Motion Control of an Underactuated Parallel Robot with First Order Nonholonomic Constraint

Adding nonholonomic constraints in parallel manipulators, allows reduction of the actuated-joint number without affecting the reachable workspace. This principle applies to wrist robot in some underactuated designs. This paper studies steady state motion control for an nS-2SPU underactuated parallel wrist robot. First, a suitable Euler angles representation is selected and a new method for forward kinematic problem without extra sensor is proposed. Next, differential kinematics of the robot is analyzed considering first order nonholonomic constraint on angular velocity of the robot. By some manipulations, the derived equations are transformed into chain form, and a hierarchical sliding mode controller is designed for the system. Closed-loop performance of the proposed controller is compared to that of a traditional controller reported in the literature through simulations.