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Finite-time attitude stabilization for rigid bodies without angular velocity measurement

This paper investigates the finite-time output feedback stabilization of rigid body attitude dynamics without velocity measurement on the special orthogonal group ( SO(3)). We first transform the stabilization problem on SO(3) into the stabilization issue on its Lie algebra (so(3)) via the logarithm map. The proposed approach consists of exponential coordinates of SO(3) and the output of a nonlinear filter without the knowledge of the control input. Then the finite-time stability of the resulting closed-loop system is proven based on Lyapunov stability theory and geometric homogeneity technique. Since the set of singularities is zero measure, the proposed velocity-free feedback controller guarantees almost global finite-time stability, which is as strong as the topology of SO(3) can permit. Finally, simulations demonstrate the effectiveness of the proposed approach.