Advanced Modeling and Adaptive Control of a Nonholonomic Differential-Drive Mobile Robot Using Deep Physics-Informed Neural Networks

This research integrates deep physics-informed neural networks (PINNs) with Krupková’s geometrical theory to propose a novel framework for modeling and directing nonholonomic robotic systems. We derive reduced equations of motion for a differential-drive mobile robot under dynamic constraints, such as time-varying payloads and terrain-induced friction, using geometrical mechanics. Deep PINNs are employed to solve these nonlinear equations and develop an adaptive control framework for robust trajectory tracking and motion planning. The originality lies in the seamless fusion of classical geometrical mechanics with modern deep learning, while the novelty is demonstrated through the application of deep PINNs to address nonholonomic constraints and nonconservative effects. Under nominal, high payload, and high friction situations, extensive numerical comparisons with Runge–Kutta (RK4) confirm the method’s higher accuracy (36–60% lower RMSE) and efficiency (25–30% faster computation). This work develops nonholonomic mechanics and robotics, with applications in autonomous navigation and planetary exploration.