Optimal Uncertainty-Aware Calibration for the AX=YB Problem

• URL: http://arxiv.org/abs/2605.04809v1
• Date: Wed, 06 May 2026 12:00:03 GMT
• Title: Optimal Uncertainty-Aware Calibration for the AX=YB Problem
• Abstract summary: This article proposes a general optimization framework for solving hand-eye calibration problem.<n>An iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed.<n> Numerical simulations and real-world experiments validate the effectiveness of the proposed approach.
• Score: 7.193339960011095
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed. During the optimization process, the method strictly preserves the structural constraints of the calibration parameters and enables synchronized updates between calibration parameters. Recognizing that data used in real-word hand-eye calibration often contain uncertainty, especially in over-loading and large workspace industrial robot scenarios, which can significantly degrade accuracy, and accurately modeling such uncertainty is inherently difficult, this article avoids explicit uncertainty modeling. Instead, an uncertainty metric to evaluate the relative uncertainty between data sources is introduced and used to dynamically refine the iterative process. To further enhance convergence efficiency, an effective initial solution generation method that improves overall stability and accuracy is designed. Numerical simulations and real-world experiments validate the effectiveness of the proposed approach, and in synthetic datasets, the proposed approach improves the estimation accuracy by at least 67\% under high-uncertainty conditions compared with the existing methods.

Related papers

• Principled Algorithms for Optimizing Generalized Metrics in Binary Classification [53.604375124674796]
  We introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds.<n>Our approach reformulates metric optimization as a generalized cost-sensitive learning problem.<n>We develop new algorithms, METRO, with strong theoretical performance guarantees.
  arXiv  Detail & Related papers  (2025-12-29T01:33:42Z)
• Adaptive Learning-based Surrogate Method for Stochastic Programs with Implicitly Decision-dependent Uncertainty [1.5412450351033007]
  We consider a class of programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error.<n>We develop an adaptive learning-based surrogate method that integrates the simulation scheme and statistical estimates to construct estimation-based surrogate functions.
  arXiv  Detail & Related papers  (2025-05-12T07:35:06Z)
• Mixed-Precision Conjugate Gradient Solvers with RL-Driven Precision Tuning [0.0]
  This paper presents a novel reinforcement learning (RL) framework for dynamically optimizing numerical precision.<n>We employ Q-learning to adaptively assign precision levels to key operations, striking an optimal balance between computational efficiency and numerical accuracy.<n>Results demonstrate the effectiveness of RL in enhancing solver's performance, marking the first application of RL to mixed-precision numerical methods.
  arXiv  Detail & Related papers  (2025-04-19T11:35:03Z)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• Optimal Learning via Moderate Deviations Theory [3.9725974446759342]
  We develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach.<n>It is shown that the proposed confidence intervals are statistically optimal in the sense that they satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property.
  arXiv  Detail & Related papers  (2023-05-23T19:57:57Z)
• Sharp Calibrated Gaussian Processes [58.94710279601622]
  State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance. We present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance. Our approach is shown to yield a calibrated model under reasonable assumptions.
  arXiv  Detail & Related papers  (2023-02-23T12:17:36Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Online Calibrated and Conformal Prediction Improves Bayesian Optimization [10.470326550507117]
  This paper studies which uncertainties are needed in model-based decision-making and in Bayesian optimization. Maintaining calibration, however, can be challenging when the data is non-stationary and depends on our actions. We propose using simple algorithms based on online learning to provably maintain calibration on non-i.i.d. data.
  arXiv  Detail & Related papers  (2021-12-08T23:26:23Z)
• Improving model calibration with accuracy versus uncertainty optimization [17.056768055368384]
  A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We demonstrate our approach with mean-field variational inference and compare with state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-12-14T20:19:21Z)
• Automatically Learning Compact Quality-aware Surrogates for Optimization Problems [55.94450542785096]
  Solving optimization problems with unknown parameters requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in a complex training model pipeline results in predictions of iteration of unobserved decision making. We show that we can improve solution quality by learning a low-dimensional surrogate model of a large optimization problem.
  arXiv  Detail & Related papers  (2020-06-18T19:11:54Z)
• Efficient Ensemble Model Generation for Uncertainty Estimation with Bayesian Approximation in Segmentation [74.06904875527556]
  We propose a generic and efficient segmentation framework to construct ensemble segmentation models. In the proposed method, ensemble models can be efficiently generated by using the layer selection method. We also devise a new pixel-wise uncertainty loss, which improves the predictive performance.
  arXiv  Detail & Related papers  (2020-05-21T16:08:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.