Deep Dynamics: Vehicle Dynamics Modeling with a Physics-Constrained Neural Network for Autonomous Racing

TL;DR

The paper tackles high-speed autonomous racing dynamics by integrating physics with deep learning through a physics-constrained neural network (PCNN) called Deep Dynamics. It learns unknown single-track model coefficients within physical bounds using a History τ and a Physics Guard, enabling accurate open- and closed-loop predictions and seamless integration with MPC. Compared to the prior Deep Pacejka Model, Deep Dynamics delivers substantially lower prediction errors, more physically plausible parameter estimates, and real-time inference on standard GPUs, while eliminating the need for exact inertia values. The approach is validated on both real Indy car data and a 1:43 scale simulator, demonstrating superior trajectory prediction and control performance, with potential for deployment on full-scale autonomous racecars.

Abstract

Autonomous racing is a critical research area for autonomous driving, presenting significant challenges in vehicle dynamics modeling, such as balancing model precision and computational efficiency at high speeds (>280km/h), where minor errors in modeling have severe consequences. Existing physics-based models for vehicle dynamics require elaborate testing setups and tuning, which are hard to implement, time-intensive, and cost-prohibitive. Conversely, purely data-driven approaches do not generalize well and cannot adequately ensure physical constraints on predictions. This paper introduces Deep Dynamics, a physics-constrained neural network (PCNN) for vehicle dynamics modeling of an autonomous racecar. It combines physics coefficient estimation and dynamical equations to accurately predict vehicle states at high speeds and includes a unique Physics Guard layer to ensure internal coefficient estimates remain within their nominal physical ranges. Open-loop and closed-loop performance assessments, using a physics-based simulator and full-scale autonomous Indy racecar data, highlight Deep Dynamics as a promising approach for modeling racecar vehicle dynamics.

Figures (4)

• Figure 1: The dynamic single-track vehicle model.
• Figure 2: Deep Dynamics uses a DNN to learn a vehicle's single-track model coefficients from historical states and control inputs.
• Figure 3: A real-world, full-scale autonomous racecar was used to collect data at the Putnam Park Road Course and Las Vegas Motor Speedway. In simulation, laps were driven on Track 1 and Track 2.
• Figure 4: Timestamped trajectories for MPC run using estimated coefficients from DPM (GT, +20, -20) and DDM in the vehicle dynamics simulator.