New problems of optimal path coordination for multi-vehicle systems

New problems of optimal path coordination for multiple vehicles are introduced, formulated and solved in the framework of dynamic optimization. The novelty of these problems arises in several ways. The cost function and the dynamics include non-trivial dependencies, modeled through existential quantification over groups of vehicles - this leads to non-Lipschitz behavior and to non-standard optimal control problems. There are consumable resources, modeled with the help of integral constraints - the structure of the constraints suggested new strategies for optimal cooperation which outperform the results obtained with standard formulations with state-constraints. Our formulation uses the structure of the problem to decouple the overall optimization into simpler coupled problems in lower-dimensional spaces. This is expressed in the form of the solution, which is encoded as the composition of value functions in lower-dimensional spaces.