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Research Papers

Feedback Game-Based Shared Control Scheme Design for Emergency Collision Avoidance: A Fuzzy-Linear Quadratic Regulator Approach

[+] Author and Article Information
Xuewu Ji

The State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China
e-mail: Jixw@mail.tsinghua.edu.cn

Kaiming Yang

The State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China
e-mail: ykm739@126.com

Xiaoxiang Na

Department of Mechanical Engineering,
Cambridge University,
Cambridge CB2 1PZ, UK
e-mail: xnhn2@cam.ac.uk

Chen Lv

Advanced Vehicle Engineering Center,
Cranfield University,
Cranfield MK43 0AL, UK
e-mail: C.Lyu@cranfield.ac.uk

Yulong Liu

The State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China
e-mail: liuyl16@mails.tsinghua.edu.cn

Yahui Liu

The State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China
e-mail: liuyahui@tsinghua.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 30, 2017; final manuscript received February 6, 2019; published online March 25, 2019. Assoc. Editor: Mahdi Shahbakhti.

J. Dyn. Sys., Meas., Control 141(8), 081005 (Mar 25, 2019) (13 pages) Paper No: DS-17-1640; doi: 10.1115/1.4042880 History: Received December 30, 2017; Revised February 06, 2019

Driver-machine shared control scheme opens up a new frontier for the design of driver assistance system, especially for improving active safety in emergency scenario. However, the driver's stress response to steering assistance and strong tire nonlinearity are main challenges suffered by controller designing for collision avoidance. These unfavorable factors are particularly pronounced during emergency steering maneuvers and sharply degrade shared control performance. This paper proposes a fuzzy-linear quadratic regulator (LQR) game-based control scheme to simultaneously enhance vehicle stability while compensating driver's inappropriate steering reaction in emergency avoidance. A piecewise linear-based Takagi–Sugeno (T–S) fuzzy structure is presented to mimic driver's knowledge about vehicle lateral nonlinearity, and the control authority is shared between driver and emergency steering assistance (ESA) system through steer-by-wire (SBW) assembly. An identical piecewise internal model is chosen for ESA and the shared lane-keeping problem is modeled as a fuzzy linear quadratic (LQ) problem, where the symmetrical fuzzy structure further enhances vehicle's ability to handle extreme driving conditions. In particular, the feedback Stackelberg equilibrium solutions of the fuzzy-LQ problem are derived to describe the interactive steering behavior of both agents, which enables the ESA to compensate driver's irrational steering reaction. Hardware-in-the-loop (HIL) experiment demonstrates the ESA's capability in compensating driver's aggressive steering behavior, as well as the copiloting system's excellent tracking and stabilizing performance in emergency collision avoidance.

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Figures

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Fig. 3

Piecewise linear approximation and actual nonlinear lateral dynamic surfaces comparison: (a) v˙y surface given by PWA model, (b) ψ¨y surface given by PWA model, (c) v˙y surface given by MF model, (d) ψ¨y surface given by MF model, (e) v˙y errors between MF and PWA model, and (f) ψ¨y errors between MF and PWA model

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Fig. 4

Instantaneous stiffness approximations for the front and rear tires: (a) front tire and (b) rear tire

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Fig. 5

Fuzzy partitions with scheduling in front and rear stiffness

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Fig. 6

Open-loop trajectories of the MF-based nonlinear vehicle model (solid line) and T–S model (dash-dotted line)

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Fig. 7

Comparison of T–S fuzzy-based and PWA-based DLC control

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Fig. 10

Basic structure of the HIL experiment system

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Fig. 11

Target paths of both agents in the two cases

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Fig. 8

Steer-by-wire interface for shared control system

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Fig. 14

Steering inputs and vehicle trajectories at the speed of 30 m/s on μ = 0.6 road: (a) trajectories of the vehicle and (b) steering inputs of both agents

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Fig. 2

Vehicle lateral dynamics model and its motion within the road

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Fig. 17

Vehicle states responses of the three schemes on μ = 0.5 road: (a) path tracking performances, (b) steering angle input by the driver and the ESA, (c) motion response comparison, and (d) phase plane trajectory of the tire slip angles

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Fig. 18

Membership values of each linearized cell for the front and rear tire forces given by the proposed FB shared scheme on a μ = 0.5 road

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Fig. 19

Tracking and stabilizing performance evaluation of the three schemes in emergency collision avoidance: (a) tracking performance and (b) stabilizing performance

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Fig. 9

Driver and ESA's target path preview

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Fig. 1

Structure of symmetrical shared steering control scheme for emergency collision avoidance

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Fig. 12

Steering gains of the driver: (a) for driver's yaw angle preview and (b) for ESA's yaw angle preview

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Fig. 13

Steering inputs and vehicle trajectories at the speed of 20 m/s on μ = 1 road: (a) trajectories of the vehicle and (b) steering inputs of both agents

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Fig. 15

Vehicle states responses of the three schemes on μ = 1 road: (a) path tracking performances, (b) steering angle input by the driver and the ESA, (c) motion response comparison, and (d) phase plane trajectory of the tire slip angles

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Fig. 16

Membership values of each linearized cell for the front and rear tire forces on μ = 1 road

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