Probabilistic approaches to the $$ AXB = YCZ $$ calibration problem in multi-robot systems

Ma, Qianli; Goh, Zachariah; Ruan, Sipu; Chirikjian, Gregory S.

doi:10.1007/s10514-018-9744-3

Cited by 38 publications

(12 citation statements)

References 22 publications

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“…This paper focused on the theoretical properties of our algorithm-we intend to include further experimentation on challenging real datasets in its sequel. Additionally, extensions to the closely related robot-world calibration problem [10], probabilistic cost function variants [17], and robust problem formulations [11] all hold promise for our technique. Finally, while the issue of highly accurate joint spatio-temporal extrinsic calibration has been explored for various extrinsic calibration problems [40], [41], [42], [43], a certifiable algorithm has not, to our knowledge, been proposed.…”

Section: Discussionmentioning

confidence: 99%

“…Principled probabilistic (i.e., maximum likelihood) formulations of hand-eye calibration are the subject of [6] and [7]. A similar approach is applied to a related multi-robot calibration problem in [17]. Our technique eschews a probabilistic cost function in order to leverage the simplicity of a classic geometric formulation, however combining the two approaches is a promising future direction.…”

Section: A Hand-eye Calibrationmentioning

confidence: 99%

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Certifiably Optimal Monocular Hand-Eye Calibration

Wise

Giamou

Khoubyarian

et al. 2020

2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)

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Correct fusion of data from two sensors is not possible without an accurate estimate of their relative pose, which can be determined through the process of extrinsic calibration. When two or more sensors are capable of producing their own egomotion estimates (i.e., measurements of their trajectories through an environment), the 'hand-eye' formulation of extrinsic calibration can be employed. In this paper, we extend our recent work on a convex optimization approach for hand-eye calibration to the case where one of the sensors cannot observe the scale of its translational motion (e.g., a monocular camera observing an unmapped environment). We prove that our technique is able to provide a certifiably globally optimal solution to both the known-and unknown-scale variants of hand-eye calibration, provided that the measurement noise is bounded. Herein, we focus on the theoretical aspects of the problem, show the tightness and stability of our convex relaxation, and demonstrate the optimality and speed of our algorithm through experiments with synthetic data.

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Section: Discussionmentioning

confidence: 99%

Section: A Hand-eye Calibrationmentioning

confidence: 99%

Certifiably Optimal Monocular Hand-Eye Calibration

Wise

Giamou

Khoubyarian

et al. 2020

2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)

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“…TCP calibration is to obtain the actual position and frame of the tool center point using external measurements and fitting algorithms. The essence of this problem is to solve the problem of AX = B, and many researchers have already given solutions [ 31 , 32 , 33 ]. With regard to a surgical assistant robot, on the one hand, it requires high accuracy of the TCP, and on the other hand, it must reduce the difficulty of the doctors’ operations using the robot.…”

Section: Methodsmentioning

confidence: 99%

Physician-Friendly Tool Center Point Calibration Method for Robot-Assisted Puncture Surgery

Zhang

Fan

et al. 2021

Sensors

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After each robot end tool replacement, tool center point (TCP) calibration must be performed to achieve precise control of the end tool. This process is also essential for robot-assisted puncture surgery. The purpose of this article is to solve the problems of poor accuracy stability and strong operational dependence in traditional TCP calibration methods and to propose a TCP calibration method that is more suitable for a physician. This paper designs a special binocular vision system and proposes a vision-based TCP calibration algorithm that simultaneously identifies tool center point position (TCPP) and tool center point frame (TCPF). An accuracy test experiment proves that the designed special binocular system has a positioning accuracy of ±0.05 mm. Experimental research shows that the magnitude of the robot configuration set is a key factor affecting the accuracy of TCPP. Accuracy of TCPF is not sensitive to the robot configuration set. Comparison experiments show that the proposed TCP calibration method reduces the time consumption by 82%, improves the accuracy of TCPP by 65% and improves the accuracy of TCPF by 52% compared to the traditional method. Therefore, the method proposed in this article has higher accuracy, better stability, less time consumption and less dependence on the operations than traditional methods, which has a positive effect on the clinical application of high-precision robot-assisted puncture surgery.

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“…However, measurement errors were not explicitly modeled, thus the results were sensitive to the measurement noise. Therefore, Ma proposed a method to increase the robustness against noise, including a hybrid method that combines traditional AXB=YCZ solvers with probabilistic methodology and an iterative method for the refinement to increase the robustness in the case of noisy experimental data [22]. Fu proposed a closedform method based on dual quaternion to solve the calibration problem, which effectively improved the calibration accuracy [23].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Calibration of the Hand-Eye, Flange-Tool and Robot-Robot Relationship in Dual-Robot Collaboration Systems

Qin

Geng

et al. 2022

Sensors

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A multi-robot collaboration system can complete more complex tasks than a single robot system. Ensuring the calibration accuracy between robots in the system is a prerequisite for the effective inter-robot cooperation. This paper presents a dual-robot system for orthopedic surgeries, where the relationships between hand-eye, flange-tool, and robot-robot need to be calibrated. This calibration problem can be summarized to the solution of the matrix equation of AXB=YCZ. A combined solution is proposed to solve the unknown parameters in the equation of AXB=YCZ, which consists of the dual quaternion closed-form method and the iterative method based on Levenberg–Marquardt (LM) algorithm. The closed-form method is used to quickly obtain the initial value for the iterative method so as to increase the convergence speed and calibration accuracy of the iterative method. Simulation and experimental analyses are carried out to verify the accuracy and effectiveness of the proposed method.

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Probabilistic approaches to the $$ AXB = YCZ $$ calibration problem in multi-robot systems

Cited by 38 publications

References 22 publications

Certifiably Optimal Monocular Hand-Eye Calibration

Certifiably Optimal Monocular Hand-Eye Calibration

Physician-Friendly Tool Center Point Calibration Method for Robot-Assisted Puncture Surgery

Simultaneous Calibration of the Hand-Eye, Flange-Tool and Robot-Robot Relationship in Dual-Robot Collaboration Systems

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