管道曲面上轮式机器人的极值轨道研究

对轮式机器人在管道曲面上的极值轨道问题进行了研究。在管道曲面上建立了轮式机器人的动态模型,证明轮式机器人是可控的,并且存在时间最优轨道,利用庞特里亚金最大值原理给出了轮式机器人最小时间控制的必要条件,并给出了极值轨道的结构方程,通过结构方程分析了管道曲面上移动机器人的极值轨道,指出极值轨道的控制变量完全由结构方程来确定,并且机器人的极值轨道由2种基本轨道类型的有限组合而成,给出了这2种基本轨道类型控制变量的变化情况。

Extremum Trajectories of Wheeled Robot on Pipeline Surfaces

The extremum trajectories of wheeled robot on pipeline surfaces was studied. The dynamic model of the wheeled mobile robot on pipeline surfaces was presented, and then the controllability of robots and the existence of time optimal trajectories were proved. By applying Pontryagin's maximum principle, the necessary conditions of time optimal control were obtained, and the structure equations of extremal trajectories were given. The extremum trajectories were studied with the analysis of structure equations. It was notified that control variables of the extremum trajectories were defined by structure equations. The extremum trajectories were combined finitely by two basic types of trajectories. Moreover, the exact values for the control variables of this two basic types were given.