Comparative Study of Physics-Enhanced Deep Learning Methods for Predicting Behavior of a Dynamic Mobile Robotic System subject to Coulomb Friction

Dynamic systems such as robotic arms, drones, and satellites exhibit complex underlying physics that must be understood to ensure safe and reliable operations. The ability to predict the behavior of dynamic systems is helpful for human operators and autonomous agents to complete successful missions. Predicting the behavior of a system can be used for control, collision avoidance, or fault detection. However, these predictions can be time-consuming and computationally inefficient, as they often rely on numerical solutions of differential equations that represent the physics models. These drawbacks prevent the use of behavior prediction in real-time feedback systems, such as digital twins or model-based control. These limitations motivate the exploration of alternative approaches that can provide fast, accurate predictions while maintaining physical consistency. Deep learning has emerged as a promising tool for approximating the behavior of dynamic systems. In this study, three deep learning approaches—a Deep Neural Network (DNN), a Physics-Guided Neural Network (PGNN), and a Physics-Informed Neural Network (PINN)—are implemented to predict the dynamic behavior of a mobile robotic system. The goal is to compare their accuracy and computational efficiency against traditional numerical solvers. A physics-based simulation of the mobile robot performing a task is used to generate training data. That task is to reach a target objective with its end effector. Each simulation uses a random target to create variation in the training data, and the results consist of state trajectories and their corresponding time steps. Once trained, these models approximate the physics-based solutions and provide rapid predictions of future system states. Each approach incorporates physics in a unique way. The DNN is a purely data-driven model that minimizes the mean squared error (MSE) between predictions and ground-truth simulation data. The PGNN extends this approach by incorporating physics-based constraints into the loss function, using the predicted states in forward kinematics and dynamics equations to enforce consistency with real-world physics. The PINN further enhances this by using numerical gradients of the predicted states in place of explicit state predictions, ensuring that the learned representations adhere to governing physical laws. Testing of the trained models was conducted by running simulations of the mobile robot system with chosen target objectives. Using known target objectives, rather than random ones, allowed for a fair comparison of each model. Experimental results indicate that all three models achieve accurate predictions of the system’s kinematics and dynamics while significantly reducing computational costs compared to traditional ordinary differential equation (ODE) solvers. Speed comparisons show that deep learning models can generate predictions orders of magnitude faster than iterative solvers, making them viable for real-time feedback applications. However, the added complexity of physics-informed loss functions comes with increased training time and model tuning requirements. The findings highlight the potential of deep learning to enhance real-time behavior prediction for dynamic systems. This has broad applications in robotics, autonomous navigation, and adaptive control. Future work will focus on extending these methods to more complex multi-body systems, looking into different deep learning techniques, and testing the prediction algorithms using a real-world robotics system.