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

Abstract Forward kinematics is fundamental to robotic perception, planning, and control, yet it is often modeled as a deterministic mapping that neglects variability arising from sensor noise, actuation imperfections, calibration errors, and unmodeled dynamics. Existing uncertainty estimation methods either rely on local linearization, which is limited in capturing nonlinear and configuration-dependent effects, or use sampling-based techniques such as Monte Carlo simulation, which incur substantial computational cost. Learning-based alternatives frequently assume homoscedastic uncertainty and therefore fail to represent the state-dependent variability observed in real robotic systems. This article proposes a physics-informed framework for fast, configuration-dependent uncertainty quantification in robot forward kinematics using experimental data. A physics-based forward kinematics model is retained as the deterministic mean, while heteroscedastic residual uncertainty is learned as a configuration-dependent function from real-robot observations. The method is evaluated on a UR3 industrial manipulator and compared with homoscedastic and representative learning-based baselines. Experimental results demonstrate improved probabilistic calibration, reliable empirical coverage for both translational and rotational components, and microsecond-level central processing unit (CPU) inference, supporting real-time uncertainty-aware robotic applications.