| 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). Stimulated by the growing interest in biomimicry of the mechanisms of foraging and swarming for use in engineering applications, this dissertation focuses on mathematical modeling and analysis of stability properties of swarms.; A high-level view of a swarm suggests that the organisms are cooperating to achieve some purposeful behavior and achieve some goal. Stability is a basic qualitative property of a swarm since if it is not present, then it may be impossible for the swarm to achieve any other group objective. Stability analysis of swarms is still an open problem but there have been several areas of relevant progress. In this dissertation, we characterize swarm “cohesiveness” as a stability property and provide conditions under which collision-free convergence can be achieved for an asynchronous swarm 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 asynchronous mobile swarm following (or pushed by) an “edge-leader” can maintain cohesion during movements even in the presence of sensing delays and asynchronism. We start by studying one-dimensional asynchronous swarms. Then, swarm stability for the M ≥ 2 dimensional case with a fixed communication topology is investigated, where we assume there exists a fixed communication topology among swarm members and each member only communicates with fixed neighbors via the topology. The movement flexibility of mobile swarms is also analyzed. Simulation studies are provided to illustrate swarm convergence properties.; Such stability analysis is of fundamental importance if one wants to understand the coordination mechanisms for groups of autonomous vehicles or robots where inter-member communication channels are less than perfect and collisions must be avoided. |
