A Hamilton-Jacobi Formulation for Cooperative Control of Multi-Agent Systems

Coordination of autonomous non-point agents is studied in this work. Interactions between vehicles together with their internal dynamics have been modeled as a continuous, unconstrained differential game. In particular, collision prediction is shown to be achievable in a cooperative scheme through solving the boundary value equation associated with the dual problem. Optimal control formulation has been further applied in order to solve the coordination problem while coping with both time constraints and energy aspects of the system. The developed control scheme is further contrasted with the traditional negated gradient laws, which on the other hand can be shown to correspond to Nash Equilibria of non-cooperative strategies, in terms of its complexity and resultant trajectories. Furthermore, state feedback formation control is combined with the proposed cooperative scheme to alleviate its computational concerns. In addition, conflict-free navigation and convergence properties of the proposed scheme are verified in simulation.