A new method for the planning of robot trajectories is presented. The method 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 is particularly suited for periodic robot motions. Of all possible periodic joint trajectories which pass through a specified set of knots, the trajectory derived is the best. The performance criterion used is the integral (over one period) of the square of a combination of the joint velocity and the joint jerk