Passive decomposition of multiple mechanical systems under coordination requirements

We propose a general control framework for multiple mechanical systems interacting with environments and/or humans under coordination requirements. The key innovation is the passive decomposition which enables us to achieve the two requirements of such systems simultaneously: motion coordination and energetic passivity of the closed-loop system. It decomposes the system dynamics into shape system addressing the coordination aspect, locked system representing overall dynamics of the coordinated system, and dynamic couplings between the locked and shape systems. The dynamic couplings can be cancelled out without violating passivity. Thus, the coordination aspect (shape system) and the dynamics of the coordinated system (locked system) can be decoupled from each other while enforcing passivity. Also, by designing the locked and shape controls to enforce passivity of their respective systems, passivity of the closed-loop system is guaranteed. We analyze and exhibit geometry of the passive decomposition and the locked and shape systems.