arXiv:2603.27382v3 Announce Type: replace-cross 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 constrained rigid-body attitude stabilization. The effectiveness of our approach is demonstrated through simulation results on the 2-sphere and the 3-sphere in the presence of star-shaped constraint sets.