A passive decomposition framework for the formation and maneuver controls for multiple rigid bodies is proposed. In this approach, the group dynamics of the multiple agents is decomposed into two decoupled systems: The shape system representing internal group formation shape (formation, in short), and the locked system abstracting the overall group maneuver as a whole (maneuver, in short). The decomposition is natural in that the shape and locked systems have dynamics similar to the mechanical systems, and the total energy is preserved. The shape and locked system can be decoupled without the use of net energy. The decoupled shape and locked systems can be controlled individually to achieve the desired formation and maneuver tasks. Since all agents are given equal status, the proposed scheme enforces a group coherence among the agents. By abstracting a group maneuver by its locked system whose dynamics is similar to that of a single agent, a hierarchical control structure for the multiple agents can be easily imposed in the proposed framework. A decentralized version of the controller is also proposed, which requires only undirected line communication (or sensing) graph topology.
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