Journal ArticleDOI
Stabilisation of infinitesimally rigid formations of multi-robot networks
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It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold of the multivehicle system.Abstract:
This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.read more
Citations
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Journal ArticleDOI
Formation stability analysis of unmanned multi-vehicles under interconnection topologies
TL;DR: It is proved that the overall formation control system consisting of N number of nonlinear vehicles is not only asymptotically stable, but also exponentially stable in the sense of Lyapunov within a neighbourhood of the desired formation.
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Taming inter-distance mismatches in formation-motion control for rigid formations of second-order agents
TL;DR: This paper presents an analysis on the influence of distance mismatches in the standard gradient-based rigid formation control for second-order agents and shows how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.
Journal ArticleDOI
Symbol functions for symmetric frameworks
TL;DR: In this paper, it was shown that intertwiners for the bilateral shift on l 2 (Z ) are unitarily equivalent to multiplication operators on L 2 (T ) for bar-joint frameworks with an abelian symmetry group.
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Formation Control with Triangulated Laman Graphs
TL;DR: In this paper, the authors propose a partial solution to this problem by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations, and they show how to design a decentralized control law whose stable equilibrium are all target configurations in the case of a general rigid graph.
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Cooperative Manipulation via Internal Force Regulation: A Rigidity Theory Perspective.
TL;DR: This paper introduces the notion of bearing and distance rigidity for graph frameworks in SE(3) and shows that the associated cooperative manipulation grasp matrix is related to the rigidity matrix via a range-nullspace relation, based on which novel results are provided on the relation between the arising interaction and internal forces and consequently on the energy-optimal force distribution on a cooperative manipulation system.
References
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Coverage control for mobile sensing networks
TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.