Globally stabilizing proportional-integral-derivative control laws for rigid-body attitude tracking

A hybrid proportional-integral-derivative (PID) law with hysteresis is proposed, which achieves global asymptotic stability. Since quaternion parameters are employed, the stability of a disconnected, two-point set in the state space is considered to avoid the unwinding phenomenon. It is shown that for the attitude tracking problem, it achieves globally asymptotically stable attitude trajectory tracking without the unwinding phenomenon and singular orientation, even in the presence of external constant disturbance torques. Moreover, the proposed hybrid control law is robust to measurement noise. Numerical tests were conducted, and the results demonstrate the asymptotic stability and the robustness to measurement noise.