Abstract
We propose a novel framework, which, under a certain geometric condition, enables us to decompose the second-order Lagrangian dynamics of the multiple nonholonomic mechanical systems into two decoupled systems according to the two most fundamental aspects of the group behaviour: shape system describing the formation aspect (i.e. group's internal shape); and locked system abstracting the maneuver aspect (i.e. group's overall motion). By controlling these decoupled locked and shape systems individually, we can then control the formation and maneuver aspects separately without any crosstalk between them. Moreover, the framework enables us to do this while respecting/utilizing the Lagrangian structure/passivity of the system's open-loop dynamics. Due to this property, we call this framework nonholonomic passive decomposition. A control design example with numerical simulation is also given to highlight some properties of the proposed framework.
Published Version
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