Dynamic Constrained Stabilization on the n-sphere

TL;DR

This paper introduces a control strategy for stabilizing second-order systems on the n-sphere with constraints, ensuring safety and near-global convergence, demonstrated through simulations.

Contribution

It presents a novel constraint proximity-based dynamic damping control method for stabilization on the n-sphere, applicable to rigid-body attitude control.

Findings

Ensures safe, almost global asymptotic stabilization under star-shaped constraints.

Effective in constrained rigid-body attitude stabilization.

Validated through simulation on the 2-sphere.

Abstract

We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic stabilization of the target point in the presence of star-shaped constraints on the n-sphere. It is also shown that the proposed approach can be used to deal with the constrained rigid-body attitude stabilization. The effectiveness of the proposed approach is demonstrated through simulation results on the 2-sphere in the presence of star-shaped constraint sets.