Collision avoidance and trajectory tracking control based on approximations of the maximum function

In this paper, convergent over approximations of the maximum function (previously introduced and used for designing strategies for multiple players in pursuit-evasion games) are used to accomplish two objectives for multiple vehicles scenarios: collision avoidance and trajectory tracking. The fact that these approximations are upper approximations of the maximum functions allows us to establish guarantees on the performance (in terms of achieving the objectives) of the vehicles. We combine the approximations of the maximum function with the receding horizon control approach to design control laws. Finally, the method is illustrated by a representative example, where the control laws are designed for nonholonomic vehicles with actuator constraints.