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

Abstract

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 ...

Minimum Size Highly Redundantly Rigid Graphs in the Plane

“…graph on n vertices is equal to 2n À 2 (2n, 5n 2 , resp.). Again, the first bound is easy, the other two can be found in [11,16]. These results are valid for n large enough (compared to k).…”

“…The special case k ¼ 3 of Theorem 8 was proved earlier by Motevallian, Yu and Anderson [11], who showed that L 2 n is 3-vertex globally rigid. Our proof method gives a more general statement by showing that it is in fact 4-vertex rigid.…”

Optimization of communication topology for persistent formation in case of communication faults

“…When a communication fault prevents the current communication topology from being used to maintain the formation shape, if the communication topology is not adjusted in time, this communication fault may lead to collision accidents between agents. [25] Therefore, after a communication fault occurs, the communication topology must be quickly reconstructed to ensure the safety of the agents and restore the formation shape. After the communication topology reconstruction, the security of the persistent formation is ensured.…”

“…These communication faults may cause some communication links in the current communication topology to no longer be usable or some agents to withdraw from the formation. [25] As a result, the formation shape cannot be maintained, and agent collisions may even occur in serious cases. Therefore, it is necessary to optimize the communication topology after such communication faults to ensure the safety of all agents and continue to maintain the formation shape while reducing the formation communication cost as much as possible.…”

Adaptation Strategy for a Distributed Autonomous UAV Formation in Case of Aircraft Loss

“…Paper [6] proposes a novel approach that relies on a Negative Imaginary (NI) theory-based control algorithm that keeps a decentralized system of single integrators stable when several agents are lost. Work [7] covers an agent loss-tolerant multiagent system. One of the approaches covered therein consists in adding redundant links to make the group robust to agent loss.…”