Steering Feedback Mathematical Simulation of Effects on Driver and VehicleNew steering technologies offer potential for performance improvement, but the associated design freedom brings the risk of high development cost and non-optimal design. The Driver-Vehicle Dynamics Group at Cambridge University Engineering Department (United Kingdom) is taking a multi-disciplinary approach to the problem. The work being presented aims at moving engineering activity from the expensive development phase to the low-cost design phase by using a mathemat-ical model of the driver.

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1 Introduction

There is currently strong interest in the use of advanced steering technology to improve safety, performance and effi-ciency of road vehicles. Sophisticated sys-tems that actively modify the steering angle and torque are now in production. Much of the development work is per-formed using test drivers and prototype vehicles. A consequence is that product development is time-consuming and ex-pensive, and the technology may not be exploited to its full potential. Elsewhere in the vehicle engineering process, math-ematical models are used extensively to support decision-making in the low-cost design phase. An absence of significant theoretical understanding of human steering control behaviour has limited the use of mathematical simulation in the design of steering system dynamics. The Driver-Vehicle Dynamics Group at Cambridge University Engineering De-partment is taking a multi-disciplinary approach to the problem, Figure 1. Know-ledge of vehicle dynamics, neuroscience, control theory and machine learning is being brought together to advance un-derstanding of the dynamic interaction between driver and vehicle.

� Neuromuscular System

Figure � shows the major components of the human neuromuscular system (NMS).

In steering a car the brain acts upon sig-nals from the sensory organs such as the eyes. The brain processes the signals and calculates how the muscles should be ac-tivated to achieve the desired vehicle mo-tion. Signals from the brain travel to al-pha motor neurons and gamma motor neurons in the spinal cord. The alpha motor neurons directly activate the main force-producing fibres of the muscle, which in turn act on the handwheel. This is essentially feed-forward control of the muscle, and works well if there are no unexpected disturbances on the steer-ing system.

The gamma motor neurons activate special fibres in the muscle called spin-dles. The gamma motor neurons adjust the length of the spindles according to the muscle length (or handwheel angle) expected by the brain. If the muscle length differs from the expected length the spindles are strained and send a sig-nal to the alpha-motor neurons, which in turn activate the muscle to achieve the expected muscle length. This closed-loop feedback control of muscle length is known as the spinal reflex and is most easily observed by tapping the patellar tendon just below the patella (knee cap).

3 Driver-Vehicle Model

The block diagram of a driver-vehicle model incorporating the NMS is shown in Figure 3. The steering block defines

The Author

Dr. David Coleis Senior Lecturer at the Department of En-gineering, University of Cambridge (United Kingdom).

Figure 1: Multi-disciplinary approach to understanding driver-vehicle dynamics

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how the road wheel steer angle is related to the torque and angle at the handwheel and to the vehicle responses. This struc-ture permits a variety of steering designs, from conventional manual steering to electrically-assisted steering with torque overlay and angle overlay functions.

The muscle and arm block includes inertia of the arms, stiffness and damp-ing of the muscle and force generation by the muscle. The internal structure of the muscle and arm block arises from Hoult’s [1] linearisation of a physiologi-cally-based muscle model and overcomes limitations of existing well-known mus-cle models. The muscle is activated by the output of the alpha motor neuron block, which sums the signals from the brain and from the reflex loop.

The blocks on the left of the diagram represent the brain. The path following control block is a model predictive con-troller [2]. The controller receives sensory information about the current state of the vehicle and NMS and also looks ahead at the target path. A time delay is included to represent the time required for the brain to receive and process the sensory signals and to transmit signals to the motor neurons.

The forward model block represents the driver’s learnt knowledge of the muscle and arm, steering and vehicle dy-namics. The forward model calculates

the handwheel angle expected to result from the brain’s direct activation of the alpha motor neuron. The output of the forward model is sent to the reflex sys-tem, mathematical models of which are well established [3].

In many existing driver models it is necessary to decide whether the driver controls angle or torque at the hand-wheel. By including the NMS in the driv-er model it is not necessary to make this decision. However it is necessary to un-derstand how the driver can adapt the

NMS to suit the characteristics of the ve-hicle and steering system. The driver can adjust the stiffness of the arms by co-con-tracting or tensing the muscles and can adjust the gain of the reflex loop. This is the subject of ongoing research [1, 4].

4 Model Identification

The parameters of the vehicle and steer-ing blocks are easily determined using well-known procedures. The parameters of the blocks associated with the driver’s brain and NMS are less easily determined. An experiment that can reveal much about the dynamic properties of the NMS is shown in Figure 4. The test subject holds onto a handwheel driven by a servo mo-tor. A random torque is generated by the motor and the angular response of the handwheel is measured. The magnitudes of typical torque to angle frequency re-sponse functions are shown in Figure 5. The blue line is for the muscles in a re-laxed condition, the red line is for the muscles in a tensed, or co-contracted, condition. The graph shows that the tensed muscles have greater stiffness than the relaxed muscles. The frequency responses can also be used to identify the inertia, damping and reflex gain [1, 5].

In the experiment described above the path following controller has little influence and therefore cannot be iden-tified. Pick [3] and Odhams [6] have per-formed driving simulator experiments

Figure �: Neuromuscular system

Figure 3: Driver-vehicle model including NMS

Figure 4: Measurement of torque to angle frequency response function

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to successfully identify the path follow-ing controller and delay. Keen [7, 8] has extended the technique to instrumented test vehicles.

Further data to identify the model can be obtained using surface electromyogra-phy. Electrodes stuck to the skin directly above the muscle of interest measure a voltage that is related to the output of the alpha motor neurons. Using this tech-nique it has been possible to identify the muscles involved in generating torque at the handwheel, and to measure the mus-cle co-contraction (and thus muscle stiff-ness) during steering activity [9].

5 Driver and Vehicle Response to a Steering Fault

To demonstrate an application of the model, the driver and vehicle responses to a fault in a steering system are simu-lated. A saloon car with an angle-overlay steering mechanism is modelled. The ve-

hicle speed is 20 m/s and the target path is a straight line. The NMS is in a tensed condition and the delay in the brain is 0.3 s. At 1.0 s the fault occurs; an angular offset of 12 ° is introduced by the steering mechanism over a period of 100 ms, after which the offset is maintained at 12 °.

Figure 6 (a) shows the lateral displace-ment of the vehicle and Figure 6 (c) shows the yaw rate. The lateral displacement reaches 0.04 m at the time when the driver’s path following control begins at 1.3 s. The lateral displacement subse-quently reaches a maximum of 0.3 m.

Figure 5: Magnitude of torque to angle frequency response function for muscles in relaxed and tensed conditions 0 dB = 1 rad/Nm

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The handwheel torque and angle are shown in Figure 6 (b) and Figure 6 (d). The responses between 1.0 s and 1.3 s arise from interaction between the vehi-cle, steering mechanism and NMS. At 1.0 s the handwheel angle increases as a result of the steering fault and soon af-terwards the reflex system attempts to return the handwheel angle to zero. From 1.3 s the brain’s path following control dominates the response and the vehicle is brought back to the target path at about 3.5 s. A steady handwheel angle of 12 ° remains, to compensate for the uncorrected steering fault.

6 Model Development

In this paper steering feedback is consid-ered to dynamically couple the driver and vehicle. The model enables the effect of various feedback strategies and fault conditions to be investigated. The model suggests that good steering performance will arise from an absence of disturbanc-es and from the driver having an accu-rate forward model. When either of these conditions is not satisfied the unexpect-ed feedback from the steering affects the response of the driver and the vehicle.

It could be argued that the steering task would be easier without any feed-back from the steering. The driver could rely on vision and motion senses to meas-ure the vehicle state. However, human sensory and motor signals have very sig-nificant noise components. The human senses also have some dynamic limita-tions. Additional feedback from the steer-ing through the hands and arms pro-vides the driver with more data with which to compensate for the noise and to generate accurate estimates of the vehi-cle state. The steering feedback also plays

a role in warning the driver that the fric-tion limit of the tyres is being ap-proached. This might be through mak-ing the feedback change in a way that the driver interprets as a warning, for ex-ample, by reducing the handwheel torque as the friction limit is approached. Progress in modelling these aspects of steering feedback has been made and will be reported in due course [10].

References[1] Hoult, W.: A neuromuscular model for driver simu-

lation, PhD thesis, Cambridge University Engineer-ing Department, to be submitted September 2008

[2] Cole, D.J.; Pick, A.J.; Odhams, A.M.C.: Predictive and linear quadratic methods for potential applica-tion to modelling driver steering control, Vehicle System Dynamics, 44 (3), March 2006, pp. 259-284

[3] Pick, A.J.M.; Cole, D.J.: A mathematical model of driver steering control including neuromuscular dy-namics, ASME Journal of Dynamic Systems, Measurement and Control, 130 (3), May 2008, 9pp

[4] Pick, A.J.; Cole, D.J.: Measurement and analysis of muscle activation during a lane change manoeuvre, Vehicle System Dynamics, 45 (9), 2007, pp. 781-805

[5] Pick, A.J.; Cole, D.J.: Dynamic properties of a driv-er’s arms holding a steering wheel, Proc. IMechE Part D, Vol. 221, 2007, pp. 1475-1486

[6] Odhams, A.M.C.: Identification of driver steering and speed control, PhD thesis, Cambridge Universi-ty Engineering Department, September 2006

[7] Keen, S.D.; Cole, D.J.: Steering control using model predictive control and multiple internal models, Proc 8th International Symposium on Advanced Ve-hicle Control, AVEC 2006, Taiwan, August 2006

[8] Keen, S.D.: Modeling driver steering behavior us-ing multiple-model predictive control, PhD thesis, Cambridge University Engineering Department, submitted August 2008

[9] Pick, A.J.; Cole, D.J.: Measurement of driver steer-ing torque using electromyography, ASME Journal of Dynamic Systems, Measurement and Control, 128 (4), 2006, pp. 960-968

[10] www.vehicledynamics.org

Figure 6: Simulated responses to a steering fault. The fault occurs at t = 1.0 s. The driver’s path following control action begins at t = 1.3 s

Acknowledgment

The support provided by TRW Conekt and TRW Automotive for parts of the work de-scribed in this paper is gratefully acknowl-edged. The author also thanks past and cur-rent members of the Driver-Vehicle Dynamics Group for their contributions.

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