Minimum order bang-bang guidance for feedforward obstacle avoidance steering maneuvers of vehicles

In this paper, a new methodology is presented for computing time-optimal obstacle avoidance maneuvers for ground vehicles. Usually, the problem of obstacle avoidance is addressed in two parts. In the first part a path is planned. In the second an appropriately designed vehicle controller tracks the desired path. In view of the fact that the main problem concerning emergency maneuvers remains the development of an optimal control for minimum time and maximum maneuverability — with respect to the slip risk due to saturation of the tire forces — the authors propose an alternative approach. Considering that the time optimal control according to Pontryagin’s Maximum Principle (PMP) is of bang-bang type the investigations concern the minimum order and magnitude bang-bang control for “feedforward” steering maneuvers with the target of minimizing the computation time and simplifying the algorithm. This is accomplished by keeping the basic PMP logic but transforming the computational algorithm from an exact to a least squares control problem. Furthermore, the paper addresses how to solve the problem of guiding the vehicle from a non rest to a rest position. Simulations of obstacle avoidance maneuvers illustrate the performance of the controller.