A MATHEMATICAL MODEL FOR DRIVER STEERING CONTROL BASED ON INTERMITTENT GENERALIZED PREDICTIVE CONTROL THEORY

Philippe Micheau1, René Roy1 and Paul Bourassa2

1 GAUS, Mechanical Engineering Department, Université de Sherbrooke, Canada2 Research Centre on Aging, Université de Sherbrooke, Canada

UNIVERSITÉ DE

ReferenceDoman and Anderson, A fixed-order optimal control model of human operator response, Automatica, vol. 36, 409-418, 2000.Horiuchi S., Tamatsukuri T., Nohtomi S., An automotive lateral controller based on generalized predictive control theory, JSAE Review, vol. 21, p. 53-59, 200.Loram I. D. and Lakie Martin, Human balancing of an inverted pendulum: position control by small, ballistic-like throw and catch movements, Journal of Physiology, 540.3, pp. 1111-1124, 2002.MacAdam C.C., Application of an optimal preview control for simulation of closed-loop automobile driving, IEEE transactions on systems, man, and cybernetics, vol. 11(6), p. 393-399, 1981.R. Roy, La commande prédictive généralisée intermittente comme modèle cognitif de conducteur automobile, mémoire de maîtrise, 2002.

Context : Human operator models using optimal control theory have been found to be agree with experimental data (Doman and Anderson, 2000). But, these models were applied with continuous data. Objective: to evaluate the performance of driver working with data (past and

preview) captured at a fixed intermittent period.

Method : simulation of the driver model joined to a vehicle dynamics model. Comparison between simulation results and experimental measurements.

Model of the driver (Doman and Anderson (2000) : -a time-delay representing a reaction time delay 0.2 s;- a first-order transfer function representing the neuromuscular actuation delays chosen to 0.1 s;- look ahead preview;- intermittent control of the steering

Validations of the simulator for the case without intermittence : 1 : comparisons of GPC and car model with results published by Horiuchi et al (2000).2 : validation with measurements published by MacAdam (1981).

The IGPC : the penalty coefficient is used to balance the future error path ye(t) and the future steering command increments c(t) over the prediction horizon L :

Intermittent control : past and present data about the vehicle, and the future data about the road were captured and actualized every W seconds.

Main results :i) For the optimal penalty coefficient, it is not possible to dissociate an optimal driver using intermittent data between one using continuous data.ii) When the look ahead preview is increased, the allowable intermittence period values is also increased.

Comparison between simulation and experimental measurement of the steering command with L=2s,W=0.16s, =105

Comparison : The similitude of IGPC with the measurements is evaluated with the cost function J(W,)= || - *||2

It exists a value of such that intermittence is

possible without loss of fit with experimental

measurement.

Future works : it will be to apply the IPGC to other types of motor control such that the posture control where throw and catch movements (Loram and Lakie, 200) could be explained by intermittent control.

dttdttyJ c

L

dte

L

dt)()( 22

Past t d W L delay Intermittence Preview

Time (s)

Next steering command

Information allowable to calculate the command

J

The Intermittent Generalized Predictive Control

Driver uses continuous data or intermittent data ?

Main results

This work was supported by

Problem : Is there a difference between optimal driver using intermittent data and optimal driver using continuous data ?