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    Journals >Chinese Journal of Ship Research >Volume 17 >Issue 5 >Page 157 > Article
    • Chinese Journal of Ship Research
    • Vol. 17, Issue 5, 157 (2022)
    Cooperative path following control of UAV and USV cluster for maritime search and rescue
    Haoliang WANG1, Chenyang YIN1, Liyu LU1, Dan WANG2, and Zhouhua PENG2
    Author Affiliations
  • 1College of Marine Engineering , Dalian Maritime University, Dalian 116026, China
  • 2College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China
    • show less
    DOI: 10.19693/j.issn.1673-3185.02916 Cite this Article
    Haoliang WANG, Chenyang YIN, Liyu LU, Dan WANG, Zhouhua PENG. Cooperative path following control of UAV and USV cluster for maritime search and rescue[J]. Chinese Journal of Ship Research, 2022, 17(5): 157 Copy Citation Text show less

    Abstract

    Objectives

    This paper studies a three-dimensional (3D) cooperative path-following control problem in the process of maritime search and rescue for a heterogeneous unmanned cluster system composed of unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs).

    Methods

    First, kinematic models of the UAVs and USVs are established under a fixed coordinate system and body coordinate system. In order to design a 3D path-following controller suitable for motion control, an air coordinate system is established, and the path tracking error models of the UAVs and USVs are established in the Serret-Frenet coordinate system. Next, a 3D line-of-sight (LOS) guidance law is designed at the kinematic level, and a cooperative path-following control method suitable for heterogeneous clusters of marine vehicles is proposed, allowing the UAVs and USVs to track the preset parameterized path. Finally, the stability of the control system is analyzed based on the Lyapunov stability theory.

    Results

    The simulation results verify the effectiveness of the proposed cooperative path-following control method for heterogeneous clusters of marine vehicles.

    Conclusions

    The results of this study can provide references for maritime search and rescue by using the proposed cooperative path-following control method.

    Keywords

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    $ \left\{ x˙si=usicos⁡ψsi−vsisin⁡ψsiy˙si=usisin⁡ψsi+vsicos⁡ψsiψ˙si=rsi \right. $(1)

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    $ \left\{ x˙ai=uaicos⁡ψaicos⁡θai+vai(cos⁡ψaisin⁡θaisin⁡ϕai−sin⁡ψai⋅sin⁡ϕai)+wai(sin⁡ψaisin⁡ϕai+cos⁡ψaisin⁡θaicos⁡ϕai)y˙ai=uaisin⁡ψaicos⁡θai+vai(cos⁡ψaicos⁡ϕai+sin⁡ψaisin⁡θaisin⁡ϕai)+wai(sin⁡ψaisin⁡θaicos⁡ϕai−cos⁡ψaisin⁡ϕai)z˙ai=−uaisin⁡θai+vaicos⁡θaisin⁡ϕai+waicos⁡θaicos⁡ϕaiϕ˙ai=(paicos⁡θai+qaisin⁡ϕaisin⁡θai+raicos⁡ϕaisin⁡θai)/cos⁡θaiθ˙ai=qaicos⁡ϕai+raisin⁡ϕaiψ˙ai=(qaisin⁡ϕai+raicos⁡ϕai)/cos⁡θai \right. $(2)

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    $ \left\{ x˙si=Usicos⁡ψsiWy˙si=Usisin⁡ψsiWψ˙siW=rsi+βsid\right. $(3)

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    $ {\psi _{{\text{s}}i{\text{d}}}} = {\text{atan}}2\left( {{{y}'_{{\text{s}}i{\text{d}}}},{{x}'_{{\text{s}}i{\text{d}}}}} \right) $(4)

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    $ \left[ {xsieysie} \right] = {\left[ {cos⁡ψsid−sin⁡ψsidsin⁡ψsidcos⁡ψsid} \right]^{\text{T}}}\left[ {xsi−xsid(χsi)ysi−ysid(χsi)} \right] $(5)

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    $ \left\{ x˙sie=Usicos⁡(ψsiW−ψsid)+ψ˙sidysie−Usid∗χ˙siy˙sie=Usisin⁡(ψsiW−ψsid)−ψ˙sidxsie\right. $(6)

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    $ \left\{ x˙ai=Uaicos⁡Ψaicos⁡Θaiy˙ai=Uaisin⁡Ψaicos⁡Θaiz˙ai=−Uaisin⁡ΘaiΘ˙ai=qai−α˙aiΨ˙ai=raicos⁡θai+β˙ai \right. $(7)

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    $ \left\{ θaid(χai)=arctan⁡(−zaid′(χai)xaid′2(xai)+yaid′2(χai))ψaid(χai)=arctan⁡(yaid′(χai)xaid′(χai))\right. $(8)

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    $ {\boldsymbol{R}}_{{\text{Fa}}i}^{\text{I}} = \left( {cos⁡θaidcos⁡ψaid−sin⁡ψaidsin⁡θaidcos⁡ψaidcos⁡θaidsin⁡ψaidcos⁡ψaidsin⁡θaidsin⁡ψaid−sin⁡θaid0cos⁡θaid} \right) $(9)

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    $ {{\boldsymbol{\varepsilon }}_{{\text{a}}i}} = {\boldsymbol{R}}_{{\text{Fa}}i}^{{\text{IT}}}\left( {{{\boldsymbol{\eta }}_{{\text{a}}i}} - {{\boldsymbol{\eta }}_{{\text{a}}i{\text{d}}}}} \right) $(10)

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    $ {{\boldsymbol{\dot \varepsilon }}_{{\text{a}}i}} = {\boldsymbol{\dot R}}_{{\text{Fa}}i}^{{\text{IT}}}\left( {{{\boldsymbol{\eta }}_{{\text{a}}i}} - {{\boldsymbol{\eta }}_{{\text{a}}i{\text{d}}}}} \right) + {\boldsymbol{R}}_{{\text{Fa}}i}^{{\text{IT}}}\left( {{{{\boldsymbol{\dot \eta }}}_{{\text{a}}i}} - {{{\boldsymbol{\dot \eta }}}_{{\text{a}}i{\text{d}}}}} \right) $(11)

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    $ {{\boldsymbol{S}}_{{\text{Fa}}i}} = \left[ {0−ψ˙aidcos⁡θaidθ˙aidψ˙aidcos⁡θaid0ψ˙aidsin⁡θaid−θ˙aid−ψ˙aidsin⁡θaid0} \right] $(12)

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    $ {\boldsymbol{R}}_{{\text{Aa}}i}^{\text{F}} = \left[ {cos⁡θaieFcos⁡ψaieF−sin⁡ψaieFsin⁡θaieFcos⁡ψaieFcos⁡θaieFsin⁡ψaieFcos⁡ψaieFsin⁡θaieFsin⁡ψaieF−sin⁡θaieF0cos⁡θaieF} \right] $(13)

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    $ {{\boldsymbol{\dot \eta }}_{{\text{a}}i}} = {\boldsymbol{R}}_{{\text{Fa}}i}^{\text{I}}{\boldsymbol{R}}_{{\text{Aa}}i}^{\text{F}}{{\boldsymbol{U}}_{{\text{a}}i{\text{A}}}} $(14)

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    $ \boldsymbolε˙ai=\boldsymbolSFaiT\boldsymbolRFaiIT(\boldsymbolηai−\boldsymbolηaid)+\boldsymbolRFaiIT(\boldsymbolη˙ai−\boldsymbolη˙aid)=\boldsymbolSFaiT\boldsymbolεai+\boldsymbolRFaiIT\boldsymbolUaiA−\boldsymbolRFaiIT\boldsymbolη˙aid$(15)

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    $ \left\{ x˙aie=Uaicos⁡ψaieFcos⁡θaieF+ψ˙aidcos⁡θaidyaie−θ˙aidzaie−Uaid∗χ˙aiy˙aie=Uaisin⁡ψaieFcos⁡θaieF−ψ˙aidcos⁡θaidxaie−ψ˙aidsin⁡θaidzaiez˙aie=−Uaisin⁡θaieF+θ˙aidxaie+ψ˙aidsin⁡θaidyaie\right. $(16)

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    $ \underset{t\to \infty }{\mathrm{lim}}\left|{x}_{i\text{e}}\right|\to 0,\underset{t\to \infty }{\mathrm{lim}}\left|{y}_{i\text{e}}\right|\to 0,\underset{t\to \infty }{\mathrm{lim}}\left|{\textit{z}}_{i\text{e}}\right|\to 0 $(17)

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    $ \underset{t\to \infty }{\mathrm{lim}}\left|{\chi }_{i}-{\chi }_{j}\right|\to 0 $(18)

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    $ \left\{ Θaie=θai−αai−ΘaiθΨaie=ψai+βai−Ψaiψχ˙ai=va−ωai \right. $(19)

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    $ \left\{ x˙aie=Uai−Uaisin2((ψaieF+θaieF)/2)+ψ˙aidcos⁡θaidyaie−Uaisin2((ψaieF−θaieF)/2)−θ˙aidzaie−Uaid∗χ˙aiy˙aie=Uaisin⁡ψaieFcos⁡θaieF−ψ˙aidcos⁡θaidxaie−ψ˙aidsin⁡θaidzaiez˙aie=−Uaisin⁡θaieF+θ˙aidxaie+ψ˙aidsin⁡θaidyaieΘ˙aie=qaiq−α˙ai−Θ˙aiθΨ˙aie=rair/cos⁡θai+βai−Ψ˙aiψ \right. $(20)

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    $ \left\{ UaiU=−kai1xaie/Πaix+Uaisin2((ψaieF+θaieF)/2)+Uaisin2((ψaieF−θaieF)/2)+Uaid∗vaΘaiθ=θaid+θaieFΨaiψ=ψaid+ψaieFqaiq=−kai2Θaie/Πaiθ+α˙ai+Θ˙aiθrair=−kai3Ψaiecos⁡θai/Πaiψ−(β˙ai−Ψ˙aiψ)cos⁡θai \right. $(21)

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    $ \left\{ x˙aie=−kai1xaie/Πaix+Uaid∗ωi+ψ˙aidcos⁡θaidyaie−θ˙aidzaiey˙aie=−Uaicos⁡θaieFyaie/Πaiy−ψ˙aidcos⁡θaidxaie−ψ˙aidsin⁡θaidzaiez˙aie=−Uaizaie/Πaiz+θ˙aidxaie+ψ˙aidsin⁡θaidyaieΘ˙aie=−kai2Θaie/ΠaiθΨ˙aie=−kai3Ψaie/Πaiψ\right. $(22)

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    $ \left\{ Ψsie=ψsiW−ψsirχ˙si=vs−ωsi \right. $(23)

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    $ \left\{ x˙sie=Usi−2Usisin2(ψsiW−ψsid2)+ψ˙sidysie−Usid∗(vs−ωsi)y˙sie=Usisin⁡(ψsir−ψsid)+ϱsi−ψ˙sidxsieΨ˙sie=rsi+βsid−ψ˙sir \right. $(24)

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    $ \left\{ Usir=−ksi4xsie/Πsix+Usid∗vs+2Usisin2(ψsiW−ψsid2)rsir=−ksi5Ψsie/Πsiψ−βsid+ψ˙sir−ysieϱsi/Ψsie \right. $(25)

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    $ {\psi _{{\text{s}}ir}} = {\psi _{{\text{s}}i{\text{d}}}} + \arctan \left( { - \frac{{{y_{{\text{s}}i{\text{e}}}}}}{{{l _{{\text{s}}i}}}}} \right) $(26)

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    $ \left\{ x˙sie=−ksi4xsie/Πsix+Usid∗ωsi+ψ˙sidysiey˙sie=−Usiysie/Πsiy+ϱsi−ψ˙sidxsieΨ˙sie=−ksi5Ψsie/Πsiψ−ysieϱsi/Ψsie\right. $(27)

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    $ {e}_{i}=\sum _{j=1}^{N}{a}_{ij}\left({\chi }_{i}-{\chi }_{j}\right) $(28)

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    $ {\omega _i} = {\,\mu _i}{e_i} - {\,\mu _i}U_{i{\text{d}}}^*{x_{i{\text{e}}}} $(29)

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    $ \left\{ x˙sie=−ksi4xsie/Πsix+Usid∗ωsi+ψ˙sidysiey˙sie=−Usiysie/Πsiy+ϱsi−ψ˙sidxsieΨ˙sie=−ksi5Ψsie/Πsiψ−ysieϱsi/Ψsiex˙aie=−kai1xaie/Πaix+Uaid∗ωi+ψ˙aidcos⁡θaidyaie−θ˙aidzaiey˙aie=−Uaicos⁡θaieFyaie/Πaiy−ψ˙aidcos⁡θaidxaie−ψ˙aidsin⁡θaidzaiez˙aie=−Uaizaie/Πaiz+θ˙aidxaie+ψ˙aidsin⁡θaidyaieΘ˙aie=−kai2Θaie/ΠaiθΨ˙aie=−kai3Ψaie/Πaiψe˙i=−\boldsymbolLωi \right. $(30)

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    $ V1=12∑i=1M{xsie2+ysie2+Ψsie2}+12∑i=M+1N{xaie2+yaie2+zaie2+Θaie2+Ψaie2}+\boldsymbolχT\boldsymbolL\boldsymbolχ $(31)

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    $ V1=12∑i=1M{xsie2+ysie2+Ψsie2}+12∑i=M+1N{xaie2+yaie2+zaie2+Θaie2+Ψaie2}+\boldsymboleT\boldsymbolPe $(32)

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    $ V˙1⩽∑i=1M{−ksi4xsie2Πsix+Usid∗ωixsie−Usiysie2Πsiy−ksi5Ψsie2Πsiψ}+∑i=M+1N{−kai1xaie2Πaix−Uaicos⁡θaieFyaie2Πaiy−Uaizaie2Πaiz−kai2Θaie2Πaiθ−kai3Ψaie2Πaiψ+Uaid∗ωixaie}−\boldsymbolχT\boldsymbolL\boldsymbolω⩽∑i=1M{−ksi4xsie2Πsix−Usiysie2Πsiy−ksi5Ψsie2Πsiψ}+∑i=M+1N{−kai1xaie2Πaix−Uaicos⁡θaieFyaie2Πaiy−Uaizaie2Πaiz−$()

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    $ \left. \frac{{{k_{{\text{a}}i2}}\varTheta _{{\text{a}}i{\text{e}}}^2}}{{{\varPi _{{\text{a}}i\theta }}}} - \frac{{{k_{{\text{a}}i3}}\varPsi _{{\text{a}}i{\text{e}}}^2}}{{{\varPi _{{\text{a}}i\psi }}}} \right\} - {\lambda _{\min }}\left(\boldsymbol{ \,\mu } \right){\left\| \boldsymbol{\vartheta } \right\|^2} $(33)

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    $ {{\boldsymbol{e}}^{\text{T}}}{\boldsymbol{Pe}}\ge {\lambda }^{\ast }{\left\| \boldsymbol{\chi} -{\boldsymbol{1}}_{N}\frac{1}{N}\sum _{i=1}^{N}{\chi }_{i}\right\| }^{2} $(34)

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    Haoliang WANG, Chenyang YIN, Liyu LU, Dan WANG, Zhouhua PENG. Cooperative path following control of UAV and USV cluster for maritime search and rescue[J]. Chinese Journal of Ship Research, 2022, 17(5): 157
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