Abstract
This paper studies the robust stabilization of rigid-body attitudes represented by a special orthogonal matrix. A geometric proportional–integral–derivative (PID) controller is proposed with all the input commands defined in the dual space so*(3) of a Lie algebra for left-invariant systems evolving on a Lie group SO(3). Almost global asymptotic stability (AGAS) of the close system is proved by constructing a gradient-descent Lyapunov function after explicitly performing two stages of variable change. The attitudes are stabilized to the stable equilibrium despite the influence of inertially fixed biases. The convergent behaviors and the robustness to biases are verified by numerical simulations.
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