Dynamics Computation of Closed Link Robots and Optimization of Actuational Redundancy

Abstract

This paper discusses a general and systematic computational scheme of the inverse dynamics of closed link mechanisms. The scheme works even for multi-loop closed link mechanisms. It is derived by using d'Alembert's principle and obtained without computing the Lagrange multipliers. To account for the constraints, only the Jacobian matrix of the passive joint angles in terms of actuated ones is required. Given a non-redundant actuator system, this allows a unique representation of the constraints even for a complicated multi-loop closed link mechanisms. The scheme is computationally efficient because the computation concerning the Lagrange multipliers is not required. The inverse dynamics of closed link mechanisms that contain redundant actuators and their redundancy optimization are also discussed. Closed link mechanisms with redundant actuators are underdeterminate in computing inverse dynamics. For a redundant actuation system that contains Nr redundant actuators, the passive joint angles are represented by Nr+1 independent ways as functions of actuated joints. Using their Jacobian matrices, the actuational redundancy of closed link mechanism is parameterized by an Nr-dimensional arbitrary vector in a linear equation. For the case with one redundant actuator, the computational algorithm to minimize the joint torque taking account of their limits is presented. Numerical examples are also given to show the computational efficiency of inverse dynamics computation and the possibility of closed link manipulators with actuational redundancy.