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

Abstract

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.