Research ArticleAUTONOMOUS VEHICLES

Neural network vehicle models for high-performance automated driving

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Science Robotics  27 Mar 2019:
Vol. 4, Issue 28, eaaw1975
DOI: 10.1126/scirobotics.aaw1975
  • Fig. 1 Simple feedforward-feedback control structure used for path tracking on an automated vehicle.

    Possible models for use in generating feedforward steering commands consist of the physics-based model or a neural network model.

  • Fig. 2 Automated and human driving.

    (A) “Shelley,” Stanford’s autonomous Audi TTS designed to race at the limits of handling. (B) Human driver’s MAD median path projected onto the first five turns of Thunderhill Raceway Park in Willows, California. (C) Shelley’s MAD median path scaled by a factor of 4 to highlight relative differences. (D) MAD median path for both the human driver and Shelley (in red) along with Shelley’s mean absolute deviation from the intended path (in blue). (E) Segment times from the champion amateur race driver benchmarked to Shelley.

  • Fig. 3 Neural network dynamics model with input design based on the physics-based model.

    FC1 and FC2 denote fully connected layers in our two-layer feedforward neural network dynamics model.

  • Fig. 4 Experimental model comparisons.

    (A) Experiment track map, showing corresponding sections 1, 2, and 3 in experimental data plots. (B) Picture of Volkswagen GTI experimental autonomous race vehicle. (C) Experimental comparison between physics-based controller and neural network controller showing lower tracking error at the limits on oval test track. (D) Histogram showing difference in lateral error distributions of neural network and physics-based controllers on oval test track.

  • Fig. 5 Training and testing.

    (A) Training process for simulated data including multiple effects of model mismatch between data generation and optimization models. (B) Testing process for simulated data, showing generalization capability of learned models. (C) Training process for real collected vehicle data under various friction conditions. (D) Testing process for real vehicle data showing generalization capabilities of learned models.

  • Fig. 6 Physics-based model and tire model.

    (A) Schematic of planar bicycle model including error states, referred to in this paper as the physics-based model. (B) Front and rear tire curves, with brush Fiala model fit to empirical tire data.

  • Fig. 7 Schematic of control process using a learned neural network model.
  • Table 1 Physics model definitions.
    ParameterSymbolUnits
    Front axle to CGam
    Rear axle to CGbm
    Front lateral forceFyfN
    Front longitudinal forceFxfN
    Front tire slipαfrad
    Rear lateral forceFyrN
    Rear tire slipαrrad
    Steer angle inputδrad
    Yaw raterrad/s
    Sideslipβrad
    Lateral path deviationem
    Heading deviationΔΨrad
    Longitudinal velocityUxm/s
    Lateral velocityUym/s

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/4/28/eaaw1975/DC1

    Fig. S1. Measured and predicted sideslip from experimental control comparison.

    Fig. S2. Measured longitudinal speeds from experimental control comparison.

    Table S1. Test dataset results from simulation learning study.

    Table S2. Test dataset results from experimental data learning study.

    Movie S1. Neural network controller implemented on automated GTI, tested on oval track at Thunderhill Raceway Park.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Measured and predicted sideslip from experimental control comparison.
    • Fig. S2. Measured longitudinal speeds from experimental control comparison.
    • Table S1. Test dataset results from simulation learning study.
    • Table S2. Test dataset results from experimental data learning study.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Neural network controller implemented on automated GTI, tested on oval track at Thunderhill Raceway Park.

    Files in this Data Supplement:

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