An Obstacle Avoidance Algorithm for Manipulators Based on Six-Order Polynomial Trajectory Planning

一种基于六次多项式轨迹规划的机械臂避障算法

¹ Laboratory of Precision Physical Quantity Measurement, Xi'an Institute of Optics and Precision Mechanics, Xi'an 710119, China
² College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China

Received: 25 February 2019

Abstract

Aiming at a series of requirements of obstacle avoidance trajectory planning of manipulators, a new algorithm based on six-order polynomial trajectory planning is proposed. Firstly, the six-order polynomial is used for the trajectory planning of the manipulator. Assuming that the coefficients of the sixth order term in the curve equation are undetermined parameters, by adjusting these parameters, the shape of the curve can be changed to make manipulators avoid the obstacle and to optimize performance indicators of the trajectory simultaneously. Thus, the obstacle avoidance trajectory planning of manipulators is transformed into a multi-objective optimization problem. Secondly, combining collision detection results and kinematics indexes, a fitness function is defined by the weighting coefficient method. At last, an ideal collision-free trajectory that is collaborative optimized in kinematics, trajectory length and rotation angle is planned in the joint space through genetic algorithm optimization. Additionally, the algorithm is validated by simulation experiments with MATLAB, the results show that the method of this study can effectively plan obstacle-free trajectories satisfying the performance requirements of the manipulator.

摘要

针对机械臂避障轨迹规划的一系列需求，提出了一种基于六次多项式轨迹规划的机械臂避障算法。首先，采用六次多项式对机械臂轨迹进行规划。设曲线方程中六次项系数为待定参数，通过调整参数，改变曲线形状，使机械臂绕过障碍物的同时优化轨迹的性能指标，从而将机械臂避障轨迹规划问题转化为约束条件下的多目标优化问题；其次，综合碰撞检测结果、运动学指标，通过加权系数法建立适应度函数；最后，通过遗传算法进行优化，在关节空间中规划出一条无碰撞，同时运动学、轨迹长度、转动角度等要求一起协同优化的理想运动轨迹。此外，通过MATLAB对该算法进行了仿真实验验证，结果表明，该方法能够有效地规划出满足机械臂性能要求的无障碍运动轨迹。