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 he 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 obtaiend.
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