A new min-max methodology for computing optimised obstacle avoidance steering manoeuvres of ground vehicles

In this paper, a new methodology for computing optimised obstacle avoidance steering manoeuvres for ground vehicles is presented and discussed. Most of the existing methods formulate the obstacle avoidance problem as an optimal control problem which is hard to solve or as a numerical optimisation problem with a large number of unknowns. This method is based on a reformulation of Pontryagin's Maximum Principle and leads to the solution of an adjustable time optimal controller. The control input is significantly simplified and permits its application in a sample and hold sense. Furthermore, with the proposed approach the maximum tyre forces exerted during the manoeuvre are minimised. In this study, it is shown how to warm start the proposed algorithm and which constraints to relax. Numerical examples and benchmark tests illustrate the performance of the proposed controller and compare it with other standard controllers. A sensitivity analysis for different vehicle parameters is performed and finally conclusions are drawn. A significant advantage of the method is the small computational complexity. The overall simplicity of the controller makes it attractive for application on autonomous vehicles.