Proceedings ArticleDOI
Distance-Based Planar Formation Control using Orthogonal Variables
Tairan Liu,Marcio de Queiroz,Farid Sahebsara +2 more
- pp 64-69
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TLDR
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.read more
Citations
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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.
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An Orthogonal Basis Approach to Formation Shape Control (Extended Version).
Tairan Liu,Marcio de Queiroz +1 more
TL;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.
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2-D Directed Formation Control Based on Bipolar Coordinates
TL;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.
Journal ArticleDOI
2-D Directed Formation Control Based on Bipolar Coordinates
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.
References
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Journal ArticleDOI
Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence
TL;DR: This paper generalizes the notion of persistence, which has been originally introduced for two-dimensional formations, to R^d for d>=3, to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane.
Journal ArticleDOI
Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane
TL;DR: This paper proposes a decentralized control law where each agent executes its control using only the relative position measurements of agents to which it must maintain its distance, and applies center manifold theory to show local exponential stability of the desired formation shape.
Journal ArticleDOI
An almost global notion of input-to-State stability
TL;DR: A new definition of almost global input-to-state stability for systems on differentiable manifolds is discussed and specific examples are shown which can be treated by means of dual Lyapunov techniques.
Notes on the Rigidity of Graphs
TL;DR: The first reference to the rigidity of frameworks in the mathematical literature occurs in a problem posed by Euler in 1776, see [8] and as discussed by the authors, where a polyhedron P in 3-space is viewed as a 2-dimensional panel-and-hinge framework and the edges are 1-dimensional hinges, subject to the constraints that the shapes of the panels and the adjacencies between pairs of panels are preserved.
Journal ArticleDOI
Formation shape control with distance and area constraints
Brian D. O. Anderson,Brian D. O. Anderson,Zhiyong Sun,Toshiharu Sugie,Shun-ichi Azuma,Kazunori Sakurama +5 more
TL;DR: A formation control problem in which a target formation is defined with both distance and signed area constraints, to drive spatially distributed agents to reach a unique target rigid formation shape with desired inter-agent distances is discussed.
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