Distance-Based Planar Formation Control using Orthogonal Variables
01 Aug 2020-pp 64-69
TL;DR: A novel approach to the problem of augmenting distance-based formation controllers with a secondary feedback variable for the purpose of preventing formation ambiguities is proposed, introducing two variables that form an orthogonal space and uniquely characterize a triangular formation in two dimensions.
Abstract: In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary feedback variable for the purpose of preventing formation ambiguities. We introduce two variables that form an orthogonal space and uniquely characterize a triangular formation in two dimensions. We show that the resulting controller ensures the almost-global asymptotic stability of the desired formation for an $n$ -agent system without conditions on the triangulations of the desired formation or control gains.
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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.
7 citations
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05 Dec 2020TL;DR: 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.
4 citations
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02 Aug 2021TL;DR: In this article, a 2D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyCLic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape is proposed.
Abstract: This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in the agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, various simulation studies clarify and verify the proposed approach.
TL;DR: In this paper , a 2D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyCLic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape is proposed.
Abstract: This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.
References
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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.
1,751 citations
"Distance-Based Planar Formation Con..." refers methods in this paper
...This method, which is commonly referred to as distance-based formation control [3], has the main advantage of being implementable in a fully decentralized manner....
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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.
Abstract: We regard a graph G as a set { 1,...,v) together with a nonempty set E of two-element subsets of (1, . . ., v). Letp = (Pi, . . . &) be an element of RIv representing v points in RI. Consider the figure G(p) in RI consisting of the line segments [pi, pj in RI for {i,j) E E. The figure G (p) is said to be rigid in RI if every continuous path in RI', beginning atp and preserving the edge lengths of G(p), terminates at a point q E RIV which is the image (Tp1, . . ., Tpv) of p under an isometry T of RW. Otherwise, G (p) is flexible in RW. Our main result establishes a formula for determining whether G (p) is rigid in RI for almost all locations p of the vertices. Applications of the formula are made to complete graphs, planar graphs, convex polyhedra in R3, and other related matters.
566 citations
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.
Abstract: This article sets out the rudiments of a theory for analyzing and creating architectures appropriate to the control of formations of autonomous vehicles. The theory rests on ideas of rigid graph theory, some but not all of which are old. The theory, however, has some gaps in it, and their elimination would help in applications. Some of the gaps in the relevant graph theory are as follows. First, there is as yet no analogue for three-dimensional graphs of Laman's theorem, which provides a combinatorial criterion for rigidity in two-dimensional graphs. Second, for three-dimensional graphs there is no analogue of the two-dimensional Henneberg construction for growing or deconstructing minimally rigid graphs although there are conjectures. Third, global rigidity can easily be characterized for two-dimensional graphs, but not for three-dimensional graphs.
554 citations
"Distance-Based Planar Formation Con..." refers background in this paper
...If rigid frameworks (G, p) and (G, p̂) are equivalent but not congruent, they are flip- or flex-ambiguous [13]....
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...A rigid framework is minimally rigid if and only if |E| = 2N − 3 [13]....
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TL;DR: 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.
511 citations
"Distance-Based Planar Formation Con..." refers methods in this paper
...A well-known method for solving this problem involves regulating a set of inter-agent distances to values prescribed by the desired shape [1], [2]....
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TL;DR: In this article, a graph G is viewed as a set {1,…, v} together with a nonempty set E of two-element subsets of { 1,.., v}.
319 citations