基于特殊正交群的工业机器人姿态插补研究

Research on Attitude Interpolation of Industrial Robot Based on Special Orthogonal Group

针对工业机器人因多姿态插补存在的路径不平滑、运动时间过长、速度波动率大等问题,提出了一种基于特殊正交群的机器人多姿态插补方法。首先,采用特殊正交群将获得的姿态转换为其对应的指数坐标,进而将姿态插值问题转换为对向量插值问题;其次,为保证姿态路径的连续性同时减小姿态路径的曲率对速度影响,利用三次非均匀有理B样条(NURBS)曲线和非支配排序遗传算法(NSGA-Ⅱ)以曲率L_(2)范数和长度为优化目标减小姿态路径的曲率和长度;最后,引入S形加减速对生成的姿态路径进行分段自适应加减速控制,结合弦截法和抛物线(Muller)法提出一种参数密化算法完成姿态插补。研究结果表明:与单位四元数的球面四边形插值(Squad)相比,NURBS插值的姿态路径具有C~2连续性;与标准NURBS曲线插补运动相比,优化插补运动时间缩短8.7%;与弦截法相比,所提算法的绝对平均速度波动率降低73%。

A multi-attitude interpolation method for robots based on a special orthogonal group is proposed to deal with the problems of unsmooth path,long movement time and large velocity fluctuation of industrial robots due to multi-pose interpolation.Firstly,a special orthogonal group was used to convert the attitude into its corresponding exponential coordinates,and then the attitude interpolation problem was transformed into a pair vector interpolation problem;Secondly,in order to ensure the continuity of the attitude path and reduce the influence of the curvature of the attitude path on the speed,the cubic NURBS curve and NSGA-Ⅱ algorithm were used to reduce the curvature and length of the attitude path with the curvature L_2 norm and length as the optimization objectives;Finally,the S-shaped acceleration/deceleration was used to perform piecewise adaptive acceleration and deceleration control for the generated attitude path,and a parameters dense algorithm is proposed to complete the attitude interpolation by combining the Secant method and the Muller method.The results show that the attitude path of NURBS interpolation has C~2 continuity compared with the Squad of unit quaternion,the optimized interpolation motion time is shortened 8.7% compared with the standard NURBS curve interpolation motion,and the absolute average velocity volatility of the proposed algorithm is reduced 73% compared with the Secant Method.