Quaternion Constrained Robust Attitude Control Using Barrier Lyapunov Function Based Back-stepping

Abstract

A novel, robust quaternion constrained attitude control law for rigid bodies is presented in this paper. The controller is formulated using the backstepping philosophy, and Barrier Lyapunov Functions (BLFs) are used to prevent attitude constraint violation. This is done by ensuring the boundedness of BLFs in the closed-loop Lyapunov stability analysis. The analogy between a standard Quadratic Lyapunov Function based attitude control law and the BLF based control law is highlighted, and a systematic procedure to select control constants is detailed. Finally, the BLF based control law is verified by carrying out numerical simulations of the rigid body in the presence of initial attitude errors and bounded disturbance torques. In the first case, the attitude errors are asymptotically driven to zero while strictly satisfying the quaternion constraints. In the presence of bounded disturbance torques, the attitude errors remain bounded within the constraint boundary.