在n球面上带有锥形和星形约束的受约束稳定化
Constrained Stabilization on the n-Sphere with Conic and Star-shaped Constraints
AI总结：
本文提出了一种在n球面上避免星形约束的受约束稳定化方法，通过测地线引导和反极点转向策略，实现目标位置的几乎全球稳定性。
摘要：
在星形约束下对n球面上的受约束稳定化问题进行了研究。我们提出了一种控制策略，该策略能够将状态几乎全球地引导到期望位置，同时避免在n球面上的星形约束。根据状态与不安全区域的接近程度，状态要么沿着连接目标与状态的测地线被引导到目标位置，要么被引导到预定义点的反极点，该点位于最近不安全区域的内部。我们证明了在所提出的连续、时间不变反馈控制律下，目标位置几乎全球渐近稳定。在2球面和3球面上的非平凡仿真结果展示了理论结果的有效性。
英文摘要：
The problem of constrained stabilization on the n-sphere under star-shaped constraints is considered. We propose a control strategy that allows one to almost globally steer the state to a desired location while avoiding star-shaped constraints on the n-sphere. Depending on the state's proximity to the unsafe regions, the state is either guided towards the target location along the geodesic connecting the target to the state or steered towards the antipode of a predefined point lying in the interior of the nearest unsafe region. We prove that the target location is almost globally asymptotically stable under the proposed continuous, time-invariant feedback control law. Non-trivial simulation results on the 2-sphere and the 3-sphere demonstrate the effectiveness of the theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
