PhyNRnet: Physics-Informed Newton–Raphson Network for Forward Kinematics Solution of Parallel Manipulators

Abstract Despite significant performance advantages, the intractable forward kinematics have always restricted the application of parallel manipulators to small posture spaces. Traditional analytical methods and Newton–Raphson method usually cannot solve this problem well due to lack of generality or latent divergence. To address this issue, this study employs recent advances in deep learning to propose a novel physics-informed Newton–Raphson network (PhyNRnet) to rapidly and accurately solve this forward kinematics problem for general parallel manipulators. The main strategy of PhyNRnet is to combine the Newton–Raphson method with the neural network, which helps to significantly improve the accuracy and convergence speed of the model. In addition, to facilitate the network optimization, semi-autoregression, hard imposition of initial/boundary conditions (I/BCs), batch normalization, etc. are developed and applied in PhyNRnet. Unlike previous data-driven paradigms, PhyNRnet adopts the physics-informed loss functions to guide the network optimization, which gives the model clear physical meaning and helps improve generalization ability. Finally, the performance of PhyNRnet is verified by three parallel manipulator paradigms with large postures, where the Newton–Raphson method has generally diverged. Besides, the efficiency analysis shows that PhyNRnet consumes only a small amount of time at each time-step, which meets the real-time requirements.