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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.

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References

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Figures

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Fig. 1

Bicycle model of a RWD vehicle

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Fig. 2

P1, a by-wire test vehicle

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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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.

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Fig. 7

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

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Fig. 8

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

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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.

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Fig. 10

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

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Fig. 11

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

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Fig. 12

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

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