H∞ control of rigid robots

Abstract In the present paper we propose a possible strategy for set point control and disturbance attenuation for a rigid robot using the notion of L 2 -gain of a system. In particular we discuss the use of H ∞ control for trajectory tracking and we show, for the particular case of rigid robots, that a PD controller suffices to render the closed loop system from the reference signal to the error variable dissipative with respect to the supply rate associated with the notion of L 2 -gain. Furthermore we consider the problem of attenuating torque disturbances, always by mean of a PD controller.