Configuration-Dependent Robot Kinematics Model and Calibration

TL;DR

This work tackles configuration-dependent non-geometric errors in serial robot kinematics by introducing a configuration-dependent calibration framework. It identifies locally near-nominal POE parameter sets at multiple configurations and interpolates them into a global model using a Fourier-basis representation parameterized by shoulder and elbow angles, achieving sub-millimeter accuracy with high training efficiency. The approach is validated on two 6-DoF industrial robots and a dual-robot task, showing more than a 50% reduction in maximum positioning error compared with the nominal model and competitive performance relative to neural-network-based methods. The findings demonstrate practical applicability for precision manufacturing tasks, including collaborative robotics, and offer a scalable path to improve absolute positioning accuracy across the workspace.

Abstract

Accurate robot kinematics is essential for precise tool placement in articulated robots, but non-geometric factors can introduce configuration-dependent model discrepancies. This paper presents a configuration-dependent kinematic calibration framework for improving accuracy across the entire workspace. Local Product-of-Exponential (POE) models, selected for their parameterization continuity, are identified at multiple configurations and interpolated into a global model. Inspired by joint gravity load expressions, we employ Fourier basis function interpolation parameterized by the shoulder and elbow joint angles, achieving accuracy comparable to neural network and autoencoder methods but with substantially higher training efficiency. Validation on two 6-DoF industrial robots shows that the proposed approach reduces the maximum positioning error by over 50%, meeting the sub-millimeter accuracy required for cold spray manufacturing. Robots with larger configuration-dependent discrepancies benefit even more. A dual-robot collaborative task demonstrates the framework's practical applicability and repeatability.

Figures (7)

• Figure 1: Experimental robot calibration setup using the OptiTrack motion capture system.
• Figure 2: Kinematic diagram of a 6R robot.
• Figure 3: Minimal POE parameterization based on a set of nominal POE parameters. Redundancy in the location of ${\mathcal{O}}_i$ is removed by constraining it to lie in the plane perpendicular to the nominal joint axis through the nominal joint origin.
• Figure 4: Robot schematics in the zero configuration.
• Figure 5: Joint angle distribution in the testing dataset shows broad coverage of all joint angles.