Lyapunov recursive design of robust adaptive tracking control with L2-gain performance for electrically-driven robot manipulators

This paper develops a new Lyapunov recursive design for the tracking control problem of rigid-link electrically-driven robot manipulators with uncertainty by taking a tracking performance into account. The tracking performance is evaluated by L2-gain from a torque level disturbance signal to a penalty signal for the tracking error between outputs of the manipulator and desired trajectories. The novelty of our approach is in the strategy to construct such a Lyapunov function recursively that ensures not only stability of a tracking error system but also an L2-gain constraint, which provides a closed-form solution for non-linear H1 control problem without using a Hamilton± Jacobi inequality. Two controllers, i.e. robust and robust adaptive control laws with L2-gain performance, are designed such that the closed-loop error system is globally stable in the sense of uniform ultimate bounded stability with the L2-gain less than any given small level. Experimental works are carried out for a two-link electrically-driven manipulator. Experimental results show an enhanced tracking performance of the proposed control scheme.