Formulation and interpretation of optimal braking and steering patterns towards autonomous safety-critical manoeuvres

Abstract

Stability control of a vehicle in autonomous safety-critical at-thelimit manoeuvres is analysed from the perspective of lane keeping or lane changing, rather than that of yaw control as in traditional ESC systems. An optimal control formulation is developed, where the optimisation criterion is a linear combination of the initial and final velocity of the manoeuvre. Varying the interpolation parameter in this formulation turns out to result in an interesting family of optimal braking and steering patterns in stabilising manoeuvres. The two different strategies of optimal lane-keeping control and optimal yaw control are shown to be embedded in the formulation and result from the boundary values of the parameter. The results provide new insights and have the potential to be used for future safety systems that adapt the level of braking to the situation at hand, which is demonstrated through examples of how to exploit the results.

Computation of Autonomous Safety Maneuvers Using Segmentation and Optimization

“…Examples on the use of offline optimization methods include: a study of at-the-limit maneuvers and a comparison of vehicle models of different complexity used in optimizations (Berntorp et al, 2014); an analysis of minimum distance when an avoidance maneuver is still possible (Shiller and Sundar, 1998); or the utilization of an optimal-control based method for quantifying the maneuverability of autonomous vehicles during emergency highway-speed situations (Dingle and Guzzella, 2010). Fors et al (2018) have formulated and interpreted optimal braking patterns using optimization, to provide new insights for potential future safety systems with adaptation of the level of braking. Using the concept of attainable force volumes of optimal maneuvers, Fors et al (2019) discuss a set of control principles for lane-keeping control with close to optimal behavior.…”

Attainable force volumes of optimal autonomous at-the-limit vehicle manoeuvres

“…The problem of finding optimal steering and braking sequences is stated as finding the solution to an optimal control problem (OCP). The approach from [2] is adopted, where a continuous family of optimal braking patterns in autonomous manoeuvres was presented. More specifically, an optimisation criterion to be minimised, with a weighted combination of the initial velocity v 0 and the final velocity v f of the manoeuvre, was introduced according to…”

“…One main objective for achieving autonomy of the vehicle is situation awareness, and more specifically the ability for the vehicle to map the environment and have knowledge of the lane borders of the road for a certain look-ahead distance. This information can then be employed in the motion planning and control of the vehicle, in particular to the purpose of achieving optimal lane-keeping control [1,2]. Realisation of such control principles can give close to optimal performance, which has been described in, e.g.…”

“…By the use of numerical optimal control, the maximum initial velocity that can be handled in a left-hand turn was examined in [1], showing that braking to reduce speed was given priority over braking to contribute to a turn-in yaw moment. A continuous family of braking patterns was found in [2], by using a weighted cost function of initial and final velocity. There, significant similarities in the optimal trajectories were found between different safety-critical scenarios.…”

Trends in vehicle motion control for automated driving on public roads

“…Another non-linear tracking method is a stable tracking with the front tires of the vehicle being saturated typically occurring during overspeeding in a turn. Work on recovering from such situations was developed in [38] and more recently in [39]. In [40] control allocation for avoidance maneuvers with oncoming vehicles is developed.…”