Abstract: A method for using a special class of low-harmonic Bezier curves to plan and generate trajectory patterns for computer-controlled machinery in which desired motion information is input into a first processor. A low-harmonic trajectory is then generated from the desired motion information according to the low-harmonic Bezier curves and output into a second processor where points along the low-harmonic trajectory are computed. Each point on the trajectory is then output, amplified, and input into an actuator for performing a desired motion, but which results in an actual motion. The actual motion is then compared to the desired motion in a comparing means which computes an error. A feedback control signal is then generated to correct the error. Lastly, the method is repeated for all points on the trajectory until the trajectory is complete or the operation is terminated. Another aspect of the present invention is an apparatus for carrying out the method of the present invention.