Condition-Number Adaptive-Weight PINN (A-PINN): a High-Fidelity and Real-Time Forward Kinematics Solver for Stewart Platforms

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. Training results on a Stewart platform demonstrate a pose RMSE of 0.049 mm and 0.005 degrees with 0.141 ms inference latency, alongside a reduction in relative Jacobian error to 0.40%. 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.