考虑关节摩擦的并联机器人平滑轨迹规划

针对一种空间3自由度并联机器人，提出一种近似时间最优的平滑轨迹规划算法。与基于动力学模型的传统轨迹规划算法相比，所提出的算法模型综合考虑了所有运动关节的摩擦力矩，通过虚功原理建立了运动机构完整的动力学模型，并将运动学和动力学约束条件转换为伪速度极值曲线，同时计算出伪加速度零值边界曲线，二者相结合能更准确地反映出规划轨迹应遵循的约束条件。利用五次样条曲线分段构建相平面下伪状态、伪速度和伪加速度的平滑运动轨迹曲线，从而保证了驱动力矩、关节速度和加速度的连续性。最后利用所提出的规划方法对一种并联机器人进行轨迹规划，并通过试验验证了该方法的有效性，指出了并联机器人与串联机器人轨迹规划存在的差异，该算法可用于同类工业机器人的在线轨迹规划。

Smooth Trajectory Planning for Parallel Manipulator with Joint Friction Torque

A new smooth and near time-optimal trajectory planning approach is proposed for a parallel manipulator along a specified path. Compared with conventional planning algorithms based on dynamics, the fully dynamic model of the robot is constructed by virtual work principle with consideration of friction torque in every revolute joint. The kinematic and dynamic constraints can be converted to a pseudo-velocity limitation curve, and then a pseudo-acceleration boundary curve is calculated, both of which can determine the constraints to be obeyed by the planning algorithm. The five-order polynomial spline is applied to intersect the motion curves smoothly for the state, velocity, and acceleration in phase plane, which can guarantee the continuity of the torque, joint velocity and acceleration. The effectiveness of the planning algorithm is verified by an experiment for a parallel robot. The results show the differences between the trajectory planning of serial and parallel robot, and the feasibility of the method which can be used to online application for similar industrial robots.