PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving

TL;DR

PhysORD, a neural-symbolic approach integrating the conservation law, i.e., the Euler-Lagrange equation, into data-driven neural models for motion prediction in off-road driving, outperforms existing methods both in accuracy and efficiency and demonstrates data-efficient learning and generalization ability in long-term prediction.

Abstract

Motion prediction is critical for autonomous off-road driving, however, it presents significantly more challenges than on-road driving because of the complex interaction between the vehicle and the terrain. Traditional physics-based approaches encounter difficulties in accurately modeling dynamic systems and external disturbance. In contrast, data-driven neural networks require extensive datasets and struggle with explicitly capturing the fundamental physical laws, which can easily lead to poor generalization. By merging the advantages of both methods, neuro-symbolic approaches present a promising direction. These methods embed physical laws into neural models, potentially significantly improving generalization capabilities. However, no prior works were evaluated in real-world settings for off-road driving. To bridge this gap, we present PhysORD, a neural-symbolic approach integrating the conservation law, i.e., the Euler-Lagrange equation, into data-driven neural models for motion prediction in off-road driving. Our experiments showed that PhysORD can accurately predict vehicle motion and tolerate external disturbance by modeling uncertainties. The learned dynamics model achieves 46.7% higher accuracy using only 3.1% of the parameters compared to data-driven methods, demonstrating the data efficiency and superior generalization ability of our neural-symbolic method.

Figures (5)

• Figure 1: Overview of PhysORD and motion prediction task. Given the action, initial state, and observation, PhysORD predicts an accurate long-term trajectory (in the bottom right) by combining neural methods and the conservation law.
• Figure 2: The Architecture of PhysORD. The neural networks contain two MLPs, $dU_\theta$ for potential energy prediction and $f_\theta$ for external force estimation. Utilizing these estimated physical symbols, the symbolic model calculates the next state $\hat{s}_{t+1}$ from the current state $s_t$. The error between $\hat{s}_{t+1}$ and ground truth is backpropagated to optimize the MLPs.
• Figure 3: Comparison of training efficiency. This illustrates the lowest RMSE error achieved by both TartanDrive and PhysORD at various cumulative time points.
• Figure 4: Accuracy comparison of data efficiency. The RMSE errors for TartanDrive and PhysORD when trained with various amounts of data from 1% to 100% of training set.
• Figure 5: Qualitative analysis of PhysORD versus TartanDrive. Trajectories vary by speed change across rows and by motion type across columns, with speed and acceleration detailed in each subplot over these 20-time steps.