Adaptive control of nonlinear systems: A case study of underwater robotic systems

Abstract

Abstract The problem of controlling underwater mobile robots in 6 degrees of freedom (DOF) is addressed. Underwater mobile robots where the number of thrusters and control surfaces exceeds the number of controllable DOF are considered in detail. Unlike robotic manipulators underwater mobile robots should include a velocity dependent thruster configuration matrix B ( q ), which modifies the standard manipulator equation to: Mq + C ( q ) q + g(x) = B ( q ) u where x = J ( x ) q . Uncertainties in the thruster configuration matrix due to unmodeled nonlinearities and partly known thruster characteristics are modeled as multiplicative input uncertainty. This article proposes two methods to compensate for the model uncertainties: (1) an adaptive passivity‐based control scheme and (2) deriving a hybrid (adaptive and sliding) controller. The hybrid controller combines the adaptive scheme where M, C , and g are estimated on‐line with a switching term added to the controller to compensate for uncertainties in the input matrix B. Global stability is ensured by applying Barbalat's Lyapunov‐like lemma. The hybrid controller is simulated for the horizontal motion of the Norwegian Experimental Remotely Operated Vehicle (NEROV).