Abstract-The problem of stabilization for a class of feedback linearizable systems with multiple state constraints is addressed. The design procedure is constructive, and yields a continuous final control law which guarantees that all specified states remain within certain bounds for all time. The achieved bounds on the states are independent of the initial conditions. The procedure entails shaping the control Lyapunov function, and propagating hard-bounds imposed on the pertinent stabilising functions and associated error signals through the steps of the backstepping control design framework.

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This paper presents a bounded torque control design to solve the set-point regulation problem for robot manipulators subject to joint velocity constraints. The control objectives are achieved by exploiting the passivity properties of the system and utilizing barrier function ideas to reshape the control Lyapunov function. The structure of the modified control Lyapunov function is reminiscent of those used in the artificial potential field method. The resulting controllers are modified Proportional-Derivative controllers which are simple, intuitive, and can easily be implemented in practice. In addition, asymptotic stability of the closed-loop system is guaranteed, all joint velocity constraints are strictly satisfied for all time, and the demanded torque input is bounded in norm, irrespective of the initial condition. The effectiveness of the proposed control design is demonstrated through simulations on a 2-link planar manipulator.

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