Nonlinear trajectory tracking control of a closed-chain manipulator

A magnitude-based gain-scheduling nonlinear PD control is developed, by using a nonlinear exponential function of the error and its change. Performance benefits such as increased damping and reduced tracking error are achieved. The guidelines to determine the appropriate parameters for the proposed nonlinear PD control to guarantee the stability of the closed-loop system are addressed. The proposed nonlinear PD control is very simple and easy of implement. The comparative trajectory tracking results performed on a closed-chain manipulator in the presence of nonlinear friction with the conventional linear PD control demonstrates the effectiveness of the developed approach.