Online Trajectory Tracking Control Based on the Explicit Form of the Equations of Motion for Serial Manipulator Using the New Formulation

Abstract

In this article, the novel approach to equations of motion for serial manipulators developed in literature by Bertrand and Bruneau (2013) is extended to make it usable for manipulators with general joints (i.e., prismatic and/or rotational). In this method, the dynamic model is explicitly and directly obtained from the structural parameters of the manipulator and matrix algebra without intermediate heavy calculations such as energy derivation. The correctness and efficiency of the described method are demonstrated through simulation of the dynamical equations of a 5-DOF SCARA robot. The simulation results obtained using the new formulation were compared with those derived by Kane’s method, Lagrange–Euler formulation, and GIM (generalized inertia matrix)-Christoffel’s algorithm, which proves the efficiency and correctness of the presented model. It was concluded that the new formulation requires less CPU time to generate explicit closed-form inverse dynamics. Finally, to illustrate the power of the new formulation in real-time control, a trajectory tracking control for the SCARA manipulator based on the numeric and symbolic computation of the inverse dynamic is established, and it is shown that the numeric and symbolic approaches based on our method are equivalent. As a consequence, the applicability of the new formulation in real-time model-based control is proved.