基于测地线的移动机器人轨迹规划方法  

Method for Trajectory Planning of Mobile Robot Based on Geodesics

作　　者：刘鹏程 张连东[1] 宋雪萍[1] LIU Pengcheng;ZHANG Liandong;SONG Xueping(School of Mechanical Engineering,Dalian Jiaotong University,Dalian Liaoning 116028,China)

机构地区：[1]大连交通大学机械工程学院,辽宁大连116028

出　　处：《机床与液压》2022年第23期1-5,共5页Machine Tool & Hydraulics

基　　金：国家自然科学基金面上项目(51275065)。

摘　　要：利用测地线是度量空间内两点之间最短路径的几何性质,提出一种基于测地线的移动机器人轨迹规划方法。以两轮差分驱动机器人的左右轮子转角为参数构建移动机器人轨迹弧长平方的黎曼度量,以该黎曼度量所确定的测地线作为机器人的最优轨迹。根据黎曼度量求解测地线方程的Christoffel符号,进而求解出代表路径最短的测地线方程,直接得到轮子转角与角速度,生成测地线最优轨迹。Utilizing the geometric properties that geodesic is the shortest path between two points in metric space, a method for trajectory planning of mobile robots based on geodesic was proposed. The Riemannian metric of the square of the arc length of the mobile robot’s trajectory was constructed with the left and right wheel angles of the two-wheel differential drive robot as a parameter, and the geodesic determined by the Riemann metric was used as the optimal trajectory of the robot.The Christoffel symbol of the geodesic equation was solved according to the Riemannian metric, then the geodesic equation representing the shortest path was solved, the wheel rotation angle and angular velocity were directly obtained, and the optimal geodesic trajectory was generated.

关 键 词：移动机器人 测地线 轨迹规划 黎曼度量 

分 类 号：TP24[自动化与计算机技术—检测技术与自动化装置]