Safety-Critical Fixed-Time Distributed Formation Control for Miniature Robot Swarm Based on Embedded Dynamic Control Barrier Functions

Miniature robot swarms often conflict with dynamic obstacles during formation maneuvers in unknown environments, owing to limited sensing and communication capabilities. This article investigates the collision-free formation control problem for multiple miniature robots, which are subject to disturbances and directed communication constraints. To satisfy these time-varying high-relative-degree constraints, we first propose a novel concept of embedded dynamic control barrier function (EMB-DCBF), which extends embedded control barrier functions to handle time-varying safety constraints and system disturbances, while preserving the advantages of low computational burden. Based on EMB-DCBFs, we propose a safety-critical fixed-time distributed formation control (SC-FxTDFC) framework to achieve safety-critical control objectives. Specifically, a distributed quadratic program based on EMB-DCBFs is embedded into a fixed-time command filtered backstepping control framework. We further introduce a fixed-time extended state observer (FxTESO) for dynamic disturbance estimation, and a fixed-time target velocity estimator (FxTTVE) for dynamic obstacle velocity estimation, both enhancing performance. Our fully distributed method is theoretically proven to simultaneously achieve safety and practically fixed-time stability. Simulation and experiment results further demonstrate the effectiveness of the proposed method.