基于复合多项式的并联机器人运动轨迹规划研究

Research on motion trajectory planning of parallel robot based on compound polynomial

为了更好地规划并联机器人运动轨迹,降低其振动幅度,从而提高并联机器人使用寿命,采用复合多项式设计并联机器人角位移运动轨迹,并对角位移、角速度和角加速度进行仿真验证。建立并联机器人机构装置简图,根据三角函数和几何关系式推导出角位移运动方程式。引用三次多项式设计并联机器人运动轨迹,采用Bézier曲线对三次多项式进行改进,设计出了复合多项式变化曲线。采用Matlab软件对并联机器人角位移、角速度和角加速度变化曲线进行仿真,与三次多项式输出结果进行对比。结果显示:采用三次多项式设计的并联机器人运动轨迹,输出的角位移、角速度和角加速度最大值分别为94°,187(°)/s和1125(°)/s^2;采用复合多项式设计的并联机器人运动轨迹,输出的角位移、角速度和角加速度最大值分别为94°,136(°)/s和734(°)/s^2;采用复合多项式设计的并联机器人运动轨迹,降低了角速度和角加速度峰值,并联机器人振动幅度得到了改善,从而延长其使用寿命。

In order to better plan the trajectory of parallel robot,reduce its vibration amplitude and improve the service life of parallel robot,the compound polynomial is used to design the angular displacement trajectory of parallel robot,and the angular displacement,angular velocity and angular acceleration are simulated and verified.The device sketch of parallel manipulator is established,and the angular displacement equation is deduced according to trigonometric function and geometric relationship.The cubic polynomial is used to design the trajectory of parallel robot,and the Bézier curve is used to improve the cubic polynomial,and the compound polynomial curve is designed.The curves of angular displacement,angular velocity and angular acceleration of parallel robot are simulated by using Matlab software,and the results are compared with those of cubic polynomial output.The results show that the maximum angular displacement,angular velocity and angular acceleration of the parallel manipulator are 94°,187(°)/s and 1125(°)/s^2,respectively.The maximum angular displacement,angular velocity and angular acceleration of the parallel manipulator are 94°,136(°)/s and 734(°)/s^2,respectively.The trajectory of parallel robot designed by compound polynomial reduces the peak angular velocity and acceleration,and improves the vibration amplitude of parallel robot,thus prolonging its service life.