Global Attitude Stabilization of a Rigid Body on SO(3) via Observer-based Hybrid Feedback Under Constraints
Abstract This paper studies the global stabilization of a rigid body attitude, a task that is subject to topological obstacles. Theseobstructions preclude the existence of a globally stable equilibrium point. Consequently, the rigid body attitude cannotbe globally stabilized by continuous feedback control laws. In order to resolve this challenge, this paper presents anobserver-based hybrid feedback control law. Thereafter, in order to derive the proposed feedback law, a new kind ofsynergistic potential functions is presented which induces a gradient vector eld to globally stabilize a given set. Moreover, the gradient of the proposed synergistic potential functions is utilized to derive a hybrid angular velocityobserver. The outputs of the proposed observer are employed to produce the necessary damping from the noisy measurements of the attitude. Furthermore, this paper considers two types of constraints: angular velocity constraints, and input torque constraints. Afterward, these constraints are formulated in terms of the Linear Matrix Inequalities (LMI) optimization problem to perform constraints satisfaction at all times. Moreover, this paper introduces a novel hybrid quantizer to deal with the problem of the low-price wireless network. This paper analyzes the global asymptotic stability of the reference set via the Lyapunov's method. Finally, a comparative study in simulations is provided to assess the performance of the proposed control technique.
