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Dynamic optimization for path coordination problems

Abstract A problem of optimal path coordination for two vehicles is presented. The path cost for the first vehicle is a discontinuous function of the relative positions of the two vehicles. The second vehicle is required to return its starting point. The problem is formulated in the framework of hybrid systems to model both the discontinuous dependence of the cost function on the state variable and the operating rules. The structure of the solution is outlined in the framework of dynamic optimization. The value of cooperation is given by a value function.