Control of a three-coleader formation in the plane

Anderson, Brian D. O.; Yu, Changbin; Dasgupta, Soura; Morse, A. Stephen

doi:10.1016/j.sysconle.2007.04.004

Cited by 146 publications

(134 citation statements)

References 8 publications

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“…negatively-oriented} triangular formation and then come to rest. This finding extend the findings of [2] and [3] and provides a different perspective. In fact, the results of [2] are very similar to those in this paper; the essential differences between the two papers lie in the controls considered, the analytical methods used to analyze them, and the degrees of completeness of the proofs given [4].…”

Section: Introductionsupporting

confidence: 90%

“…In fact, the results of [2] are very similar to those in this paper; the essential differences between the two papers lie in the controls considered, the analytical methods used to analyze them, and the degrees of completeness of the proofs given [4]. We refer the reader to [2] and [3] for additional background and references on controlling triangular formations. See also the recent thesis by Krick [5] which deals with the more general question of formation control via rigidity.…”

Section: Introductionsupporting

confidence: 58%

“…The former addresses a slightly different problem and uses a control law similar to that proposed in [3]. In this paper we address the same problem using control laws of a more gradient-like nature which lend themselves to a simpler and perhaps crisper analysis than do those considered in [2] and [3]. Using straightforward arguments we prove that unique solutions to the systems of nonlinear differential equations involved exist globally.…”

Section: Introductionmentioning

confidence: 93%

“…Prompted by this, we consider the problem of maintaining a directed formation of three agents in a triangle by having each agent locally control its own position so that the distance to its co-leader {or next agent in the triangle} is constant. This particular problem has also recently been addressed in [2] and [3]. The latter considers intuitively devised local control laws which cause each agent to move in the direction of their respective co-leaders.…”

Section: Introductionmentioning

confidence: 99%

“…The latter considers intuitively devised local control laws which cause each agent to move in the direction of their respective co-leaders. The former addresses a slightly different problem and uses a control law similar to that proposed in [3]. In this paper we address the same problem using control laws of a more gradient-like nature which lend themselves to a simpler and perhaps crisper analysis than do those considered in [2] and [3].…”

Section: Introductionmentioning

confidence: 99%

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Controlling a triangular formation of mobile autonomous agents

Cao

Morse

et al. 2007

2007 46th IEEE Conference on Decision and Control

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Abstract-This paper proposes a distributed control law for maintaining a triangular formation in the plane consisting of three mobile autonomous agents. It is shown that the control law can cause any initially non-collinear, positively-oriented {resp. negatively-oriented} triangular formation to converge exponentially fast to a desired positively-oriented {resp. negativelyoriented} triangular formation. It is also shown that there is a thin set of initially collinear formations which remain collinear and may drift off to infinity as t → ∞. These findings complement and extend earlier findings cited below.

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Section: Introductionsupporting

confidence: 90%

Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controlling a triangular formation of mobile autonomous agents

Cao

Morse

et al. 2007

2007 46th IEEE Conference on Decision and Control

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A backstepping design for directed formation control of three‐coleader agents in the plane

Chen

Tian

2008

Intl J Robust & Nonlinear

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SUMMARYThis paper deals with a directed formation control problem of three agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbor, and each agent is described by a double integrator. Firstly, a directed formation control law based on the knowledge only of the neighbor's direction is designed by using the integrator backstepping technique, which can not only accomplish the desired triangle formation but also ensure that speeds of all agents converge to a common value without collision between each other during the motion. Then, with the purpose of relaxing and even overcoming the restriction of initial conditions of the agents owing to collision avoidance, we introduce the inter-agent potential functions into the design. The convergence of the proposed control algorithms is proved by using tools from LaSalle's invariance principle. Simulation results are provided to illustrate the effectiveness of the control laws.

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Addressing agent loss in vehicle formations and sensor networks

Summers

Anderson

2008

Intl J Robust & Nonlinear

Self Cite

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SUMMARYIn this paper, we address the problem of agent loss in vehicle formations and sensor networks via two separate approaches: (1) perform a 'self-repair' operation in the event of agent loss to recover desirable information architecture properties or (2) introduce robustness into the information architecture a priori such that agent loss does not destroy desirable properties. We model the information architecture as a graph G(V, E), where V is a set of vertices representing the agents and E is a set of edges representing information flow amongst the agents. We focus on two properties of the graph called rigidity and global rigidity, which are required for formation shape maintenance and sensor network self-localization, respectively. For the self-repair approach, we show that while previous results permit local repair involving only neighbours of the lost agent, the repair cannot always be implemented using only local information. We present new results that can be applied to make the local repair using only local information. We describe implementation and illustrate with algorithms and examples. For the robustness approach, we investigate the structure of graphs with the property that rigidity or global rigidity is preserved after removing any single vertex (we call the property as 2-vertex-rigidity or 2-vertex-global-rigidity, respectively). Information architectures with such properties would allow formation shape maintenance or self-localization to be performed even in the event of agent failure. We review a characterization of a class of 2-vertex-rigidity and develop a separate class, making significant strides towards a complete characterization. We also present a characterization of a class of 2-vertex-global-rigidity.

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Control of a three-coleader formation in the plane

Cited by 146 publications

References 8 publications

Controlling a triangular formation of mobile autonomous agents

Controlling a triangular formation of mobile autonomous agents

A backstepping design for directed formation control of three‐coleader agents in the plane

Addressing agent loss in vehicle formations and sensor networks

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