AM ATHEMATICAL MODEL FOR DRIVER STEERING CONTROL BASED ON

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                        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, Canada
                                                       2 Research Centre on Aging, Université de Sherbrooke, Canada



Driver uses continuous data or intermittent data ?
                                                                                                                            Problem : Is there a difference between optimal driver using intermittent
Context : Human operator models using optimal control theory have been
                                                                                                                            data and optimal driver using continuous data ?
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 Intermittent Generalized Predictive Control
                                                                                                                            The IGPC : the penalty coefficient l is used to balance the future error
                                                                                                                            path ye(t) and the future steering command increments Ddc(t) over the
                                                                                                                            prediction horizon L :
                                                                                                                                                          L                                      L
                                                                            Intermittent control :                                            J                 y (t )dt  l 
                                                                                                                                                                     2
                                                                                                                                                                     e                                 Dd (t )dt
                                                                                                                                                                                                            2
                                                                                                                                                                                                            c
                                                                            past and present data about                                                  t d                                t d
                                                                            the vehicle, and the future
                                                                            data about the road were                             Information allowable to calculate the command
                                                                            captured and actualized every
                                                                            W seconds.                                                                                              J

                                                                                                                                                      Next steering
                                                                                                                                                       command                                                          Time (s)

                                                                                                                                  Past          t           d                  W                             L
                                                                                                                                                           delay           Intermittence                  Preview


Main results

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




                                                                                                                                                                                                     It exists a value of l such
    Comparison between simulation d and experimental measurement                                            d*   of
                                                                                                                                                                                                         that intermittence is
             the steering command with L=2s,W=0.16s, l=105
                                                                                                                                                                                                     possible without loss of fit
Main results :                                                                                                                                                                                            with experimental
i) For the optimal penalty coefficient, it is not possible to dissociate an                                                                                                                                 measurement.
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.

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.

Reference
Doman 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.




                                                                                                                                              This work was supported by

				
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