Condition-Number Adaptive-Weight PINN (A-PINN): A High-Fidelity and Real-Time Forward Kinematics Solver for Stewart Platforms
Xinyu Tian, Junlin Xiao, Hang Xu, Xing Hou, Fuhua Jia, Xiaoying Yang, Salman Ijaz, Adam Rushworth
Abstract
Parallel kinematic mechanisms (PKMs) are widely adopted in precision and heavy-load applications, yet obtaining the requisite forward kinematics (FK) for closed-loop control remains a challenge. FK in PKMs typically lack a unique closed-form solution, necessitating iterative numerical solvers that are prone to ill-conditioning near singular configurations. This letter proposes a condition-number adaptive physics-informed neural network that uses the normalized Jacobian condition number to modulate physics-based loss terms. The training objective enforces an implicit Sobolev-type regularization via operator consistency, encouraging kinematic feasibility while avoiding explicit supervision that depends on unstable Jacobian inversion in ill-conditioned regions. Real-world experiments verify 1 kHz operation as a kinematic observer for real-time velocity estimation, confirming the method’s foundation for high-rate feedback and gradient-based control pipelines.
BibTeX
@inproceedings{ral2026_conditionnumbera,
title = {Condition-Number Adaptive-Weight PINN (A-PINN): A High-Fidelity and Real-Time Forward Kinematics Solver for Stewart Platforms},
author = {Xinyu Tian and Junlin Xiao and Hang Xu and Xing Hou and Fuhua Jia and Xiaoying Yang and Salman Ijaz and Adam Rushworth and Donglei Sun},
booktitle = {RA-L 2026},
year = {2026}
}