A technique is presented for controlling multiple manipulators which are holding a single object and therefore form a closed kinematic chain. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. The derivation is based on setting up constraint equations which reduce the 6*n degrees of freedom of n manipulators each having six joints. Additional constraint equations are considered when one or more degrees of freedom of the object is reduced due to external constraints. Utilizing the operational space dynamic equations, a decoupling controller is designed to control both the position and the interaction forces of the object with the environment. Simulation results for the control of a pair of two-link manipulators are presented.
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