• Laser & Optoelectronics Progress
  • Vol. 62, Issue 3, 0312001 (2025)
Baoli Guo*, Jiarui Lin, Mingxin Teng, Rao Zhang, and Jigui Zhu
Author Affiliations
  • State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/LOP241116 Cite this Article Set citation alerts
    Baoli Guo, Jiarui Lin, Mingxin Teng, Rao Zhang, Jigui Zhu. Evaluation Method for Structural Strength of Directional Network of Workshop Measurement and Positioning System[J]. Laser & Optoelectronics Progress, 2025, 62(3): 0312001 Copy Citation Text show less

    Abstract

    The workshop measurement and positioning system realize coordinate measurement based on the principle of multistation observation and intersection, and the accurate calibration of the pose parameters of the measuring instrument is the premise of high-precision measurement of the system. In the process of system orientation, multiple observation equations are established based on instrumental observations and geometric constraint information to construct an orientation network, and its structural strength reflects the calibration accuracy of pose parameters. In this study, based on the mathematical model of the implicit function of the system and the orientation principle, the uncertainty of the pose parameters of is derived, and the structural strength evaluation model of the directional network is proposed. The evaluation index of the structural strength of the directional network is formed based on the structural coefficients calculated by the model. The structural strength of the directional network with different configurations is compared and verified numerically and experimentally to verify the correctness of the model. Through the analysis of the influencing factors of the structural coefficients, some guiding suggestions for the layout and structural optimization of the directional network is proposed.
    akx+bky+ckz+dk=0, k=1,2
    ak'(θk)bk'(θk)ck'(θk)dk'(θk)=cosθk-sinθk00sinθkcosθk0000100001akbkckdk=R(θk)001akbkckdk ,   k=1,2
    nk'=[ak'(θk),bk'(θk),ck'(θk)]Tnk'=ak'(θk)2+bk'(θk)2+ck'(θk)2=1,k=1,2
    F1j=a1j,b1j,c1j,d1jRTθ1j001RjTj01xyz1=0F2j=a2j,b2j,c2j,d2jRTθ2j001RjTj01xyz1=0,j=1,2,,m
    R=RZ(γ)RY(β)RX(α)=cosγ-sinγ0sinγcosγ0001cosβ0sinβ010-sinβ0cosβ1000cosα-sinα0sinαcosαT=[tx,ty,tz]T
    F(θij,Pi,Xj)=0
    E(X,θ)=i=1nFX,θ2=i=1nF1i2+F2i2=i=12nFi2X=[α,β,γ,tx,ty,tz]Tθ=[θ1,θ2,,θ2n]T
    Φ(X,θ)=E(X,θ)X=E(X,θ)αE(X,θ)βE(X,θ)tz=i=12n2FiFiαi=12n2FiFiβi=12n2FiFitz=Φ1Φ2Φ6=0
    H=Xθ=Φ(X,θ)X-1Φ(X,θ)θ
    Φ(X,θ)X=Φ1XΦ2XΦ6X=i=12n2Fiα2+Fi2Fiα2i=12n2FiαFiβ+Fi2Fiαβi=12n2FiαFitz+Fi2Fiαtzi=12n2Fiβ2+Fi2Fiβ2i=12n2FiβFitz+Fi2Fiβtzsymsi=12n2Fitz2+Fi2Fitz2
    Φ(X,θ)θ=Φ1θΦ2θΦ6θ=2F12αθ12F22αθ22F32αθ32F2n2αθ2n2F12βθ12F22βθ22F32βθ32F2n2βθ2n2F12tzθ12F22tzθ22F32tzθ32F2n2tzθ2n
    QX=HQθHT
    QX=HHTσ02
    HHT=h11h12h16h22h26symsh66
    σα=h11σ0σβ=h22σ0σγ=h33σ0σtx=h44σ0σty=h55σ0σtz=h66σ0
    G=i=1NhiN×100%, hi=1,ti-t03σt0,ti-t0>3σt
    ek=ak'x'+bk'y'+ck'z'+dk'ak'2+bk'2+ck'2=ak'x'+bk'y'+ck'z'+dk',   k=1,2
    Baoli Guo, Jiarui Lin, Mingxin Teng, Rao Zhang, Jigui Zhu. Evaluation Method for Structural Strength of Directional Network of Workshop Measurement and Positioning System[J]. Laser & Optoelectronics Progress, 2025, 62(3): 0312001
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