Detection of yaw instabilities in vehicle combinations

A method of detecting a yaw instability in a vehicle combination, the vehicle combination comprising a tractor unit and at least one trailing unit, the method comprising:

• determining a current value of an understeering gradient of at least one unit of the vehicle combination;
• comparing the current value of the understeering gradient to a threshold;
• and
• if the current value of the understeering gradient is beyond the threshold, determining that a yaw instability is present in the vehicle combination;
• wherein the understeering gradient of the tractor unit, Kus,tractor, is given by:
• K
• us
• ,
• tractor
• =
• v
• 1
• ,
• r
• ⁢
• tan
• ⁢
• δ
• 1
• -
• L
• 1
• ⁢
• ω
• 1
• V
• 1
• ,
• r
• 2
• ⁢
• ω
• 1
• where v1,r is the longitudinal speed of the tractor unit, δ1 is the road wheel angle of the tractor unit, L1 is the wheelbase of the tractor unit, and ω1 is the yaw rate of the tractor;
• and/or,
• the understeering gradient of a trailing unit i, Kus,trailer, is given by:
• K
• us
• ,
• trailer
• ,
• i
• =
• v
• i
• ,
• r
• ⁢
• tan
• ⁢
• θ
• i
• -
• 1
• ,
• i
• -
• (
• L
• 1
• -
• b
• i
• -
• 1
• cos
• ⁢
• θ
• i
• -
• 1
• ,
• i
• )
• ⁢
• ω
• i
• v
• i
• ,
• r
• 2
• ⁢
• ω
• i
• where vi,r is the longitudinal speed of the trailing unit, θi−1,i is the articulation angle between the trailing unit and the unit in front, Li is the wheelbase of the trailing unit, bi−1 is the longitudinal distance from the equivalent rear axle position of the unit to the coupling point, and ω1 is the yaw rate of the trailing unit.