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中文摘要：
对移动在曲面上的机器人的动态模型进行了研究.在曲面上建立了移动机器人动态模型,通过流形上的李群理论对模型进行分析,指出曲面上移动机器人是可控的,并且在曲面上存在时间最优轨道.利用庞特里亚金最大值原理,得到移动机器人模型的结构方程,并通过结构方程来分析曲面上移动机器人的时间最优轨道,指出时间最优轨道的控制变量完全由结构方程和曲面的高斯曲率决定,并且在高斯曲率小于零的曲面上,机器人的时间最优轨道由3种基本轨道的有限组合而成,给出了这3种基本轨道以单位速度向前（后）移动时角速度变化的具体分布情况.
英文摘要：
The present work studies the dynamic mode of mobile robots on surfaces.The dynamic model of the robots moving on surfaces is established.By using Lie group theory,the analysis of the dynamic model is presented.It is noted that the mobile robots are controllable and there exist time optimal trajectories on surfaces. By applying Pontryagin′s Maximum Principle,the structure equations are obtained.The time optimal trajectories are studied by the analysis of structure equations.It is notified that control variables of the time optimal trajectories are determined by structure equations and Gaussian curvature.In the case of Gaussian curvature of surface less than zero,the time optimal trajectories are the finite combination of three basic trajectories.Moreover,in the case of the control variable of velocity for the basic trajectories is moving forward or backward,the exact variation distribution of angular velocity is presented.
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