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

With new developments in sensor technology, a new generation of vehicle dynamics controllers is developing, where the braking and steering strategies use more information, e.g. knowledge of road borders. The basis for vehicle-safety systems is how the forces from tyre–road interaction is vectored to achieve optimal total force and moment on the vehicle. To study this, the concept of attainable forces previously proposed in literature is adopted, and here a new visualisation technique is devised. It combines the novel concept of attainable force volumes with an interpretation of how the optimal solution develops within this volume. A specific finding is that for lane-keeping it is important to maximise the force in a certain direction, rather than to control the direction of the force vector, even though these two strategies are equivalent for the friction-limited particle model previously used in some literature for lane-keeping control design. More specifically, it is shown that the optimal behaviour develops on the boundary surface of the attainable force volume. Applied to lane-keeping control, this observation indicates a set of control principles similar to those analytically obtained for friction-limited particle models in earlier research, but result in vehicle behaviour close to the globally optimal solution also for more complex models and scenarios.