Breaking Symmetry-Induced Degeneracy in Multi-Agent Ergodic Coverage via Stochastic Spectral Control

2025-12-28

AI Summary

In multi-agent sweep coverage, symmetric target distributions induce gradient cancellation, trapping agents in zero-gradient manifolds—causing initialization stagnation or degenerate motion along symmetry axes. This work first rigorously characterizes the symmetry-induced invariant manifold and proposes a stochastic perturbation mechanism with a contraction term, proving that agents escape the zero-gradient region almost surely while ensuring mean-square boundedness of trajectories. The method integrates stochastic differential dynamics modeling, spectral multi-scale coverage (SMC), and Lyapunov stability analysis, grounded in symmetry and invariant manifold theory. Experiments on multimodal symmetric reference distributions demonstrate significant mitigation of transient stagnation and axial motion constraints, markedly improving coverage convergence speed and robustness.

Technology Category

• Multiagent Systems: Multiagent Planning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Addresses gradient cancellation in multi-agent coverage due to symmetry
• Introduces stochastic control to escape zero-gradient manifolds safely
• Ensures bounded trajectories while preventing stalling and constrained motion

Innovation

• Introduces stochastic perturbation to escape symmetry-induced degeneracy
• Combines contraction term for mean-square boundedness of trajectories
• Enhances Spectral Multiscale Coverage to mitigate stalling and constrained motion