Hierarchical Autonomous Navigation for Differential-Drive Mobile Robots Using Deep Learning, Reinforcement Learning, and Lyapunov-Based Trajectory Control

Ramón Jaramillo-Martínez, Ernesto Chavero-Navarrete, Teodoro Ibarra-Pérez

Autonomous navigation in mobile robots operating in dynamic and partially known environments demands the coordinated integration of perception, decision-making, and control while ensuring stability, safety, and energy efficiency. This paper presents an integrated navigation framework for differential-drive mobile robots that combines deep learning-based visual perception, reinforcement learning (RL) for high-level decision-making, and a Lyapunov-based trajectory reference generator for low-level motion execution. A convolutional neural network processes RGB-D images to classify obstacle configurations in real time, enabling navigation without prior map information. Based on this perception layer, an RL policy generates adaptive navigation subgoals in response to environmental changes. To ensure stable motion execution, a Lyapunov-based control strategy is formulated at the kinematic level to generate smooth velocity references, which are subsequently tracked by embedded PID controllers, explicitly decoupling learning-based decision-making from stability-critical control tasks. The local stability of the trajectory-tracking error is analyzed using a quadratic Lyapunov candidate function, ensuring asymptotic convergence under ideal kinematic assumptions. Experimental results demonstrate that while higher control gains provide faster convergence in simulation, an intermediate gain value (K = 0.5I) achieves a favorable trade-off between responsiveness and robustness in real-world conditions, mitigating oscillations caused by actuator dynamics, delays, and sensor noise. Validation across multiple navigation scenarios shows average tracking errors below 1.2 cm, obstacle detection accuracies above 95% for human obstacles, and a significant reduction in energy consumption compared to classical A* planners, highlighting the effectiveness of integrating learning-based navigation with analytically grounded control.