Lagrangian Neural Network-Based Control: Improving Robotic Trajectory Tracking via Linearized Feedback

Abstract

This paper introduces a control framework that leverages Lagrangian neural networks (LNNs) for computed torque control (CTC) of robotic systems with unknown dynamics. Unlike prior LNN-based controllers that are placed outside the feedback-linearization framework (e.g., feedforward), we embed an LNN inverse-dynamics model within a CTC loop, thereby shaping the closed-loop error dynamics. This strategy, referred to as LNN-CTC, ensures a physically consistent model and improves extrapolation, requiring neither prior model knowledge nor extensive training data. The approach is experimentally validated on a robotic arm with four degrees of freedom and compared with conventional model-based CTC, physics-informed neural network (PINN)-CTC, deep neural network (DNN)-CTC, an LNN-based feedforward controller, and a PID controller. Results demonstrate that LNN-CTC significantly outperforms model-based baselines by up to 30% in tracking accuracy, achieving high performance with minimal training data. In addition, LNN-CTC outperforms all other evaluated baselines in both tracking accuracy and data efficiency, attaining lower joint-space RMSE for the same training data. The findings highlight the potential of physics-informed neural architectures to generalize robustly across various operating conditions and contribute to narrowing the performance gap between learned and classical control strategies.