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A Nonlinear Programming Method for Time-Optimal Control of an Omni-Directional Mobile Robot

The time-optimal control problem of a three-wheeled omni-directional mobile robot is studied in this paper. In contrast to traditional methods, in which the Pontryagin's Minimum Principle is usually used, an iterative procedure is proposed to transform the time-optimal problem into a nonlinear programming (NLP) one. In the formulated NLP problem, the number of control steps is fixed initially and the sampling period is treated as a variable to be minimized in the optimization process. An upper limit on the sampling period is set in advance considering the accuracy of discretization. If the value of the sampling period is larger than the upper limit, then an update of the number of control steps is needed. To generate initial feasible solutions of the NLP problem, a genetic algorithm is adopted. Since different initial feasible solutions can be generated, the optimization process can be started from different points to find the optimal solution. In this manner, one can find a time-optimal movement of the omni-directional mobile robot between two configurations. To show the feasibility of the proposed method, simulation results are included for illustration.