Globally optimal periodic robot joint trajectories

This paper presents a new method for the planning of robot trajectories. The method presented assumes that joint-space knots have been generated from Cartesian knots by an inverse kinematics algorithm. The method is based on the globally optimal periodic interpolation scheme derived by Schoenberg, and thus is particularly suited for periodic robot motions. Of all possible periodic joint trajectories which pass through a specified set of knots, the trajectory derived in this paper is the ‘best’. The performance criterion used is the integral (over one period) of a combination of the square of the joint velocity and the square of the joint jerk.