机械手空间圆弧位姿轨迹规划算法的实现

为提高机械手的空间圆弧作业任务的轨迹精度,提出采用齐次矩阵和四元数法分别进行位置和姿态的轨迹规划方法．对于位置规划,先对空间圆弧所在平面的圆心角做归一化处理,再按照平滑角速度曲线规划位置轨迹上的插值点,并用齐次矩阵表示插补点的位置,保证了插补点的位置始终在所求圆弧上．姿态规划采用四元数圆弧曲线函数以及分段三次有理插值保形样条函数实现C²连续的姿态轨迹．算例验证表明，提出的位姿规划方法能够保证机械手末端执行器的轨迹精度,在位置精度及姿态平稳过渡有较高要求的机械手的实际应用方面有推广价值．

An algorithm for the interpolation of circular trajectories of manipulators

To improve the arc trajectory planning accuracy of manipulators passing the non-collinear three-points,a new approach for the manipulators’ position planning and orientation planning is presented by using homogeneous matrix and quaternion respectively.For the position planning,the central angle of the arc in space is normalized,the positions of interpolation points are planed according to the smooth angular velocity curve and represented by homogeneous matrix,all the interpolation points are on the demanded arc.By using circular blending quaternion curve and a piecewise rational cubic spline together,a C2 continuous orientation path which smoothly interpolates the given sequence of the manipulators positions is obtained.Simulation example shows that the presented planning approach for position and orientation can guarantee the end trajectory precision of manipulator,and can be applied to the trajectory planning of the manipulators with high accuracy requirement.