Redundant actuation of a closed-chain manipulator

Abstract

—A method for controlling the actuation redundancy of a closed-chain manipulator is presented. The paper deals with a 2 d.o.f. direct-drive parallel robot with one additional actuator. First, the Lagrange equations of motion of the five-bar, inertially decoupled manipulator are developed. Then, the actuation redundancy is formulated and solved as a non-linear optimization problem with equality and inequality constraints, minimizing the joint torques required either to move a payload along a given path or to apply a specified end-point force. A closed-form, globally optimal solution suitable for real-time applications is obtained. The solution is verified by computing the joint torques for the same motion in both non-redundant and redundant cases. Comparison shows that actuation redundancy may increase the end-point forces in static or slow motion situations by more than 40% in certain directions. Lesser gains are achieved in the dynamic load carrying case, due to the lower torque/weight ratio of the additional motor used and the increased inertia induced by its mass. The advantage of the proposed actuation redundancy solution consists in the generality of the optimization approach, which allows to deal with various types of joint torque and other constraints.