A Game-theoretic Approach to Cooperative Robust Nonlinear Model Predictive Control for a Network of Unmanned Ground Vehicles

We propose a Pontryagin-based cooperative Robust Nonlinear Model Predictive Control (RNMPC) approach for the formation control of a network of Unmanned Ground Vehicles (UGVs). In the proposed scenario the UGV dynamics incorporates exogenous disturbances to capture real-world uncertainties, making the control problem nontrivial. The RNMPC foresees the solution of a min-max optimal control problem, where the goal is to optimize the control input to be delivered to the single UGV in the worst-case scenario. To this end, the Pontryagin-based min-max problem can be viewed as a zero-sum differential game, where the two players are the control input and the uncertainty whose solution is the Nash equilibrium. Additionally, collision avoidance for UGV is enforced through the implementation of artificial potential fields. The effectiveness and robustness of the proposed control technique have been assessed by means of numerical simulations.