Physics-Constrained Residual Learning for Refined Dynamic Identification and Robust Torque Estimation

Physically consistent and robust dynamics identification of industrial robots via PINN-based residual compensation

Identifying the Residual Dynamics of a Delta Robot: A Sparse Regression Approach for Rigid-Body Models

Accurate torque models are critical for high-performance model-based control of industrial robots, yet nominal rigid-body inverse dynamics often neglect friction and other nonlinear effects. This paper proposes a gray-box approach that identifies a sparse, interpretable residual torque model directly in torque space by regressing the mismatch between a nominal inverse-dynamics model and motor-current-based torque measurements collected from production-like pick-and-place motions of a parallel delta manipulator. The resulting correction improves agreement between predicted and measured torques on a fully held-out, unseen trajectory while retaining a compact structure with physically plausible velocity- and acceleration-dependent terms. A systematic hyperparameter study is conducted to quantify the sparsity-accuracy tradeoff and to select a model suitable for real-time model-based feedforward control.

Physics-Informed Learning for Forward Kinematics of Robotic Manipulators Under Uncertainty

Forward kinematics is a fundamental component of robotic perception, planning, and control, yet it is commonly treated as a deterministic mapping that neglects variability arising from sensor noise, actuation imperfections, calibration errors, and unmodeled physical effects. Existing approaches to kinematic uncertainty estimation generally fall into three categories: analytical methods based on local linearization, which are computationally efficient but limited in capturing nonlinear and configuration-dependent effects; sampling-based techniques such as Monte Carlo simulation, which offer high accuracy at substantial computational cost; and learning-based methods that often assume homoscedastic uncertainty, thereby failing to represent the state-dependent variability observed in real robotic systems. This paper proposes a physics-informed framework for fast, configuration-dependent uncertainty quantification of robot forward kinematics using experimental data. A calibrated physics-based forward kinematics model is retained as a deterministic mean, while heteroscedastic uncertainty is learned as a configuration-dependent residual from real robot observations. The proposed approach is evaluated on a UR3 industrial manipulator and compared against homoscedastic baselines as well as representative learning-based uncertainty models, with additional sensitivity analyses used to assess robustness with respect to key architectural and training parameters. Experimental results demonstrate that the learned uncertainty consistently bounds the observed end-effector variability for both translational and rotational components, while achieving improved probabilistic calibration, reliable empirical coverage, and significantly lower inference cost. The method supports microsecond-level CPU inference, making it suitable for real-time uncertainty-aware robotic applications.

Physics-Embedded Neural Feedback Linearization for Hydraulic Robot Joint Force Control with EKF Priors

While hydraulic robots excel in high load capacity and interference immunity, achieving precise force tracking is hindered by complex fluid dynamics, system nonlinearities, and time-varying disturbances. This paper introduces a Physics-Enhanced Neural Network (PENN) approach. This method employs an Extended Kalman Filter (EKF) as a teacher to guide the prediction of hydraulic force dynamics. By effectively leveraging both data and physical baselines, this method achieved significant performance improvements, with the MSE, RMSE, and MAE decreasing by 85.5%, 61.9%, and 65.3%, respectively, compared with the traditional EKF baseline. Consequently, we propose a Neural Input-Output Feedback Linearization (NFBL) Proportional-Integral (PI) controller to globally linearize the nonlinear dynamics and track the desired force. The online EKF-PENN identifies the autonomous response and control gain terms of the hydraulic affine nonlinear system, providing accurate control variables under designed operating conditions. The method compensates for the pressure drop during hydraulic cylinder piston movement via flow compensation, while feedforward techniques significantly enhance force control response. Experimental results verify the effectiveness of these proposed methods. The proposed method can significantly improve the locomotion performance of hydraulically actuated legged robots.

Hybrid Computed Torque Control and Soft Actor-Critic Framework for Sample-Efficient Robotic Manipulator Control

Reinforcement Learning (RL) has emerged as a promising approach for robotic control, enabling agents to learn control policies through interaction with complex and dynamic environments. However, standalone RL methods often suffer from poor sample efficiency, limiting their practicality for real-world robotic systems. To address this limitation, recent studies have combined RL with classical controllers such as proportional–integral–derivative (PID) control, where the classical controller provides a baseline policy and RL learns residual corrective actions. Nevertheless, conventional PID controllers do not explicitly incorporate the full nonlinear manipulator dynamics.This paper proposes a physics-informed residual reinforcement learning framework that combines Computed Torque Control (CTC) with Soft Actor-Critic (SAC) for trajectory tracking of a 2-DOF robotic manipulator. The CTC component utilises analytical Lagrangian dynamics to provide a nominal control torque, while SAC learns bounded residual corrections to compensate for model uncertainties and unmodelled effects. The proposed framework is evaluated in CoppeliaSim and compared against CTC-only, RL-only, and PID+SAC baselines under identical experimental conditions.Experimental results demonstrate that the proposed CTC+SAC framework achieves the lowest mean and steady-state tracking errors among all evaluated methods, with a 4.9% reduction in mean error over RL-only and a 3.3% reduction over PID+SAC within the considered simulation setup. The results suggest that incorporating analytical robot dynamics into the residual learning framework improves tracking performance and sample efficiency compared to both pure RL and classical controller baselines.

Physics-guided online adaptive vehicle dynamics modeling via decoupled residual learning

A Decoupled Hybrid Residual Model for online adaptive prediction of vehicle dynamics is proposed, demonstrating that the proposed architecture effectively improves prediction accuracy, robustness, and implementation feasibility under varying driving conditions.