Robust global bimodal rest-to-rest attitude control of rigid body using unit quaternion

This work proposes a hysteresis-based controller with two binary logic variables for the rest-to-rest control of attitude represented by quaternions. The control system has a hybrid nature given by the presence of a switching logic variable that indicates which quaternion representation of the reference attitude should be followed and by a second logic variable which indicates the chattering prone region and has the overall effect of adapting the hysteresis width. It is presented a formal proof that the proposed bimodal control leads to global stability without unwinding and is robust against chattering for any measurement noise with magnitude less than or equal to a given maximum value. Simulation results indicate that the proposed adaptive hysteresis width controller can be advantageous when the initial and final angular velocities have small magnitudes as is the case of the rest-to-rest attitude control problem.