8 research outputs found
A Class of Minimal Generically Universally Rigid Frameworks
Following a review of related results in rigidity theory, we provide a
construction to obtain generically universally rigid frameworks with the
minimum number of edges, for any given set of n nodes in two or three
dimensions. When a set of edge-lengths is compatible with only one
configuration in d-dimensions, the framework is globally rigid. When that
configuration is unique even if embedded in a higher dimensional space, the
framework is universally rigid. In case of generic configurations, where the
nodal coordinates are algebraically independent, the minimum number of edges
required is equal to dn-d(d+1)/2+1, that is, 2n-2 for d=2, and 3n-5 for d=3.
Our contribution is a specific construction for this case by introducing a
class of frameworks generalizing that of Gr\"{u}nbaum polygons. The
construction applies also to nongeneric configurations, although in this case
the number of edges is not necessarily the minimum. One straightforward
application is the design of wireless sensor networks or multi-agent systems
with the minimum number of communication links.Comment: 8 page
Multiagent LQR-based Control Design and Gain tuning for Quadcopters Fleet
An LQR-based Control design and gain tuning strategies proposals for a multi-agent system are presented in this article, the agents are connected in an undirected graph. Controller gains tuning are adjusted by selecting the Q and R weighting matrices of the Linear Quadratic Regulator. Agreement (consensus) is one of the fundamental problems in multi-agent control, where a set of agents must agree on a joint state value. In the proposed design, first considering that the behavior of the agreement protocol is undirected and static, the main objective is to highlight the complexity of the relationship between the convergence properties of this protocol and the structure of adjacent interconnections. The effects on the formation due to static geometry are analyzed from the resulting data according to the proximity between the agents, where behavior and stability are analyzed based on the desired formation geometry through the construction of the Laplacian matrix
Multi-agent Path Planning and Network Flow
This paper connects multi-agent path planning on graphs (roadmaps) to network
flow problems, showing that the former can be reduced to the latter, therefore
enabling the application of combinatorial network flow algorithms, as well as
general linear program techniques, to multi-agent path planning problems on
graphs. Exploiting this connection, we show that when the goals are permutation
invariant, the problem always has a feasible solution path set with a longest
finish time of no more than steps, in which is the number of
agents and is the number of vertices of the underlying graph. We then give
a complete algorithm that finds such a solution in time, with
being the number of edges of the graph. Taking a further step, we study time
and distance optimality of the feasible solutions, show that they have a
pairwise Pareto optimal structure, and again provide efficient algorithms for
optimizing two of these practical objectives.Comment: Corrected an inaccuracy on time optimal solution for average arrival
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Automatic Generation of Persistent Formations for Multi-Agent Networks Under Range Constraints
© Springer Science + Business Media, LLC 2009DOI: 10.1007/s11036-009-0153-xIn this paper we present a collection of graphbased methods for determining if a team of mobile robots, subjected to sensor and communication range constraints, can persistently achieve a specified formation. What we mean by this is that the formation, once achieved, will be preserved by the direct maintenance of the smallest subset of all possible pairwise interagent distances. In this context, formations are defined by sets of points separated by distances corresponding to desired inter-agent distances. Further, we provide graph operations to describe agent interactions that implement a given formation, as well as an algorithm that, given a persistent formation, automatically generates a sequence of such operations. Experimental results are presented that illustrate the operation of the proposed methods on real robot platforms