Addressing agent loss in vehicle formations and sensor networks

IEEE Conference on Decision and Control and European Control Conference

2011

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Abstract-In this paper we study the robustness of information architectures to control a formation of autonomous agents. If agents are expected to work in hazardous environments like battle-fields, the formations are prone to multiple agent/link loss. Due to the higher severity of agent loss than link loss, the main contribution of this paper is to propose information architectures for shape-controlled multi-agent formations, which are robust against the loss of multiple agents. A formation is said to be rigid if by actively maintaining a designated set of inter-agent distances, the formation preserves its shape. We will use the rigidity theory to formalize the robust architecture problem. In particular we study the properties of formation graphs which remain rigid after the loss of any set of up to k − 1 vertices. Such a graph is called k-vertex rigid. We provide a set of distinct necessary and sufficient conditions for these graphs. We then show that 3-vertex rigidity is the highest possible robustness one can achieve by just adding a small number of edges to a minimally rigid graph, i.e. retention of rigidity given the loss of 3 or more agents of a formation requires many more inter-agent distances to be specified than when maintaining rigidity with no, one or two agent losses. Based on this result, we further focus on 3-vertex rigid graphs and characterize a class of information architectures (with minimum number of control links) which are robust against the loss of up to two agents.

Section: B Redundant Rigiditymentioning

confidence: 99%

Section: Growing Strongly Minimal 3-vertex Rigid Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multi-agent rigid formations: A study of robustness to the loss of multiple agents

Motevallian

IEEE Conference on Decision and Control and European Control Conference

2011

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Closing ranks in rigid multi-agent formations using edge contraction

Fi̇dan

Hendrickx

Int. J. Robust Nonlinear Control

2010

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SUMMARYThis paper proposes a systematic approach to solve the closing rank problem for a rigid multi-agent formation, viz. restoring rigidity after loss of an agent. The approach is based on a particular graph operation, the edge contraction operation. It is proven that when an agent is lost in an arbitrary two-dimensional rigid formation, rigidity can always be restored by transferring all links to which this agent was incident on to one of its neighbors, though not in general any arbitrary one of them. From a graph theoretical point of view, this corresponds to contraction of a certain edge incident to the vertex representing the agent being lost. It is established, for any two-dimensional rigid formation (graph), that there exists at least two such edges that can be contracted to solve the closing ranks problem. Later, it is demonstrated that any potential decentralized algorithm to check if an arbitrary edge is contractible would need to use information on vertices and edges that can be at arbitrarily large distance from the edge considered; and a set of rigid graph theoretical results are established for several general settings, which can be used in selection of the edge to contract in these settings in order to solve the corresponding closing ranks problems. Partial results are also obtained for three-dimensional formations, and it is shown that the two-dimensional results do not generalize as such to higher dimension.

On the robustness to multiple agent losses in 2D and 3D formations

Motevallian

Int. J. Robust Nonlinear Control

2014

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Multi-agent formations have been recently the subject of many studies. An important operational challenge, largely unaddressed in the literature, is to ensure that functionality of the formation is retained should agents be lost through misadventure, mission reassignment, and so on. In the context of sensor networks, it is also important to allow for the loss of multiple sensors as the low quality of sensor hardware, common unattended implementations, and so on makes it a common issue. In this paper, we address these issues by proposing information structures that are tolerant to the loss of multiple agents. Using graph theory (and more specifically rigidity theory), we characterize several properties of such formations/networks in a unified framework: We characterize the k-vertex rigidity property of the underling graph of such formations. This is performed by deriving a set of useful conditions that can form a guideline for designing agent-losstolerant formations. We elaborate the study by characterizing robust formations with the optimal number of control links. We also propose a set of operations preserving the tolerance to multiple agent losses in such formations. These operations provide flexibility in designing the formations in terms of several designing parameters (e.g., geometry, diameter, and max degree). Especially in the case of formations, the ability to handle controller adjustments in a distributed way is important, and the paper addresses this issue for a number of the robustness problems considered. MULTIPLE AGENT LOSSES IN 2D AND 3D FORMATIONS1655 of agents to a desired formation shape. Their proposed method assumes that the control links are bidirectional, that is, both agents at the ends of a link cooperate with each other to maintain the desired length of that link. This work is extended in [2] where the authors studied the global stability of such formations. In [8], the authors studied the conditions required for designing directional control laws (from each pair of agents, at most one of them maintains the distance).It is emphasized in [9] that the rigidity of the formation is a key prerequisite property in finding the shape variables of the formation and an appropriate potential function. In [7], the authors proposed a time-varying control law that can maintain the rigidity of the formation. The main drawback of this technique though is that it requires centralized information to generate the controller input.The common assumption in most of aforementioned distributed control techniques is the rigidity of the formation. Although the proposed control laws are distributed and can be efficiently implemented in practice, rigidity itself is a global property of the formation, that is, it is impossible to decide using only the local information whether the whole formation is rigid or not. Therefore, the information structure of the formation must be designed globally prior to the formation operation. Considering this, the approaches to the FSC problem can be categorized into two levels: a. In ...