Abstract

In this paper, we develop multiple synergistic hybrid feedback control laws for mechanical systems on matrix Lie groups with left-invariant metrics. With the goal of globally asymptotically tracking a desired reference trajectory, we propose a hybrid proportional-derivative (PD) type control law and an output feedback version which only utilizes configuration measurements. Moreover, to ensure global asymptotic tracking in the presence of a constant and unknown disturbance in the system dynamics, we introduce two novel proportional-integral-derivative (PID) type control laws with slightly different properties in terms of gain selection and integral action. The theoretical developments are validated through numerical simulation of an underwater vehicle.

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