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Research Papers

The Optimality of the Handbrake Cornering Technique

[+] Author and Article Information
Davide Tavernini

Department of Automotive Engineering,
Cranfield University,
College Road, Cranfield,
Bedfordshire MK43 0AL, UK
e-mail: d.tavernini@cranfield.ac.uk

Efstathios Velenis

Department of Automotive Engineering,
Cranfield University,
College Road, Cranfield,
Bedfordshire MK43 0AL, UK
e-mail: e.velenis@cranfield.ac.uk

Roberto Lot

Department of Industrial Engineering,
University of Padova,
Via Venezia 1,
Padova 35131, Italy
e-mail: roberto.lot@unipd.it

Matteo Massaro

Department of Industrial Engineering,
University of Padova,
Via Venezia 1,
Padova 35131, Italy
e-mail: matteo.massaro@unipd.it

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 25, 2013; final manuscript received February 3, 2014; published online April 15, 2014. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 136(4), 041019 (Apr 15, 2014) (11 pages) Paper No: DS-13-1245; doi: 10.1115/1.4026836 History: Received June 25, 2013; Revised February 03, 2014

The paper investigates the optimality of the handbrake cornering, a strategy widespread among rally drivers. Nonlinear optimal control techniques are used to mimic real driver behavior. A proper yet simple cost function is devised to induce the virtual optimal driver to control the car at its physical limits while using the handbrake technique. The optimal solution is validated against experimental data by a professional rally driver performing the handbrake technique on a loose off-road surface. The effects of road surface, inertial properties, center of mass position, and friction coefficient are analyzed to highlight that the optimality of the maneuver does not depend on the particular vehicle data set used. It turns out that the handbrake maneuvering corresponds to the minimum time and minimum (lateral) space strategy on a tight hairpin corner. The results contribute to the understanding of one of the so-called aggressive driving techniques.

Copyright © 2014 by ASME
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Figures

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Fig. 1

FWD test vehicle driven by a professional driver during data collection on a loose off-road surface

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Fig. 2

Experimental handbrake cornering data of the FWD test vehicle on a loose off-road surface. (a) Wheel spin signals ω are from the vehicle standard sensors, (b) steering angle δ is from an additional potentiometer, vehicle slip/drift angle β is from Racelogic VBox twin GPS antenna sensor, and (c) brake pressures are from two additional pressure sensors.

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Fig. 3

Experimental handbrake cornering data of the FWD test vehicle on a loose off-road surface. Trajectory is from Racelogic VBox twin GPS antenna sensor.

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Fig. 4

Car model with variables and main parameters

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Fig. 5

Curvilinear coordinates

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Fig. 6

(a) Distribution of the two terms of the cost function on the hairpin: The lateral deviation cost is applied from the beginning of the corner till the finish line, while the minimum time cost is applied all along the maneuver. (b) Geometry of the hairpin.

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Fig. 7

Tire–road friction coefficient μ as a function of the slip σ: solid line is for paved asphalt road and dashed line is for off-road

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Fig. 8

Comparison between numerical simulation (solid line) and experimental data (dotted line) of the FWD test vehicle

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Fig. 9

(a) 3D representation of the comparison between simulations results and (b) experimental data of the FWD test vehicle

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Fig. 10

Handbrake cornering simulation results of the FWD test vehicle: off-road and fixed initial lateral position sn. (a) Front and rear wheel spin ωF,R, (b) drift angle β and steer angle δ, (c) front and rear normalized tire load nF,R, and (d) front and rear normalized torque γF,R and handbrake hb.

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Fig. 11

Comparison between numerical simulations and experimental data of the FWD test vehicle: (a) numerical simulation with fixed initial position matching experimental initial position; (b) experimental data; (c) numerical simulation with free initial position; and (d) superimposition of trajectories of simulations and experimental data reported in (a)–(c). Numbers in squares are the numerical simulation time and experimental logging time.

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Fig. 12

Handbrake cornering simulation results of the FWD test vehicle: off-road and free initial lateral position sn. (a) Front and rear wheel spin ωF,R, (b) drift angle β and steer angle δ, (c) front and rear normalized tire load nF,R, and (d) front and rear normalized torque γF,R and handbrake hb.

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Fig. 13

Handbrake cornering simulation results of the FWD test vehicle: asphalt road and free initial lateral position sn. (a) Front and rear wheel spin ωF,R, (b) drift angle β and steer angle δ, (c) front and rear normalized tire load nF,R, and (d) front and rear normalized torque γF,R and handbrake hb.

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Fig. 14

Effect of the handbrake on the cornering simulation with free initial lateral position sn for the FWD test vehicle: (a) asphalt road with handbrake, (b) asphalt road with handbrake inhibited, and (c) asphalt road with no cost on the lateral deviation from the inner road limit (pure minimum time)

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Fig. 15

Effect of yaw vehicle inertia on handbrake cornering simulation for the FWD test vehicle. Numbers in squares are the road curvilinear abscissa ss. (a) normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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Fig. 16

Effect of position of the center of mass on handbrake cornering simulation for the FWD test vehicle. Numbers in squares are the road curvilinear abscissa ss. (a) Normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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Fig. 17

Different tire–road friction curves used for the sensitivity analysis on friction peak

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Fig. 18

Effect of friction coefficient on handbrake cornering simulation for the FWD test vehicle. Numbers in squares are the road curvilinear abscissa ss. (a) Normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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Fig. 19

Effect of maximum steering angle δmax on handbrake cornering simulation for the FWD test vehicle. (a) Normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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Fig. 20

Effect of maximum steering rate δ·max on handbrake cornering simulation for the FWD test vehicle. (a) Normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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Fig. 21

Effect of maximum torque rate T·max=γ·tmaxMg=h·bmaxMg on handbrake cornering simulation for the FWD test vehicle. (a) Normalized handbrake torque hb, (b) front and rear wheel spin ωF,R, and (c) drift angle β.

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