Simultaneous Hand-Eye and Robot-World Calibration by Solving the $AX=YB$ Problem Without Correspondence

Objective: The hand-eye calibration is used to determine the transformation between the end-effector and the camera marker of the robot. But the robot movement in traditional method would be time-consuming, inaccurate and even unavailable in some conditions. The method presented in this article can complete the calibration without any movement and is more suitable in clinical applications. Methods: Instead of solving the classic non-linear equation AX ¼ XB, we collected the points on X and Y axes of the tool coordinate system (TCS) with the visual probe and fitted them using the singular value decomposition algorithm (SVD). Then, the transformation was obtained with the data of the tool center point (TCP). A comparison test was conducted to verify the performance of the method. Results: The average translation error and orientation error of the new method are 0.12 ± 0.122 mm and 0.18 ± 0.112 respectively, while they are 0.357 ± 0.347 mm and 0.416 ± 0.234 correspondingly in the traditional method. Conclusions: The high accuracy of the method indicates that it is a good candidate for medical robots, which usually need to work in a sterile environment.

show abstract

“…Moreover, some extension studies based on AX ¼ XB are also in progress, such as transforming the equation to AX ¼ YB [15].…”

Section: Discussionmentioning

confidence: 99%

A new hand-eye calibration approach for fracture reduction robot

Wang

Tang

et al. 2017

Computer Assisted Surgery

Self Cite

View full text Add to dashboard Cite

show abstract

“…When θ is zero, we can replace it with a small value near zero to accurately compute x. Once θ and x are obtained, we can use any pair of (22)-(23), (24)-(25), or (26) - (27). Using (22)-(23) is easier since we do not involve q 3 (θ) for which we need to convert θ to get q 3 (θ).…”

Section: Fig 3 the Position Vectors Defined In The Mechanismmentioning

confidence: 99%

External Kinematic Calibration of Hybrid Kinematics Machine Utilizing Lower-DOF Planar Parallel Kinematics Mechanisms

Rosyid

El‐Khasawneh

Alazzam

2019

Int. J. Precis. Eng. Manuf.

View full text Add to dashboard Cite

This paper presents the implementation of nonlinear least squares and iterative linear least squares algorithms for external kinematic calibration of a hybrid kinematics machine composed of two 3PRR planar parallel kinematics mechanisms by utilizing a laser tracker. First the hand-eye and robot-world transformations were obtained by a separable closed-form solution and refined by the nonlinear least squares. Subsequently, the geometric parameters of the machine's mechanisms were estimated using the two algorithms. Due to the rank deficiency, we implemented the nonlinear least squares algorithm through a subset selection approach in which we performed the estimation in two steps. We iterated the closed-form solution of the linear least squares until the solution converges to the actual values. We have shown that the nonlinear least squares algorithm successfully refined the hand-eye and robot-world transformations and outperformed the iterative linear squares algorithm in the estimation of the geometric parameters of the mechanisms.

show abstract

“…In this formulation, A and B are the homogeneous transformations measured directly from sensors. Quite a few AX = Y B solvers have been proposed in the literature [9,11,12,14,15,17,25]. Most of the existing AX = XB and AX = Y B solvers deal with the case where there is an exact correspondence between the data pairs A i and B i .…”

Section: A Related Workmentioning

confidence: 99%

“…However, this is generally not true in real applications due to asynchronous sensors or missing data. [2] and [15] proposed probabilistic approaches for solving the AX = XB and AX = Y B problems respectively, and both of them show the superiority of the probabilistic approaches over the traditional solvers when handling data without a priori knowledge of correspondence.…”

Section: A Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems

Goh

Chirikjian

Robotics: Science and Systems XII

Self Cite

View full text Add to dashboard Cite

Abstract-In recent years, the topic of multi-robot systems has become very popular. These systems have been demonstrated in various applications, including exploration, construction, and warehouse operations. In order for the whole system to function properly, sensor calibrations such as determining the camera frame relative to the IMU frame are important. Compared to the traditional hand-eye & robot-world calibration, a relatively new problem called the AXB = Y CZ calibration problem arises in the multi-robot scenario, where A, B, C are rigid body transformations measured from sensors and X, Y, Z are unknown transformations to be calibrated. Several solvers have been proposed previously in different application areas that can solve for X, Y and Z simultaneously. However, all of the solvers assume a priori knowledge of the exact correspondence among the data streams {Ai}, {Bi} and {Ci}. While that assumption may be justified in some scenarios, in the application domain of multi-robot systems, which may use ad hoc and asynchronous communication protocols, knowledge of this correspondence generally cannot be assumed. Moreover, the existing methods in the literature require good initial estimates that are not always easy or possible to obtain. In this paper, we propose two probabilistic approaches that can solve the AXB = Y CZ problem without a priori knowledge of the correspondence of the data. In addition, no initial estimates are required for recovering X, Y and Z. These methods are particularly well suited for multi-robot systems, and also apply to other areas of robotics in which AXB = Y CZ arises.

show abstract

Simultaneous Hand-Eye and Robot-World Calibration by Solving the $AX=YB$ Problem Without Correspondence

Cited by 59 publications

References 24 publications

A new hand-eye calibration approach for fracture reduction robot

A new hand-eye calibration approach for fracture reduction robot

External Kinematic Calibration of Hybrid Kinematics Machine Utilizing Lower-DOF Planar Parallel Kinematics Mechanisms

Probabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems

Contact Info

Product

Resources

About