Stochastic stabilization of rigid body motion of a spacecraft on SE(3)

Abstract

This paper considers a stochastic systems modelling and stabilization of the rigid body motion of a spacecraft with stochastic disturbances. To rigorously deal with dynamics disturbed by a stochastic process, the rigid body motion is described by a stochastic differential equation on . This enables us to quantitatively evaluate the uncertainty using stochastic calculus. We present a stochastic stabilizing controller and a stability theorem, which claim that the error of the rigid body motion with respect to a given desired motion is exponentially ultimately bounded in the mean square sense. The resultant stochastic model has no equilibrium point due to persistent noise effect. This makes stability analysis more difficult than the conventional stochastic stability concepts. However, the present stability theorem guarantees that the error exponentially converges to the vicinity of the target state and then remains bounded even under persistent noise. Finally, numerical simulations validate the proposed method.