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 C ² 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.