Transformer- and GRU-Based Identification of Open-Chain Robot Kinematics Using Product-of-Exponentials Coordinates

This paper addresses the data-driven identification of open-chain robot morphology from finite windows of heterogeneous signals, including commanded joint references, measured joint states, and end-effector pose observations. Unlike conventional calibration procedures that assume a known kinematic topology, the proposed formulation estimates both discrete structural quantities and continuous kinematic coordinates: the number of active joints, the revolute/prismatic token sequence, Product-of-Exponentials (POE) screw axes, and the home pose of the end effector. A temporal transformer encoder is used as the main estimator and compared with a gated recurrent unit (GRU) baseline on the same dataset, with the same output heads and a multitask physics-aware objective. The continuous target is expressed in POE coordinates rather than as a Denavit–Hartenberg table because POE directly represents spatial joint axes and avoids several frame-assignment ambiguities. Simulated results on a noisy benchmark of 48 serial-robot families show that both sequence models recover the discrete structure on the tested in-library trajectories, while their continuous reconstruction errors reveal different trade-offs in screw-axis, home-pose, and trajectory reconstruction accuracy. The study also discusses inactive-slot masking, out-of-library behavior, synthetic-to-real limitations, persistent excitation, and the role of the learned model as an initialization for subsequent calibration refinement.