This paper presents a generalized approach for controlling various cases of the constrained robot system. To accomplish specific tasks successfully by a constrained robot system, both the constraint forces/torques and the motion of the manipulator end-effector must be specified and controlled. Using the Jacobian matrix of the constraint function, the generalized coordinates of the constrained robot system can be partitioned into two sets; this leads to partitioning the constrained robot system into two subsystems. The constraint forces/torques in each subsystem can be decomposed into two components: the motion-independent and the motion-dependent forces/torques. Using the constraint function in the Cartesian space, the motion-independent forces/torques can be expressed by a generalized multiplier vector and the Jacobian matrix of the constraint function. The motion-dependent forces/torques can be determined by the motion of the manipulator end-effector, the motion-independent forces/torques, and other known quantities. This decomposition of the constraint robot system into subsystems leads to the design of a nonlinear decoupled controller with a simple structure, which takes the constraints into consideration for controlling the constrained robot system. Applying the proposed nonlinear decoupled controller to each subsystem and using the relation between the motion-independent forces/torques in the subsystems, we can show that both the errors in the manipulator end-effector motion and the constraint forces/torques approach zero asymptotically. Typical examples of the constrained robot systems are analyzed and discussed.
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