Spline Path Following for Redundant Mechanical Systems

Path following controllers make the output of a control system approach and traverse a prespecified path with no
a priori
time-parametrization. In this paper, we present a method for path following control design applicable to framed curves generated by splines in the workspace of kinematically redundant mechanical systems. The class of admissible paths includes self-intersecting curves. Kinematic redundancies are resolved by designing controllers that solve a suitably defined constrained quadratic optimization problem. By employing partial feedback linearization, the proposed path following controllers have a clear physical meaning. The approach is experimentally verified on a four-degree-of-freedom (four-DOF) manipulator with a combination of revolute and linear actuated links and significant model uncertainty.