Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology

Coordinated dynamical swarm behavior occurs when certain types of animals forage for food or try to avoid predators. Analogous behaviors can occur in engineering, systems (e.g., in groups of autonomous mobile robots or air vehicles). In this paper, we study a model of an M-dimensional (M greater than or equal to 2) asynchronous swarm with a fixed communication topology, where each member only communicate with fixed neighbors, to provide conditions under which collision-free convergence can be achieved with finite-size swarm members that have proximity sensors, and neighbor position sensors that only provide delayed position information. Moreover, we give conditions under which an M-dimensional asynchronous mobile swarm with a fixed communication topology following an "edge-leader" can maintain cohesion during movements even in the presence of sensing delays and asynchronism. In addition, the swarm movement flexibility is analyzed. Such stability analysis is of fundamental importance if one wants to understand the coordination mechanisms for groups of autonomous vehicles or robots, where intermember communication channels are less than perfect and collisions must be avoided.