Dynamic Constrained Stabilization on the $n$-sphere
Provides a control method for safe stabilization on spheres with constraints, relevant to robotics and aerospace applications.
The paper addresses constrained stabilization of second-order systems on the n-sphere, proposing a control strategy with dynamic damping that achieves almost global asymptotic stabilization under star-shaped constraints. Simulations on the 2-sphere demonstrate effectiveness.
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.