Lagrangian Neural Network-Based Control: Improving Robotic Trajectory Tracking Via Linearized Feedback
Manuel Weiss, Alexander Pawluchin, Jan-Hendrik Ewering, Thomas Seel, Ivo Boblan
AI summary
Problem
Traditional computed torque control requires precise analytic dynamics models that are often impractical for complex robots, while existing learning-based controllers suffer from poor generalization, high data demands, or inadequate disturbance rejection within feedback-linearization frameworks.
Approach
The authors embed a Lagrangian neural network that learns the robot's inverse dynamics directly inside a computed torque control loop, replacing the need for an explicit analytic model while preserving physical consistency and stabilizing closed-loop error dynamics.
Key results
- Reduces joint-space tracking RMSE by up to 34.3% compared to model-based CTC with identical gains
- Outperforms PINN, DNN, and feedforward LNN baselines in both accuracy and data efficiency
- Maintains robust tracking under parameter uncertainties and external end-effector disturbances
- Achieves high-precision control using only approximately 100 seconds of real-world training data
Why it matters
It provides a physically consistent, data-efficient control alternative that narrows the performance gap between classical model-based and learned strategies for real-world robotic systems.
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 net- work (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.