Quaternion-based Hybrid Feedback for Global Asymptotic Attitude Stabilization on S3

This paper peruses the attitude control problem of a rigid body, a task that is subjected to topological obstructions. These topological obstructions express that there is no globally asymptotically stable equilibrium point for a system evolving on a compact manifold. Therefore, there exist no continuous or discontinuous feedback control laws to globally stabilize the desired rigid body attitude. Thereafter, this paper presents quaternion-based hybrid feedback to defeat these topological obstacles. The proposed control law is derived from a new kind of centrally synergistic potential functions which is introduced in this paper. This function induces a gradient vector field that globally asymptotically stabilizes the desired attitude. Finally, a simulation study depicts the superior performance of the proposed quaternion-based hybrid feedback control technique. This paper peruses the attitude control problem of a rigid body, a task that is subjected to topological obstructions. These topological obstructions express that there is no globally asymptotically stable equilibrium point for a system evolving on a compact manifold. Therefore, there exist no continuous or discontinuous feedback control laws to globally stabilize the desired rigid body attitude. Thereafter, this paper presents quaternion-based hybrid feedback to defeat these topological obstacles. The proposed control law is derived from a new kind of centrally synergistic potential functions which is introduced in this paper. This function induces a gradient vector field that globally asymptotically stabilizes the desired attitude. Finally, a simulation study depicts the superior performance of the proposed quaternion-based hybrid feedback control technique.

Automated summary

This paper investigates the attitude control problem of a rigid body, and proposes a novel quaternion-based hybrid feedback control method to overcome topological obstacles by introducing centrally synergistic potential functions. Simulation studies demonstrate the superior performance of the proposed control technique.