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An Orthogonal Basis Approach to Formation Shape Control (Extended Version).
Tairan Liu,Marcio de Queiroz +1 more
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In this paper, the authors propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities.Abstract:
In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled variables that form an orthogonal space and uniquely characterize a tetrahedron formation in 3D. This orthogonal space incorporates constraints on the inter-agent distances and the signed volume of tetrahedron substructures. The formation is modeled using a directed graph with a leader-follower type configuration and single-integrator dynamics. We show that the proposed decentralized formation controller ensures the \textit{global} asymptotic stability and the local exponential stability of the desired formation for an \textit{n}-agent system with no ambiguities. Unlike previous work, this result is achieved without conditions on the tetrahedrons that form the desired formation or on the control gains.read more
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Journal ArticleDOI
An orthogonal basis approach to formation shape control
Tairan Liu,Marcio de Queiroz +1 more
TL;DR: A novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities by introducing three controlled variables that form an orthogonal space and uniquely characterize a tetrahedron formation in 3D.
Journal ArticleDOI
Gradient free cooperative seeking of a moving source
TL;DR: In this article , a composite control law, blending extremum seeking with formation control, is proposed to converge to the extrema faster by minimising the gradient estimation error, and a novel analysis is provided to prove the convergence of the network to a bounded neighbourhood of the field's time varying extresma.
Journal ArticleDOI
A Virtual Point-Oriented Control for Distance-Based Directed Formation and Its Application to Small Fixed-Wing UAVs
TL;DR: In this paper , the authors proposed a new algorithm to solve the control problem for a special class of distance-based directed formations, namely directed-triangulated Laman graphs.
Journal ArticleDOI
Directed Distance-Based Formation Control of Nonlinear Heterogeneous Agents in 3-D Space
Reza Babazadeh,Rastko R. Selmic +1 more
TL;DR: In this paper , a distributed, distance-based formation control scheme for a set of heterogeneous, nonlinear agents over a particular class of minimally, structurally persistent, directed graphs in a 3D space, namely, directed trilateral Laman graphs, is proposed.
References
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A survey of multi-agent formation control
TL;DR: A survey of formation control of multi-agent systems focuses on the sensing capability and the interaction topology of agents, and categorizes the existing results into position-, displacement-, and distance-based control.
BookDOI
CRC Standard Mathematical Tables and Formulae
TL;DR: In this article, the authors present an algebraic version of elementary mathematics proofs without words, including the concept of special numbers and the notion of numbers without words in elementary algebra.
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The rigidity of graphs
L. Asimow,B. Roth +1 more
TL;DR: In this paper, the authors considered the problem of determining whether a graph G(p) is rigid in RIV with respect to the line segments of a continuous path in RI.
Journal ArticleDOI
Rigid graph control architectures for autonomous formations
TL;DR: In this paper, a theory for analyzing and creating architectures appropriate to the control of formations of autonomous vehicles is presented. The theory is based on ideas of rigid graph theory, some but not all of which are old.
Journal ArticleDOI
Stabilisation of infinitesimally rigid formations of multi-robot networks
TL;DR: It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold of the multivehicle system.
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