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

Abstract

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.

Minimum vehicle slip path planning for automated driving using a direct element method

“…A uniform element decomposition is chosen. The desired lateral displacement Y of the vehicle is shown in Figure 4(a), and the computed steering input d (equations (23) to (27)) in Figure 4(b). The responses of the yaw rate rate r and the lateral velocity v using the direct element method, and their comparison with the numerical results obtained when integrating the vehicle equations (the integration method) (equations ( 1) and ( 2)), are shown in Figure 5.…”

“…A third variant of the first category is the optimal control framework. 22,23 In this framework, the trajectories are computed as the solution to an optimisation problem that seeks to minimise the manoeuvring time. Optimal control solutions for typical driving scenarios using tyre and chassis models of different complexities have been studied, and the results were extensively analysed and discussed.…”

A collision-avoidance system for an electric vehicle: a drive-by-wire technology initiative

“…The control design from the caution distance to the halt distance is derived from of the assessment by [17] that a vehicle's anti-collision system should apply the brake at minimum speeds (less than 50 km/h), while the steering can be applied at maximum speeds. In addition, [4] asserted that vehicles could efficiently apply automatic brakes to a deceleration limit of 0.4 g.…”

Virtual tyre force sensors: An overview of tyre model-based and tyre model-less state estimation techniques

“…This expression can be solved using a first-order discrete approximation to obtain the orientation angles of I b with respect to I 0 . 72 Nevertheless, this absolute angle cannot be used directly in expressions (55) and (56) as they include the sprung mass rotations in addition to the road-fixed frame orientation angles. A rigorous approach demands the computation of the inverse rotation matrix between the frames I b and I r .…”

“…32 Nevertheless, if the lateral velocity is treated as a system state, and therefore its estimation is necessary (e.g. for ESP action), the road bank angle must be introduced in the lateral dynamics equation (56). Finally, apart from the gravity compensation, road bank angle estimation is important for roll stability control systems (RSC).…”