The Multi-Agent Rendezvous Problem. An Extended Summary

Stability of leaderless discrete-time multi-agent systems

“…Problems of this nature arise in many different fields such as in the theory of coupled oscillators [7,12,17,22], in neural networks [10], in economics or in the maneuvring of groups of vehicles [1,6,14,23]. For instance in [15,16], the so-called rendezvous problem is considered, namely how to design a local updating rule, based on nearest neighbor interactions, which would ensure convergence of all of the agents to an unspecified common meeting point. Emergence of a global behavior is therefore a consequence of the local updating rule, without the need for a leader nor of centralized directions being broadcasted.…”

Randomized consensus algorithms over large scale networks

“…, N } and a measure x i for every node i ∈ V . The average consensus problem consists in computing the average x A = N −1 i x i in an iterative distributed way, exchanging information among nodes exclusively along the available edges in G. This problem appears in a number of different contexts since the early 80's (decentralized computation [1], load balancing [2], [3], [4]) and, recently, has attracted much attention for possible applications to sensor networks (data fusion problems [5], [6], [7], [8], [9], clock syncronization [10]) and to coordinated control for mobile autonomous agents [11], [12], [13], [14], [15], [16], [17]. Other places where consensus algorithms have been studied in general are [18], [19], [20], [21], [22], [23] Several algorithms for average consensus can be found in the literature: they differentiate on the basis of the amount of communication and computation they use, on their scalability with respect to the number of nodes, on their adaptability to time-varying graphs, and, finally, they can be deterministic or random.…”

Multirobot Rendezvous With Visibility Sensors in Nonconvex Environments

“…As a consequence, it follows from Corollary IV. 6(ii) that the connected components of G r-vis, Qǫ are also preserved at the next time instant. Thus, we have found constraint sets (5) for the input that are larger than the constraint sets (4), and are yet sufficient to preserve the connectivity of the overall group.…”

“…In addition to the issues that might arise in a practical implementation of the Perimeter Minimizing Algorithm, 6 For each connected component of Gsens, the graph having nodes as the robot locations and with an edge between two nodes whenever the corresponding motion discs of the robots intersect is connected another important consideration is the time taken for a robot to complete each step of the algorithm. This is dependent on the computational complexity of the algorithm, that we characterize in the following.…”