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

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.