A Stochastic Global Optimization Algorithm for the Two-Frame Sensor Calibration Problem

In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices X,Y that best fit a set of equalities of the form A i X = YB i , i=1,..., N, where the {(A i , B i )} are pairs of homogeneous transformations obtained from sensor measurements. The m...

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Vydáno v:	IEEE transactions on industrial electronics (1982) Ročník 63; číslo 4; s. 2434 - 2446
Hlavní autoři:	Junhyoung Ha, Donghoon Kang, Park, Frank C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.04.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Bismuth Calibration Cameras geometric optimization hand-eye calibration Lie groups Noise measurement Optimization Optimization algorithms Robot sensing systems Robot sensor calibration robot-world calibration Sensors stochastic global optimization Yttrium stochastic global optimization robot sensor calibration Geometric optimization hand–eye calibration robot–world calibration
ISSN:	0278-0046, 1557-9948
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Abstract	In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices X,Y that best fit a set of equalities of the form A i X = YB i , i=1,..., N, where the {(A i , B i )} are pairs of homogeneous transformations obtained from sensor measurements. The measurements are often subject to varying levels of noise and the resulting optimization can have numerous local minima that exhibit high sensitivity in the choice of optimization parameters. As a first contribution, we present a fast and numerically robust local optimization algorithm for the two-frame sensor calibration objective function. Using coordinate-invariant differential geometric methods that take into account the matrix Lie group structure of the rigid-body transformations, our local descent method makes use of analytic gradients and Hessians, and a strictly descending fast step-size estimate to achieve significant performance improvements. As a second contribution, we present a two-phase stochastic geometric optimization algorithm for finding a stochastic global minimizer based on our earlier local optimizer. Numerical studies demonstrate the considerably enhanced robustness and efficiency of our algorithm over existing unit quaternion-based methods.
AbstractList	In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices X,Y that best fit a set of equalities of the form A i X = YB i , i=1,..., N, where the {(A i , B i )} are pairs of homogeneous transformations obtained from sensor measurements. The measurements are often subject to varying levels of noise and the resulting optimization can have numerous local minima that exhibit high sensitivity in the choice of optimization parameters. As a first contribution, we present a fast and numerically robust local optimization algorithm for the two-frame sensor calibration objective function. Using coordinate-invariant differential geometric methods that take into account the matrix Lie group structure of the rigid-body transformations, our local descent method makes use of analytic gradients and Hessians, and a strictly descending fast step-size estimate to achieve significant performance improvements. As a second contribution, we present a two-phase stochastic geometric optimization algorithm for finding a stochastic global minimizer based on our earlier local optimizer. Numerical studies demonstrate the considerably enhanced robustness and efficiency of our algorithm over existing unit quaternion-based methods. In the two-frame sensor calibration problem, the objective is to find rigid-body homogeneous transformation matrices [Formula Omitted] that best fit a set of equalities of the form [Formula Omitted], [Formula Omitted], where the [Formula Omitted] are pairs of homogeneous transformations obtained from sensor measurements. The measurements are often subject to varying levels of noise and the resulting optimization can have numerous local minima that exhibit high sensitivity in the choice of optimization parameters. As a first contribution, we present a fast and numerically robust local optimization algorithm for the two-frame sensor calibration objective function. Using coordinate-invariant differential geometric methods that take into account the matrix Lie group structure of the rigid-body transformations, our local descent method makes use of analytic gradients and Hessians, and a strictly descending fast step-size estimate to achieve significant performance improvements. As a second contribution, we present a two-phase stochastic geometric optimization algorithm for finding a stochastic global minimizer based on our earlier local optimizer. Numerical studies demonstrate the considerably enhanced robustness and efficiency of our algorithm over existing unit quaternion-based methods.
Author	Donghoon Kang Park, Frank C. Junhyoung Ha
Author_xml	– sequence: 1 surname: Junhyoung Ha fullname: Junhyoung Ha email: hjhdog1@gmail.com organization: Dept. of Cardiovascular Surg., Med. Sch., Harvard Univ., Boston, MA, USA – sequence: 2 surname: Donghoon Kang fullname: Donghoon Kang email: kimbab.moowoo@gmail.com organization: Imaging Media Center, Korea Inst. of Sci. & Technol., Seoul, South Korea – sequence: 3 givenname: Frank C. surname: Park fullname: Park, Frank C. email: fcp@snu.ac.kr organization: Dept. of Mech. & Aerosp. Eng., Seoul Nat. Univ., Seoul, South Korea
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Keywords	stochastic global optimization robot sensor calibration Geometric optimization hand–eye calibration robot–world calibration
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SubjectTerms	Bismuth Calibration Cameras geometric optimization hand-eye calibration Lie groups Noise measurement Optimization Optimization algorithms Robot sensing systems Robot sensor calibration robot-world calibration Sensors stochastic global optimization Yttrium
Title	A Stochastic Global Optimization Algorithm for the Two-Frame Sensor Calibration Problem
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