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Bayesian Optimal Experimental Design for Robot Kinematic Calibration

Ersin Das, Thomas Touma, Joel W. Burdick

TL;DR

The paper tackles online, data-efficient kinematic calibration by learning forward-kinematics errors on $\mathbb{S}^3 \times \mathbb{R}^3$ using a geometry-aware Gaussian process and Bayesian optimization. It introduces a Riemannian Matérn kernel on $\mathbb{S}^3$ combined with a Euclidean kernel on $\mathbb{R}^3$, with geodesic-based distances $d_{\mathbb{S}^3}$ and $d_{\mathrm{SE(3)}}$ guiding similarity; end-effector poses are optimized in task space via GP-UCB. End-effector measurements from fiducial markers enable sampling of the objective and iterative refinement of the kinematic error model, which is then corrected by solving a quadratic program to update the DH parameters. The approach is validated in simulations and on NASA JPL's OWLAT testbed, showing improved data efficiency and reliable recalibration with a limited number of poses.

Abstract

This paper develops a Bayesian optimal experimental design for robot kinematic calibration on ${\mathbb{S}^3 \!\times\! \mathbb{R}^3}$. Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on Riemannian Matérn 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).

Bayesian Optimal Experimental Design for Robot Kinematic Calibration

TL;DR

The paper tackles online, data-efficient kinematic calibration by learning forward-kinematics errors on using a geometry-aware Gaussian process and Bayesian optimization. It introduces a Riemannian Matérn kernel on combined with a Euclidean kernel on , with geodesic-based distances and guiding similarity; end-effector poses are optimized in task space via GP-UCB. End-effector measurements from fiducial markers enable sampling of the objective and iterative refinement of the kinematic error model, which is then corrected by solving a quadratic program to update the DH parameters. The approach is validated in simulations and on NASA JPL's OWLAT testbed, showing improved data efficiency and reliable recalibration with a limited number of poses.

Abstract

This paper develops a Bayesian optimal experimental design for robot kinematic calibration on . Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on Riemannian Matérn kernels over . 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).
Paper Structure (9 sections, 1 theorem, 24 equations, 3 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 24 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Bayesian Optimization on S3 x R3
  4. Experimental Design for Calibration
  5. Optimization-Based Kinematic Calibration
  6. Simulations and Experiments
  7. Simulations
  8. System Hardware and Experiments
  9. Conclusion And Future Work

Key Result

Theorem 1

Suppose that the identification Jacobian matrix: ${\mathbf{J} \!=\! \frac{\partial \mathbf{f}_{\uptheta \to \mathbf{T}}(\Psi)}{\partial \Psi} }$, with ${\mathbf{J} \!\in\! \mathbb{R}^{7 \times 4n_j}}$, is evaluated for ${n}$ different choices of joint variables ${\Bar{\theta}_1,\ldots,\Bar{\theta}_n

Figures (3)

  • Figure 1: (Left) The high-fidelity dynamics simulator of OWLAT tevere2024. The simulation results (Right). The proposed method demonstrates superior kinematic calibration performance and data efficiency compared to the random sampling method.
  • Figure 2: The OWLAT Testbed at the NASA Jet Propulsion Laboratory (JPL). (yellow inset) custom scoop with 36h11 AprilTags installed for precise real-time localization of the end-effector's translation and rotations; (orange inset) point-of-view from the lander’s vision system of the WAM arm in one of its other various configurations used for calibration; (purple inset) segmented highlight of the WAM arm in one of its calibration poses where it is extended with a visible rotational injected encoder bias in joint-7.
  • Figure 3: The value of the objective function $\mathbf{f}$ vs. the number of measurement configurations for the experimental kinematic calibration of NASA JPL's OWLAT. The end-effector pose values are derived using DH parameters updated through solving the QP problem given in \ref{['eq:Cal-QP']} with $n$ data points. The proposed method learns the objective function $\mathbf{f}$; therefore, it minimizes the uncertainties in DH parameters via Bayesian optimization.

Theorems & Definitions (7)

  • Definition 1
  • Example 1
  • Remark 1
  • Definition 2: Local Identifiability of DH Parameters
  • Theorem 1
  • proof
  • Remark 2