Tensegrity Models and Shape Control of Vehicle Formations

Benjamin Nabet and Naomi Ehrich Leonard

arXiv:0902.3710v1 [math.OC], 2009.
Using dynamic models of tensegrity structures, we derive provable, distributed control laws for stabilizing and changing the shape of a formation of vehicles in the plane. Tensegrity models define the desired, controlled, multi-vehicle system dynamics, where each node in the tensegrity structure maps to a vehicle and each interconnecting strut or cable in the structure maps to a virtual interconnection between vehicles. Our method provides a smooth map from any desired planar formation shape to a planar tensegrity structure. The stabilizing vehicle formation shape control laws are then given by the forces between nodes in the corresponding tensegrity model. The smooth map makes possible provably well behaved changes of formation shape over a prescribed time interval. A designed path in shape space is mapped to a path in the parametrized space of tensegrity structures and the vehicle formation tracks this path with forces derived from the time-varying tensegrity model. By means of examples, we illustrate the influence of design parameters on performance measures.

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