解决多智能体覆盖中对称性导致的停滞问题，提升覆盖率稳定性。
Breaking Symmetry-Induced Degeneracy in Multi-Agent Ergodic Coverage via Stochastic Spectral Control
- 引入随机扰动与收缩项，打破对称性引起的梯度消失
- 理论证明能几乎必然逃离零梯度流形，轨迹均方有界
- 在对称多模分布上有效避免停滞和轴向约束运动
基于谱多尺度覆盖（SMC）的多智能体遍历覆盖提供了一种使群体平均轨迹匹配指定空间分布的系统框架。尽管经典SMC已展现良好性能，但在智能体初始位置靠近目标分布对称点时，易出现梯度抵消，导致停滞或沿对称轴受限运动。本文严格刻画了引发此类方向退化的初始条件与对称性诱导的不变流形。为此，提出结合随机扰动与收缩项的新方法，证明其动态可保证几乎必然逃逸零梯度流形，同时维持智能体轨迹的均方有界性。在对称多模参考分布上的仿真表明，所提随机SMC有效缓解瞬时停滞与轴向约束，且所有轨迹均保持在定义域内。
原文摘要 · Abstract (English)
Multi-agent ergodic coverage via Spectral Multiscale Coverage (SMC) provides a principled framework for driving a team of agents so that their collective time-averaged trajectories match a prescribed spatial distribution. While classical SMC has demonstrated empirical success, it can suffer from gradient cancellation, particularly when agents are initialized near symmetry points of the target distribution, leading to undesirable behaviors such as stalling or motion constrained along symmetry axes. In this work, we rigorously characterize the initial conditions and symmetry-induced invariant manifolds that give rise to such directional degeneracy in first-order agent dynamics. To address this, we introduce a stochastic perturbation combined with a contraction term and prove that the resulting dynamics ensure almost-sure escape from zero-gradient manifolds while maintaining mean-square boundedness of agent trajectories. Simulations on symmetric multi-modal reference distributions demonstrate that the proposed stochastic SMC effectively mitigates transient stalling and axis-constrained motion, while ensuring that all agent trajectories remain bounded within the domain.
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