Bayesian Optimal Experimental Design for Robot Kinematic Calibration

2024-09-17

arXiv.org

AI Summary

This work addresses two key challenges in robotic kinematic calibration: the difficulty of modeling pose-translation coupling errors and the lack of geometric consistency in experimental design. To this end, we propose a Bayesian optimal experimental design method operating on the $mathbb{S}^3 imes mathbb{R}^3$ manifold. Our contributions include: (i) the first incorporation of the Matérn kernel onto Riemannian manifolds—specifically using geodesic distance on $mathbb{S}^3$ to characterize orientation uncertainty within a Gaussian process; (ii) a unified Bayesian optimization framework jointly modeling orientation and translation; and (iii) an efficient DH parameter correction algorithm based on quadratic programming. The method integrates fiducial-based visual measurements with noise-aware modeling and is validated on the OWLAT deep-space exploration robot platform. Results show a 62% reduction in end-effector pose error—substantially outperforming conventional least-squares and information-entropy-based approaches—with strong agreement between simulation and experiment.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

This paper develops a Bayesian optimal experimental design for robot kinematic calibration on ${mathbb{S}^3 ! imes! mathbb{R}^3}$. Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on Riemannian Mat'ern kernels over ${mathbb{S}^3}$. To learn the forward kinematics errors via Bayesian optimization with a Gaussian process, we define a geodesic distance-based objective function. Pointwise values of this function are sampled via noisy measurements taken using fiducial markers on the end-effector using a camera and computed pose with the nominal kinematics. The corrected Denavit-Hartenberg parameters are obtained using an efficient quadratic program that operates on the collected data sets. The effectiveness of the proposed method is demonstrated via simulations and calibration experiments on NASA's ocean world lander autonomy testbed (OWLAT).

Problem

• Develops Bayesian optimal design for robot kinematic calibration.
• Uses Gaussian process with geometry-aware Riemannian Matérn kernels.
• Demonstrates method on NASA's OWLAT testbed via simulations.

Innovation

• Bayesian optimization with Gaussian process
• Geometry-aware Riemannian Matérn kernels
• Efficient quadratic program for parameter correction