A comparison study on the dynamic control of OpenMANIPULATOR-X by PD with gravity compensation tuned by oscillation damping based on the phase-trajectory-length concept

In this paper, the dynamic control of a 4-DOF serial manipulator, the so-called OpenMANIPULATOR-x, is investigated by means of different performance indices, including, among others, oscillation damping. To do so, the kinematics and dynamics equations are obtained from a systematic approach where both models are verified by simulating the under study robot in Simscape. The stability of the applied controller, which is a PD with gravity compensation controller, is investigated, and it reveals that it is asymptotically stable. Thereafter, the coefficient of the latter PD controller is first optimized by means of different performance indices, namely, IAE, ISE, ITAE, ITSE then, a new criterion called oscillation damping, which is based on the optimization of a cost function defined on the phase trajectory length concept is used in order to evaluate the performance of the implemented controller. The obtained results revealed that the step response of the oscillation damping controller eliminates the overshoot, but it is slower than ones tuned by other performance indices.