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西安电子科技大学理学院
纸质出版:2008
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肖刚, 余国林, 刘三阳. 曲面上CRS机器人的极值轨道[J]. 中北大学学报(自然科学版), 2008,(4):321-326.
肖刚, 余国林, 刘三阳. Extremal Trajectories for CRS Robots on Surfaces[J]. 2008, (4): 321-326.
为了解决曲面上移动CRS机器人的路径规划问题
在曲面上建立了机器人的动态模型
利用微分几何的李群理论和庞特里亚金最大值原理
证明了曲面上CRS机器人是可控的
并给出了机器人的最小时间控制的必要条件和结构方程.指出速度控制变量和角速度控制变量完全由结构方程和曲面的高斯曲率决定.通过对结构方程的分析
得到机器人的极值轨道由5种基本轨道的有限组合而成
这5种基本轨道是以单位速度向前(后)移动
并且还给出了这5种基本轨道角速度变化的具体分布情况.
In order to solve the path planning problem of mobile CRS robots on surface
a kinematic model of CRS robots on surfaces is presented.By using the Lie group theory of differential geometry and Pontryagin's maximum principle
it is pointed out that the mobile CRS robot on surface is controllable
and the necessary conditions and the structure equations of extremal trajectories are proposed.It is noted that control varies of velocity and angular velocity are definied by structure equations and Gaussian curvature.The analysis of stucture equations indicates that the extremal trajectories are combinated finitely by five basic trajectories
and that the control varies of velocity for the basic trajectories are forward or backward moving.The exact distribution for the control varies of angular velocity is presented.
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