无需中心控制，机器人集群可自主寻源并抗故障

Existing source-seeking algorithms for robot swarms typically require either direct gradient measurements or rigid geometric formations, limiting their flexibility and resilience to robot failures. We propose a fully distributed solution that overcomes these limitations by computing an ascending direction through local field measurements and distributed estimation of centroid-relative coordinates. The resulting architecture consists of three exponentially convergent algorithms operating in a slow-fast closed-loop system, enabling simultaneous estimation and motion control without central coordination. Our framework accommodates arbitrary swarm geometries and analyzes how the spatial distribution of robots affects gradient observability, robustness, and resilience to failures. We characterize optimal swarm shapes that guarantee alignment with the true gradient and show how shape morphing can maneuver the collective motion. The approach is developed for kinematic points in $\mathbb{R}^m$ and extended to 2D unicycles with constant speed. Simulations with large-scale swarms validate the methodology.