Physics informed machine learning model for inverse dynamics in robotic manipulators

In the field of robotic modelling, the challenge of parameter estimation using limited joint monitoring data presents a substantial hurdle for both traditional physics-based methods (PBMs) and machine learning (ML) techniques. PBMs grapple with modelling uncertainties, variable working conditions, diverse robotic configurations, and incomplete parameter information. ML methods face hurdles in maintaining physical consistency, interpretability, and the need for extensive training data. In response to these challenges, this paper proposes a novel approach, the Equation Embedded Neural Network (E2NN), enhanced by an innovative Liquid mechanism, which effectively blends the strengths of PBMs and ML to surmount their inherent limitations. Its primary contributions encompass: (1) a pioneering review and synthesis of hybrid frameworks integrating physical principles with ML, (2) the development and rigorous validation of the E2NN framework, and (3) the introduction of a novel physics regulator and dynamic Liquid mechanism. Particularly, the proposed E2NN leverages inverse dynamics equations to construct specialized neural network layers, featuring activation functions and interconnections expressed as composition operators, thus explicitly encoding physical knowledge. This architectural choice proves especially well-suited for tasks involving inverse dynamics and dynamic planning of robotic manipulators. The accompanying Liquid mechanism allows for dynamic adaptation of interlayer connections in response to input data, enabling real-time adjustments to changing inputs and equations of motion, ultimately enhancing flexibility and performance. Quantitative assessments of E2NN reveal its compelling performance, yielding a Mean Absolute Error (MAE) of 0.10716, closely aligned with the Benchmark Deep Residual Shrinkage Network's (DRSN) MAE of 0.10415, showcasing its competitive efficacy while achieving higher computational efficiency and a more compact model size. Robustness evaluations further confirm E2NN's adaptability, as it attains a Mean Squared Error (MSE) of 0.3, outperforming DRSN's 1.1 under varying working conditions. E2NN excels in torque trajectory fitting, achieving an impressive accuracy rate of 97.1%, underscoring its practical effectiveness. Furthermore, E2NN excels in torque prediction and parameter identification for inverse dynamics models, particularly when confronted with limited joint data and variable friction conditions. It substantially improving the discernment of robot dynamics and enhancing its applicability in real-world trajectory fitting.