Data-driven inverse dynamics modeling using neural-networks and regression-based techniques

Abstract This research proposes a novel approach for the residual modeling of inverse dynamics employed to control a real robotic device. Specifically, we use techniques based on linear regression for residual modeling while a nominal model is discovered by physics-informed neural networks such as the Lagrangian Neural Network and the Feedforward Neural Network. We introduce an efficient online learning mechanism for the residual models that utilizes rank-one updates based on the Sherman–Morrison formula. This enables faster adaptation and updates to effects not captured by the neural networks. While the time complexity of updating the model is comparable to other successful learning methods, the method excels in prediction complexity, which depends solely on the model dimension. We propose two online learning strategies: a weighted approach that gradually diminishes the influence of past measurements on the model, and a windowed approach that sharply excludes the oldest data from impacting the model. We explore the relationship between these strategies, offering recommendations for parameter selection and practical application. Special attention is given to optimizing the computation time of the weighted approach when recomputation techniques are implemented, which results in comparable or even lower execution times of the weighted controller than the windowed one. Additionally, we assess other methods, such as the Woodbury identity, QR decomposition, and Cholesky decomposition, which can be implicitly used to update the model. We empirically validate our approach using real data from a 2-degrees-of-freedom flexible manipulator, demonstrating consistent improvements in feedforward controller performance.