Orientation Trajectory Smoothing Based on Unit Sphere Projection

This paper addresses the issue of non-smooth orientation path corners in multi-point motion of industrial robots by proposing a new method. The method employs unit quaternions to describe the orientation and projects the orientation motion path onto the unit sphere, not only achieving the visualization of the orientation path but also transforming the smoothing of the orientation path corners into the smoothing of corners of a curve path on the unit sphere. Then, a C3 continuous parameter curve is constructed and inserted at each corner of the path curve on the unit sphere, ensuring smooth transitions and jerk continuity. The method is efficient and validated through simulations.