Abstract: An end effector move is executed by transforming the end effector position and orientation into joint coordinates at a large number of points on the end effector trajectory. On-line joint trajectories are determined in real time by looking ahead a few points on the end effector trajectory and generating points along the different joint trajectories. The current point and the look-ahead points are referred to as a block. An initial estimate of the slope at the block end points is made and then improved by overlapping the next block with the current block. The coefficients of the polynomials converting the points in the joint trajectories are interpolated to provide position commands to a servo control associated with the robot joint to control robot joint motion.