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Formations of Mobile Agents with Message Loss and Delay



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Formations of Mobile agents with Messages Loss and Delay Concetta Pilotto Sayan Mitra K Mani Chandy California Institute of Technology SOCAL Workshop 2008 1 Research Goal Encompassing theory Distributed Control Distributed Computing Synchronous steps Instantaneous communication Generally deterministic Arbitrary delay for channels and processors Generally non deterministic x j t c California Institute of Technology x k xj k SOCAL Workshop 2008 2 Main Contributions Use of Temporal Logic to prove convergence in continuous time systems Class of Problems Pattern formation Agents move in Euclidean space Smaller and smaller adjustments to the position but never terminate Communication model Asynchronous message passing with loss reordering and delay California Institute of Technology SOCAL Workshop 2008 3 Formations of Spatial Patters Distributed Control Robots are deployed over some area Apply very simple local protocol to update their positions synchronously Goal Converge to a target global configuration Proofs of convergence using eigen values of the transition matrix California Institute of Technology SOCAL Workshop 2008 4 Line up Pattern Formation N 1 agents with unique indices in 0 N and common coordinate system Ideal position predicate Equidistance on a straight line x0 x N i 1 K N 1 xi 0 California Institute of Technology 1 x0 2 N i i xN N N 3 4 SOCAL Workshop 2008 5 5 Line up Synchronous Protocol Starting from any initial configuration Applying infinitely often if i 0 x0 xi 1 t xi 1 t xi t 1 if 0 i N 2 if i N x N 0 1 2 3 4 t 1 t t 1 Agents converge to the ideal positions equidistance points on the line between x0 and xN California Institute of Technology SOCAL Workshop 2008 6 Line up Protocol Simulation California Institute of Technology SOCAL Workshop 2008 7 Deviation of Agents Distance between the agent s current location from its ideal location Current 2 Ideal California Institute of Technology 0 4 0 1 1 2 5 3 SOCAL Workshop 2008 4 3 5 8 Deviation Simulation



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