Time-Scaled Coordination and Diffeomorphic Mapping for Fixed-Position Convergence in Smart Transportation Systems

This paper presents a novel distributed coordination framework for multi-agent robotic swarms tailored for smart transportation applications. The proposed approach addresses the critical pre-transportation phase where a fleet of mobile robots, eventually with different sizes, must converge to fixed positions around an object to ensure effective caging within a user-defined prescribed time. By leveraging a time-varying diffeomorphic mapping based on an affine transformation, the strategy embeds prescribed-time guarantees within a swarm-inspired framework that maps agents between virtual and real reference frames. This methodology ensures the simultaneous achievement of precise target convergence, finite-time stability regardless of initial conditions, and inherent collision avoidance by explicitly considering the physical footprint of each robotic unit. The control protocol is first derived for scalar systems and subsequently extended to multidimensional robotic fleets using additional diffeomorphism-based techniques, which allow for the management of multiple non-interacting swarms to reduce network communication overhead.