自动化学报2008，Vol.34Issue(4)：445-452,8.
车型机器人的时间最优轨迹
Time-optimal Trajectories for a Car-like Robot
摘要
Abstract
This paper provides a new geometric method for achieving the sufficient family of the time-optimal trajectories to connect any two configurations of the robot in a 3-dimensional manifold based on the geometric optimal control theory. We provide a new perspective for analyzing this special type of nonlinear problems. Based on the structural characteristics of the switching functions and their derivatives from the Pontryagin's minimum principle (PMP) and the Lie algebra, we build a special coordinate system and introduce a new vector. We discover the one-to-one mapping between the rotation trajectory of this new vector and the optimal control trajectory. Furthermore, we define a switching vector that denotes the position and rotation direction of this vector, and reach a conclusion that the specified initial and final switching vectors can uniquely determine an optimal trajectory. In addition, it is the first time a condition that can be used directly for selecting a time-optimal trajectory is provided.关键词
Geometric optimal control theory, robotics, time-optimal trajectory, Pontryagin's minimum principle (PMP), LiealgebraKey words
Geometric optimal control theory, robotics, time-optimal trajectory, Pontryagin's minimum principle (PMP), Liealgebra分类
信息技术与安全科学引用本文复制引用
王慧芳,陈阳舟..车型机器人的时间最优轨迹[J].自动化学报,2008,34(4):445-452,8.基金项目
Supported by Doctoral Fund of Ministry of Education of China20060005014), National Natural Science Foundation of China 60374007) （）
