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

Fors, Victor; Olofsson, Björn; Nielsen, Lars · 2019 · OpenAlex-citations

DOI: 10.1080/00423114.2019.1608363

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Summary

This paper investigates the optimal utilization of tire-road interaction forces for autonomous vehicle safety systems, specifically focusing on lane-keeping and obstacle avoidance maneuvers. Motivated by advancements in sensor technology and onboard computing power, the authors aim to derive control principles that allow vehicles to operate at the physical limits of stability. The study addresses the challenge of translating complex numerical optimal control solutions into implementable strategies by analyzing how available forces are vectored to achieve optimal total force and moment on the vehicle. The researchers employ a double-track vehicle model incorporating longitudinal and lateral load transfer, utilizing Pacejka’s Magic Formula for nonlinear tire characteristics. They define an optimal control problem (OCP) to determine optimal steering and braking sequences for two safety-critical scenarios: a left-hand turn with constant curvature and a double lane-change based on ISO standard 3888-2. The optimization criterion minimizes a weighted combination of initial and final velocities, solved numerically using direct collocation via the JModelica.org platform. To analyze the results, the authors introduce a novel visualization technique called "attainable force volumes," which maps the set of all possible global forces and yaw moments achievable at any given time. They specifically define a "control force vector" ($F_c$) aligned with the direction perpendicular to the final velocity vector, which is critical for reducing lateral deviation. The primary finding is that optimal autonomous maneuvers consistently develop on the boundary surface of the attainable force volume. Specifically, for lane-keeping tasks, the optimal strategy prioritizes maximizing the force in the direction opposing the path deviation ($F_{c,y}$) rather than controlling the direction of the force vector itself. This behavior holds true even for complex vehicle models, mirroring analytical solutions previously derived for simpler friction-limited particle models. The study demonstrates that a local control approach, which maximizes this specific control force component, yields vehicle behavior close to the globally optimal solution. The significance of this work lies in its provision of a theoretical basis for designing real-time vehicle dynamics controllers. By identifying that optimal behavior resides on the boundary of the attainable force volume and prioritizing specific force components, the authors establish a set of control principles that are computationally efficient enough for online execution. This bridges the gap between complex offline optimal control simulations and practical, implementable active safety systems, enabling autonomous vehicles to perform near-optimal maneuvers in time-critical situations.

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• perception action locomotion