Effect of handling characteristics on minimum time cornering with torque vectoring

Abstract

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal torque vectoring strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using torque vectoring against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the optimal control problem is introduced where a closed-loop torque vectoring controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.

Autonomous Vehicle Maneuvering at the Limit of Friction

“…In Paper VI, this representation is used to plan the motion of the vehicle. It is also used in [30] for online planning and control and in [31] to ensure affine lane boundaries. Similar representations are also used for path following, e.g., [32], where the error dynamics can be linearized around the path.…”

“…The double-track model is extensively used in this thesis because of its ability to model differential braking, which is heavily influenced by the lateral load transfer [53]. Some uses for the double-track model are studying the effects of differential braking [54] or torque vectoring [31], and when utilizing differential braking for control [55].…”

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

“…It was noted that in the trade-off between reducing speed and cornering, full braking is initially required at the expense of the steering ability. Torque vectoring for minimum-time cornering was examined in [14] by using optimal steering inputs given by numerical optimal control. It was demonstrated that the performance of a vehicle capable of torque vectoring is largely insensitive to the uncontrolled understeer behaviour of the vehicle.…”

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

“…Optimal manoeuvres in a hairpin turn for different surfaces were computed using numerical dynamic optimisation in [4]. Torque vectoring for minimumtime cornering was examined in [5] by using optimal steering inputs. In [6], a comparison of the optimal manoeuvres in a turn with the criteria of minimum time and maximum exit velocity, respectively, was presented using an optimal-control approach.…”