Chauffeur braking

industrial collaborators:	Jaguar Land Rover
academic collaborators:	ESGI68
initiated :	2009/07/27
last updated:	2010/05/25

Study Group Report 2009: chauffeur braking (Jaguar Land Rover)
This is the final report on the problem of chauffeur braking, brought to ESGI68 by Jaguar Land Rover. Click on the link at the bottom to download the full report as a pdf document.

Report coordinator
Tristram Armour (Knowledge Transfer Network for Industrial Mathematics)

Executive summary
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.

Introduction
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. Once stationary, the brake pressure can be increased significantly to hold the vehicle against disturbances. The problem offered to the Study Group is to provide a comfortable ‘chauffeur’ stop feature for a luxury vehicle under full automatic longitudinal control.

Four main parts to the problem were identified.

1. Optimal control: Braking control must take account of initial conditions, end conditions and possible disturbances.
2. State estimation: Vehicle movement is detected by a ‘tone wheel’ attached directly to each of the vehicle’s road wheels. The tone wheel has teeth that generate square waves in Hall-effect sensors, which are then used to estimate vehicle speed. There are virtually no other sensors available.
3. Friction braking: The classical model of friction has sliding and static elements. Brake materials are both adhesive and abrasive and contain lubricants such as aluminium. Are there better (micromolecular) models at the stick-slip boundary?
4. Braking dynamics: There is an unknown and changing offset and gain in the (open loop) brake pressure control, owing to the brake disk condition and the effects of gradient, engine braking and torque converter creep.

The Study Group concentrated on the first three problems following advice from Phil Barber.

State estimation
Any optimal stopping problem will require that we know the initial state of the car. In reality, our model will be imperfect and so due to model and parameter uncertainties, we will need to update our optimal control as the car brakes. If we had accurate sensors available each feeding a time series of information to the control system, this might not be such a problem but the cars have limited bandwidth and space for sensors. The Study Group concentrated on a solution with the speed sensor only. The control strategy is to use the estimates of the current state of the vehicle to determine how to adjust the braking system of the car in order to affect a smooth stop.

A Hall-effect sensor together with a tone wheel acts as a speed sensor for the car. The tone wheel is a cog with 48 square teeth (see Figure 1) and each revolution of the tone wheel corresponds to the car moving 2.101 metres. The velocity is calculated by looking at the time taken until the next tooth of the cog passes the sensor. The teeth are imperfect so there will be some error to the velocity calculation which increases when the car is moving very slowly.

Figure 1: Picture of a tone wheel. (Courtesy of eHow.com).

A simple simulation of the stopping problem with a tone wheel (with simulated errors) was made. At each time step, the Kalman filter gave the control system estimates of the state of the car. The control system calculates the solution to the optimal control problem (1) for the next time step until the car comes to a stop. Figure 2 shows the last section of the simulation. The jumps in the curves indicate where new measurements were received from the tone wheel and these updates become less frequent as the vehicle slows down. The shaded area is 1 standard deviation away from our estimate and our real position is within the shaded area for the whole simulation.

Figure 2: Simulation results using the Kalman filter: The left graph shows the actual (red) and detected displacement (blue) of the car from the start point at 0 metres. The stopping distance was set at 20 metres. The right graph plots the speed of the car at the end of the simulation. The optimal stop took approximately 43 seconds.

Remarks

• Strictly, the errors come from the timings of the updates and not from the readings themselves. However, the Kalman filter is designed to operate in the presence of noise and hence it is very robust — it should still work well in our problem.
• Because of the design of the sensor and the lack of an accurate accelorometer, the control system doesn’t really know if the car has stopped. There is the need for a higher level control system which increases the brake pressure when an update has not occurred for s seconds, at which the car assumes you have stopped.

Click on the link below to view the full report.

 

related resources:

	Chauffeur braking
»	Study Group Report 2009: chauffeur braking (Jaguar Land Rover)

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