Methods for reducing high-speed off-tracking in multi-trailer heavy duty vehicles

1. A method for reducing off-tracking by a multi-trailer heavy duty vehicle during a maneuver, the method comprising obtaining a model of vehicle dynamics describing dynamics of the multi-trailer heavy duty vehicle, determining respective force trajectories for two or more axles of the vehicle as a solution to a non-linear optimal control problem, (“NOCP”), where the NOCP is formulated with an objective to at least minimize trailer off -tracking, wherein the NOCP is formulated based on the model of vehicle dynamics and a prediction of vehicle control during the maneuver, and controlling motion of the heavy duty vehicle during the maneuver based on the determined force trajectories.

2. The method according to claim 1 , comprising obtaining information related to a road friction coefficient (μ) associated with an upcoming vehicle path, wherein the NOCP is formulated to account for the road friction coefficient (μ).

3. The method according to claim 2 , further comprising configuring a limit F max on axle forces given by

F max =sμF z

where S is a safety factor smaller than 1 . 0 , and wherein the NOCP is constrained by the limit Fmax on axle forces.

4. The method according to claim 1 , further comprising configuring lateral and longitudinal wheel slip limits (λ lim ) for at least two wheels of an axle on the heavy duty vehicle, wherein lateral and longitudinal wheel slip values are related to respective lateral and longitudinal tire force values (F x , F y ) via a pre-determined combined tire slip model, wherein the NOCP is constrained by the lateral and longitudinal wheel slip limits (λ lim ).

5. The method according to claim 1 , wherein the force trajectories comprise target tire force trajectories and/or target wheel slip trajectories for at least two axles to be followed during the maneuver.

6. The method according to claim 1 , wherein the force trajectories comprise target wheel torque trajectories or target axle torque trajectories to be followed during the maneuver.

7. The method according to claim 1 , wherein the heavy duty vehicle is a multi-trailer vehicle comprising a self-powered dolly vehicle unit.

8. The method according to claim 1 , comprising solving the NOCP in real-time.

9. The method according to claim 1 , comprising obtaining a solution to the NOCP from a pre-determined look-up table, (“LUT”), wherein the LUT comprises solutions to a plurality of NOCPs solved for different NOCP input parameters, where a solution is selected from the LUT in dependence of a respective set of parameters of a current operating scenario of the heavy duty vehicle and in dependence of the maneuver.

10. The method according to claim 9 , comprising obtaining the solution to the NOCP by obtaining target brake and propulsion force trajectories from the LUT based on a steering angle of the vehicle and based on a speed of the vehicle.

11. The method according to claim 1 , wherein a set of states of the NOCP comprise longitudinal speed of a first vehicle unit, lateral speed of the first vehicle unit, yaw angle of the first vehicle unit, as well as respective derivatives, and also articulation angles of the heavy duty vehicle and their derivatives.

12. The method according to claim 1 , wherein the force trajectories for the two or more axles of the vehicle have equal tire forces for each side of the respective axle.

13. The method according to claim 2 , wherein a distance of the path is between 5-300 m.

14. A control unit comprising processing circuitry configured to perform the method according to claim 1 .

15. A heavy duty vehicle comprising the control unit according to claim 14 .

16. A dolly vehicle unit comprising the control unit according to claim 14 .