Energy-constrained Lagrangian neural networks for data-driven modeling of robotic systems: Method and prosthetic applications

Abstract

Dynamic models are crucial for model-based control of multi-degree-of-freedom systems, particularly in robotic applications. While traditional methodologies, including Newtonian and Lagrangian mechanics, have been widely employed, they exhibit limitations in accurately capturing unstructured factors such as joint friction and transmission flexibility. Inspired by the physical interpretability inherent in Lagrangian mechanics and the universal approximation capabilities of neural networks, this paper introduces a novel Energy-constrained Lagrangian Neural Network (EnLNN) modeling framework. The proposed EnLNN decomposes the acceleration field into conservative and nonconservative components, with the former represented by a Lagrangian Neural Network (LNN) and the latter by a feedforward neural network (FNN). A distinctive feature of the EnLNN is its incorporation of energy constraints, which allows the conservative component to preserve energy to the greatest extent, thereby mitigating the misallocation of force fields between conservative and nonconservative components. This approach yields a more precise Lagrangian representation than conventional LNNs. The efficacy of the EnLNN modeling approach was evaluated through numerical simulation of a double pendulum system and experimental validation on a lower limb prosthesis. The results substantiate that the EnLNN framework effectively distinguishes conservative and nonconservative components from empirical data while maintaining high modeling accuracy and demonstrating robust extrapolation capabilities.