Task space based contouring control of parallel machining systems

Since the tracking error does not reflect truly product quality, the contouring error is introduced in dynamic control of parallel machining systems. For real-time computation reason, the contouring error is approximated by the distance from the actual position to the tangent plane of the desired contour at the corresponding desired position, i.e., the error in normal direction. By attaching a moving task frame to each point on a desired trajectory, the tracking error is decomposed into tangential error and normal error. By the transformation introduced by the task frame, we obtain error dynamics in the task frame. The error dynamics is decoupled into error dynamics in tangential and normal directions by applying the computed torque control and choosing appropriate system matrices. Simulation shows that a larger bandwidth of the normal dynamics leads to smaller contouring error given fixed natural frequency for the tangential dynamics. By a comparison with the PD control in the world frame, the task space based contouring control exhibits much better performance in contouring accuracy.