Newtonian neural ordinary differential equations method for dynamics identification of serial manipulators with LuGre friction

Nonlinear dynamic parameter identification of manipulators is essential for high precision control. However, existing approaches have inherent drawbacks: Model-free methods are purely data driven, lacking physical constraints and poor interpretability; Model-based methods rely on linearization, failing to capture nonlinear friction and unknown dynamics; Hybrid methods (e.g., Lagrangian/Hamiltonian Neural Networks (LNNs/HNNs)) integrate physical constraints but suffer from inadequate interpretability and limited generalization due to meaningless subnetwork parameters. Additionally, inverse dynamics-based Differentiable Newton-Euler Algorithm requires joint acceleration—hard to measure directly, usually derived from position signal second-order differences, amplifying noise and degrading accuracy. To address these issues, this paper proposes a novel Newtonian Neural Ordinary Differential Equations method. Forward rigid body dynamics are modeled via DiffNEA, joint friction via the LuGre model, unknown dynamics via hidden states, a Gated Recurrent Unit is integrated to capture temporal memory and output residual torque, and a three-stage progressive optimization strategy is adopted. As the first work fusing DiffNEA with NODEs, the method optimizes parameters through state loss, enabling simultaneous static/dynamic friction identification without joint acceleration while ensuring physical consistency. Experiments on a 6-axis serial manipulator show superiority over LNNs: 25.6% lower training error, 21.4% lower state prediction error, and over 96% parameter reduction, lower memory footprint, and faster inference time, while accurately reproducing nonlinear dynamics. Dominated by a differentiable physics model with physically meaningful parameters, its residual learning module acts as an explicit dynamic compensator, enhancing transparency and interpretability—critical for practical high precision control. The proposed NNODEs-based dynamic modeling method incorporating LuGre friction: (a) Hybrid learning of dynamics, friction and residual dynamics; (b) Multi-stage iterative learning. • Proposes a unified framework that seamlessly integrates physics-based models (DiffNEA) with data-driven Neural ODEs (NODEs), enabling the joint identification of rigid body dynamics, friction dynamics (via a differentiable LuGre model), and unknown residual dynamics in a single end-to-end learning process. • Embeds physically meaningful parameters (e.g., dynamic and LuGre friction parameters with core state ) directly into the learnable network, aligning model parameters with real manipulator properties. This ensures strong physical interpretability and enables friction and rigid body dynamics to be consistently co-optimized. • Introduces a residual dynamics module that explicitly models hysteresis and temporal memory effects. An input normalization layer is incorporated to harmonize multi-dimensional physical variables (e.g., position, velocity, torque), improving training stability and reinforcing physical consistency. • Implements a phased training strategy guided by stability and loss thresholds, ensuring robust and stable convergence of the hybrid model through systematic parameter optimization. • Extensive validation on a real 6-DOF manipulator demonstrates comprehensive performance gains: 16.2% lower training error than HNNs, 21.4% lower state prediction error than LNNs, lower memory footprint, faster inference time, and over 96% parameter reduction—while ensuring physical consistency and delivering a more reliable and efficient dynamic model.