time optimal control problem. We propose to rewrite the problem in terms of the velocity along the path and the path itself. This way, we arrive at a fixed end-time optimal control problem that can be solved efficiently by interior-point solvers. Two challenging examples, a truck-trailer parking simulation and a quadrotor mission, illustrate the efficiency of the problem formulation and the practicality of the developed software.