Research Papers

A Controller Framework for Autonomous Drifting: Design, Stability, and Experimental Validation

[+] Author and Article Information
Rami Y. Hindiyeh

Dynamic Design Laboratory,
Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: hindiyeh@alumni.stanford.edu

J. Christian Gerdes

Associate Professor
Dynamic Design Laboratory,
Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: gerdes@stanford.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 19, 2012; final manuscript received April 16, 2014; published online July 9, 2014. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 136(5), 051015 (Jul 09, 2014) (9 pages) Paper No: DS-12-1023; doi: 10.1115/1.4027471 History: Received January 19, 2012; Revised April 16, 2014

This paper presents the development of a controller for autonomous, steady-state cornering with rear tire saturation (“drifting”) of a rear wheel drive vehicle. The controller is designed using a three-state vehicle model intended to balance simplicity and sufficient model fidelity. The model has unstable “drift equilibria” with large rear drive forces that induce deep rear tire saturation. The rear tire saturation at drift equilibria reduces vehicle stability but enables “steering” of the rear tire force through friction circle coupling of rear tire forces. This unique stability–controllability tradeoff is reflected in the controller design, through novel usage of the rear drive force for lateral control. An analytical stability guarantee is provided for the controller through a physically insightful invariant set around a desired drift equilibrium when operating in closed-loop. When implemented on a by-wire testbed, the controller achieves robust drifts on a surface with highly varying friction, suggesting that steady cornering with rear tire saturation can prove quite effective for vehicle trajectory control under uncertain conditions.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Velenis, E., and Tsiotras, P., 2005, “Minimum Time vs Maximum Exit Velocity Path Optimization During Cornering,” ISIE 2005, Croatia, Dubrovnik, June 20–23, Vol. 1, pp. 355–360.
Velenis, E., Tsiotras, P., and Lu, J., 2008, “Optimality Properties and Driver Input Parameterization for Trail-Braking Cornering,” Eur. J. Control, 14(4), pp. 308–320. [CrossRef]
Ono, E., Hosoe, S., and Tuan, H., 1998, “Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Control,” IEEE Trans. Control Syst. Technol., 6(3), pp. 412–420. [CrossRef]
Voser, C., Hindiyeh, R., and Gerdes, J., 2010, “Analysis and Control of High Sideslip Manoeuvres,” Veh. Syst. Dyn., 48, pp. 317–336. [CrossRef]
Edelmann, J., Plochl, M., Lugner, P., Mack, W., and Falkner, A., 2008, “Investigations on the Powerslide of Automobiles,” AVEC 2008, Kobe, Japan, Oct. 6–9.
Velenis, E., Katzourakis, D., Frazzoli, E., Tsiotras, P., and Happee, R., 2010, “Stabilization of Steady-State Drifting for a RWD Vehicle,” AVEC 2010, Loughborough, UK, Aug. 22–26.
Abdulrahim, M., 2006, “On the Dynamics of Automobile Drifting,” SAE World Congress 2006, Detroit, MI, April 3-6, Paper No. 2006-01-1019.
Edelmann, J., Plochl, M., and Pfeffer, P., 2011, “Analysis of Steady-State Vehicle Handling and Driver Behaviour at Extreme Driving Conditions,” IAVSD 2011, Manchester, UK, August 14–19.
Velenis, E., Frazzoli, E., and Tsiotras, P., 2010, “Steady-State Cornering Equilibria and Stabilization for a Vehicle During Extreme Operating Conditions,” Int. J. Veh. Auton. Syst., 8(2–4), pp. 217–241. [CrossRef]
Fiala, E., 1954, “Seitenkrafte am Rollenden Luftreifen,” VDI Z., 96(29), pp. 973–979.
Ryu, J., and Gerdes, J., 2004, “Integrating Inertial Sensors With GPS for Vehicle Dynamics Control,” ASME J. Dyn. Syst., Meas., Control, 126(2), pp. 243–254. [CrossRef]
Hsu, Y.-H., Laws, S., and Gerdes, J., 2010, “Estimation of Tire Slip Angle and Friction Limits Using Steering Torque,” IEEE Trans. Control Syst. Technol., 18(4), pp. 896–907. [CrossRef]
Beal, C. E., 2011, “Applications of Model Predictive Control to Vehicle Dynamics for Active Safety and Stability,” Ph.D. thesis, Stanford University, Stanford, CA.


Grahic Jump Location
Fig. 1

Bicycle model of a RWD vehicle

Grahic Jump Location
Fig. 2

P1, a by-wire test vehicle

Grahic Jump Location
Fig. 3

Equilibrium sideslip versus steer angle, Ux = 8 m/s

Grahic Jump Location
Fig. 4

Equilibrium yaw rate versus steer angle, Ux = 8 m/s

Grahic Jump Location
Fig. 5

Equilibrium rear longitudinal force versus steer angle, Ux = 8 m/s

Grahic Jump Location
Fig. 6

Magnitude of total rear force versus steer angle, Ux = 8 m/s. The rear tire friction limit is indicated by a dashed line.

Grahic Jump Location
Fig. 7

Equilibrium front lateral force versus steer angle, Ux = 8 m/s. The front tire friction limits are indicated by dashed lines.

Grahic Jump Location
Fig. 8

Flow field of sideslip and yaw rate state derivatives for Ux = Uxeq = 8  m/s indicating an open-loop unstable drift equilibrium

Grahic Jump Location
Fig. 9

2D sections of invariant set, Ux = 8–8.6 m/s. The eigenvector corresponding to the stable eigenvalue of the open-loop linearization is shown with a dashed line.

Grahic Jump Location
Fig. 10

Sideslip compared to βeq (top) and yaw rate compared to rdes (bottom) during experimental run

Grahic Jump Location
Fig. 11

Front lateral force command (top) and steering command (bottom) during experimental run

Grahic Jump Location
Fig. 12

Longitudinal velocity (top) and rear drive force command (bottom) during experimental run



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In