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

Abstract

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 frictionlimited particle model previously used in some literature for lanekeeping 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.

Autonomous Wary Collision Avoidance

“…Firstly, keeping the rear slip angles smaller increases the yaw stability of the vehicle. Secondly, the optimal behavior observed in [31] and here in Fig. 4 suggests that the optimal solution does not allocate significant tire forces to actively control the yaw moment.…”

“…2) Resulting Forces and Moment: The optimizations do not directly contain an acceleration reference θ, but using the procedure in [31], the corresponding reference can be found for a single-obstacle at-the-limit avoidance maneuver such as the one examined. The control force component F c,y turns out to be of particular interest.…”

“…The control force component F c,y turns out to be of particular interest. It is defined as the globally fixed force component perpendicular to the final velocity vector and is the force that stops the approach of the vehicle towards the obstacle [31]. Solving (14) for the passing maneuver, the force component F c,y is then computed using the vehicle longitudinal and lateral forces, F x and F y , by…”

“…where the angle ψ is the vehicle orientation and ψ v (t f ) defines the orientation of the final velocity vector. Similar to how θ is constant for the optimal single-obstacle avoidance maneuver for a friction-limited particle model [6], the optimal input u * for a simplified vehicle model can be shown to satisfy the necessary condition [31]…”

“…Here, to visualize the attainable forces during one maneuver obtained by solving (14), Fig. 4 shows the attainable force volume introduced in [31], where it is seen that the force is indeed on the boundary of F c,y and M z as indicated by (16). As also observed in [31] for a similar maneuver, it can be seen that there is not much active control of the yaw moment, with the trajectory being close to maximum F c,y .…”