Robust global asymptotic stabilization of a 6-DOF rigid body by quaternion-based hybrid feedback

The problem of robust, global asymptotic stabilization of a rigid body is hampered by major topological obstructions. These obstructions prevent a continuous state feedback from solving the problem and also lead to robustness issues when (non-hybrid) discontinuous feedback is applied. In this paper, we extend a hybrid control strategy proposed in a companion paper for robust, global asymptotic stabilization of rigid body attitude to the case where translation is also considered. Through Lyapunov analysis, we develop quaternion-based hysteretic hybrid control laws in the kinematic and dynamic settings. In the dynamic setting, two control laws are derived: one from an energy-based Lyapunov function and one by backstepping. Robustness to measurement noise is asserted by employing recently developed stability theory for hybrid systems. A comparison between discontinuous and hysteretic feedback under measurement noise is shown in simulation.