An experienced driver will `feather’ the brakes so as to unwind the suspension compliance and stop the vehicle with only just enough torque in the brakes to hold the vehicle stationary on any gradient, or against the residual torque from an automatic transmission’s torque converter. An optimal stopping problem that minimises the total jerk was formulated and solved. This model was extended by including a linear relationship between the brake pressure and the acceleration of the car where the coefficients are estimated by linear regression. Finally, a Kalman filter estimates the state of the car using the tone wheel.

Problem presented by
Phil Barber and Huw Williams, Jaguar Land Rover

Study Group contributors
David Allwright (Industrial Mathematics KTN)
Tristram Armour (Industrial Mathematics KTN)
Chris Cawthorn (University of Cambridge)
Chris Dent (University of Edinburgh)
Jeff Dewynne (University of Oxford)
Joseph Fehribach (WPI)
Gemma Fay (University of Oxford)
John Lees-Miller (University of Bristol)
Jan Van lent (University of Bath)
Jonathan Ward (University of Limerick)
Robert Whittaker (University of Oxford)