A Nonlinear Programming Method for time-optimal Control of an omni-directional Mobile Robot

可全方位運動機器人之非線性規劃最佳時間控制法

10.29548/BGYY.201109.0005

王世民(Shi-Min Wang)；吳佳儒(Chia-Ju Wu)；魏嘉延(Jia-Yan Wei)

時間最佳化控制 ； 非線性規劃 ； 全方位機器人 ； Time-optimal control ； nonlinear programming ； omni-directional robots

修平學報

23期（2011 / 09 / 01）

83 - 102

英文

本論文為探討一部三輪可全方位運動機器人的時間最佳化控制問題，這裏所提出的方法為Pontryagin的最小原則(PMP)。所使用的迭代法為非線性規劃(NLP)方法的時間最佳化題型，NLP問題的初始值在控制過程中為常數，而取樣週期在做最佳化過程中為變數，最佳化的目的是希望取樣週期要比設定的最小值更低，如此一來才可確保它的準確度。本論文所制定的NLP問題初始可行解可由遺傳演算法(GAs)來求得，因為初始可行解可求得，所以時間最佳化問題便可進行計算而得到最佳解。在這種模式下，可全方位運動機器人在空間移動時就可以找到最佳的時間運動方式。本論文所提出的方法可經由模擬結果來作說明得到驗證。

The time-optimal control problem of a three-wheeled omni-directional mobile robot is addressed in this paper. Different from usual cases, in which the Pontryagin's Minimum Principle (PMP) is used, an iterative procedure is proposed to transform the time-optimal problem into a nonlinear programming (NLP) one. In the NLP problem, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. The optimization object is to minimize the sampling period such that it is below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the formulated NLP problem, genetic algorithms (GAs) are 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.

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