L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking

2026-05-26

AI Summary

In dynamically uncertain environments, conventional control methods suffer degraded performance, while existing data-driven approaches often struggle with low sample efficiency and lack of stability guarantees. This work proposes the L-Learning framework, which uniquely integrates Lyapunov stability theory with Lagrangian mechanics to explicitly learn a system’s energy function from data, thereby embedding closed-loop stability assurance directly into the learning process. By leveraging this principled approach, the method achieves significantly improved trajectory tracking accuracy while substantially reducing sample complexity—all without compromising theoretical stability. Consequently, L-Learning unifies high sample efficiency, strong stability guarantees, and superior tracking performance, making it well-suited for real-world robotic control applications.

Abstract

This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.

Problem

• robot tracking
• stability guarantees
• sample complexity
• dynamic environments
• uncertain environments

Innovation

• Lyapunov stability
• Lagrangian mechanics
• data-driven control
• energy function learning
• sample efficiency