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Broadcast Based Control of Multi-Agent Systems for Consensus

This work addresses the problem of achieving rendezvous in a multi-agent system under various information paradigms. We consider two classes of algorithms (i) Broadcast based algorithms and (ii) Distributed control algorithms. In the first we consider both the centralized and decentralized cases. In the centralized case each agent is homogeneous and all agents are controlled by the same broadcast command from a centralized controller. This method has low communication cost. In the decentralized case each agent computes its control using the information it obtains from its neighboring agents and shares its control with its neighbours through a broadcast command. In the second case we consider each agent to implement its own control based on information gathered from its neighbours through a limited sensing capability. We show that in the distributed control algorithm, a modification in the decision domain of the agents yields significant benefits in terms of computational time, when compared with standard algorithms available in the literature. Moreover, we also show its straightforward application to higher dimensional problems which is a considerable improvement over available algorithms in the literature. Some recent work in the literature, using ideal deterministic models for mobile robots, with its model based on an actual MEMS micro-robot, has shown that it is possible to achieve point convergence in this framework for two robots and to achieve limited consensus. But perfect positional consensus cannot be obtained for larger number of robots. In the literature, an optimization problem was formulated that minimizes the maximum distance between swarm members. However, the formulation and the solution suffer from two important drawbacks. One is that the swarm members cannot achieve point convergence (or perfect consensus) even after repeated application of the strategy. They can only be brought within a certain distance of each other and no closer. The second drawback is that the optimization is rather time intensive and needs non-standard optimization techniques and software such as SOCP (second order cone programming) to obtain a solution. In our work we propose a solution for both the above drawbacks. In the case of the first drawback (that is, non-achievement of consensus) we propose a strategy that has a randomness function built into the broadcast command that will eventually help the swarm to achieve point convergence without relaxing the broadcast command paradigm of the original problem. In the second case (that is, large computation time), we will propose a LP (linear programming) based algorithm that is less computationally intensive than the SOCP based algorithm.