三维环境下采用势函数对AUV进行路径规划.pdf

Advances in Applied Mathematics A?,2024,13(4),1261-1272Published Online April 2024 in Hans.https:/www.hanspub.org/journal/aamhttps:/doi.org/10.12677/aam.2024.134116neAUV?15yXXXxxxnO?,?H vF2024c3?9FF2024c4?8FuF2024c4?15F?3ne|U?gYed(AUV)?5y.3Dn76,!646?1U,?UUuY6AUV?15y,?8I:,l,:uU?T6?:.?r5,n46n:?1U,?U35ymS?6AUV?15y,U?8I:.,N/G?1U?,?/N?766.(JL,U?U?3eAUV5y1?c5ynNThe Potential Function Is Used to Planthe Path of AUV in 3D EnvironmentMengting LeiSchool of Mathematics and Statistics,Changsha University of Science and Technology,ChangshaHunanReceived:Mar.9th,2024;accepted:Apr.8th,2024;published:Apr.15th,2024:Xx.neAUV?15yJ.A?,2024,13(4):1261-1272.DOI:10.12677/aam.2024.134116XxAbstractThe present study focuses on the path planning of an Autonomous Underwater Vehicle(AUV)in a three-dimensional environment using an improved potential function.Inthe traditional three-dimensional flow around a sphere,the superposition of uniformflow and dipole flow is limited to scenarios where the flow velocity remains constan-t in one direction,making it impossible to set a target point and only allowing forreaching the end of a flow line from a certain point.To enhance versatility,we pro-pose superimposing three-dimensional dipole flows and three-dimensional point sinks,enabling AUV path planning even when there are varying flow velocities within theplanning space and allowing for setting fixed target points.Additionally,we improveupon obstacle representation by considering ellipsoidal obstacles and their correspond-ing flows.Simulation results demonstrate that this improved potential function caneffectively plan feasible routes for AUV in different environments.KeywordsPath Planning,Potential Function,Three-Dimensional,Ellipsoidal ObstacleCopyright c?2024 by author(s)and Hans Publishers Inc.This work is licensed under the Creative Commons Attribution International License(CC BY 4.0).http:/creativecommons.org/licenses/by/4.0/1.AUV!U3Ye?.AUV?OUU3?!?Y1?,k?Ac.n5y3JpAUV5UA+uX.c5J?n5y|(A 1!Dijkstra 2)!?(3,4!V 5)!,6N?7LTNL?.N5,L:(i)?:6N?3?N.7L.L?R.X6NUB?NL,6N?(u?R)7L?u?.(ii)B:6NfUB?N.,=6N3.?7L?u.?3T:?.u?NX6N3.?7L.?(?6N6,NL?5?,6N3NL?)?DOI:10.12677/aam.2024.1341161263A?Xxy?Bly.2.3.7n?66:n!6n4f6?U.U?:=Ux+mcos4r2|:Vr=r=cos?U m2r3?v,I3 a(a),Vr=0,=:Vr|r=a=cos?U m2r3?r=a=0 a=3rm2Um=2Ua3d,7n?66?:=U cos?r+a32r2?,U!6?r.3.e AUV 5y3.1.N;O3n76,n!6n4f6U,l?/?7nN?!6.?|?!6,?UuY6 AUV?15y,S,?8I:,l,:uU?T6?:.?r5,?n4f6n:?1U,?U35ymS?6?e AUV?5yU?8I:.,n:1=m4rn46?:2=M4xr3?:?3(b,0,0)?,4f u?:?.:46?1U:=M cos4r2+m41p(x b)2+y2+z2#=M cos4r2+m4?1r2 2brcos+b2?(1)DOI:10.12677/aam.2024.1341161264A?Xx|:Vr=r=M cos2r3m4r bcos(r2 2brcos+b2)32#=12M cosr3+m2r bcos(r2 2brcos+b2)32#?v,I3 r=a(a),Vr=0,=:Vr=r=0?M cosa3+m2a bcos(a2 2bacos+b2)32=0M=m(a4 ba3cos)2cos(a2 2bacos+b2)32,m:?r,?2.M (1),?:=M cos4r2+m4?1r2 2 brcos+b2?=m4 1(r2 2brcos+b2)12a4 ba3cos2r2(a2 2bacos+b2)32!TF=?6 x,y,z?u=/x,/y,/z,?35ymS?766.46,=/N u?:?6,?O?6unm?56,N3nm?,|=?5).:(i)(8I:8Id:8I:5(.(ii)(=:=Ru?(x)8I,LO?5?.(iii)O=?:5O?8Im?Y?.(iv)?=?:=?=?.3.2.N;O35ymS3 K N,?-X5nON?)?766.b?1 k N?%I(xk,yk,zk),ak,?-X:DOI:10.12677/aam.2024.1341161265A?Xxk=Yi6=kdidk+di,dk=h(x xk)2+(y yk)2+(z zk)2i1/2 akL AUV 1 k NNL?l.Ne?6L:u=KXk=1k uk,ukN766.6=5y?-.4./GNe AUV 5y4.1.N;O7n4N?66,u C(a2,0,0)?:?,r m,u B(a2,0,0)?r?:U,/(Ou46).23 A(a1,0,0)?:,r Q,?U35ymS?6?e7$?AUV?15y,5?8I:.Figure 1.Ellipsoid 1.X 1,S:(7:),0,I(xs,0,0).U?:=Q41q(x a1)2+y2+z2m41q(x+a2)2+y2+z21q(x a2)2+y2+z2u=x=Q8x a1h(x a1)2+y2+z2i3/2+m4x+a2h(x+a2)2+y2+z2i3/2x a2h(x a2)2+y2+z2i3/2DOI:10.12677/aam.2024.1341161266A?Xx7:S?:u|x=xs,y=z=0=Q81(xs a1)2+m81(xs+a2)21(xs a2)2#=0,kQ(xs a1)2=m(xs+a2)2m(xs a2)2C?xs.3 x=0?:u|x=0=Q8a1(a21+R2)3/2+m82a2(a22+R2)3/2,R2=y2+z2.N?R0de(:2ZR00u?x=0 RdR=m|3.1!?=?N?766.4.2.N;OduN,?-X?1A?U,3 3.2!,dkL AUV 1 k NNL?l,Ku5,km?:?%(xk,yk,zk)?l,2OT:%:?:(xq,yq,zq),?:%?l,l?AUV L?l,X 2.Figure 2.Find dkdiagram 2.dk(xq,yq,zq)?:(i)DOI:10.12677/aam.2024.1341161267A?Xx?:(x xk,y yk,z zk),K:Px=xk+(x xk)tPy=yk+(y yk)tPz=zk+(z zk)t:?x xkxs?2+?y ykR0?2+?z zkR0?2=1(ii)?:IO x,y,z k?Lxq=f1(x,y,z)yq=f2(x,y,z)zq=f3(x,y,z)?u,dkL:dk=q(x xk)2+(y yk)2+(z zk)2q(xq xk)2+(yq yk)2+(zq zk)2|3.2!?-X3/N?766.Figure 3.Multiple paths at different angles 3.?eDOI:10.12677/aam.2024.1341161268A?Xx5.?5.1.e AUV 5y8I:?3(26,28,30),d 3,l:uU?8I:,4?:.?(:?:Figure 4.Arbitrary origin path 4.?:3 5,|z 15?!6U?1,d?v,U?BN,kn5.d(J,U?U?8I:,5ym:?,k|u?6|.Figure 5.Point sinks are compared with uniform flows 5.:!6?1DOI:10.12677/aam.2024.1341161269A?Xx5.2./GNe AUV 5y u?:,58I:(30,0,0),:(-30,0,-5).766X 6.Figure 6.The ellipsoid is located at the origin 6.u?:?1=?,8I:?3(28,28,0).766X 7.Figure 7.Single ellipsoid multipath 7./N?,?X 8.DOI:10.12677/aam.2024.1341161270A?XxFigure 8.Final path 8.6.(3Dn76,!646?1U,?UUuY6 AUV?15y,?8I:,Xz 15.?AUV U35ymS?6?e?15y,5?8I:,?J?U?AUVU3eyk?;,d(J,3d:?e AUV?15y,?8I:(26,28,30),l?:?T8I:,z 15!6?1,:e/?U?8I:,k5.?,?/GX/N?;,?3N?N?,8I:53(28,28,0),l?:U?T8I:.?8uXTAu?6,?/GN.z1 Li,M.and Zhang,H.(2020)AUV 3D Path Planning Based on A*Algorithm.2020 ChineseAutomation Congress(CAC),Shanghai,6-8 November 2020,11-16.2 Fink,W.,Baker,V.R.,Brooks,J.W.,et al.(2019)Globally Optimal Rover Traverse Planningin 3D Using Dijkstras Algorithm for Multi-Objective Deployment Scenarios.Planetary andSpace Science,179,Article 104707.https:/doi.org/10.1016/j.pss.2019.1047073 HernSndez,J.D.,Vallicrosa,G.,Vidal,E.,et al.(2015)On-Line 3D Path Planning for Close-Proximity Surveying with AUVs.IFAC-PapersOnLine,48,50-55.https:/doi.org/10.1016/j.ifacol.2015.06.009DOI:10.12677/aam.2024.1341161271A?Xx4 Li,D.,Li,Q.,Cheng,N.,et al.(2012)Extended RRT-Based Path Planning for Flying Robot-s in Complex 3D Environments with Narrow Passages.IEEE International Conference onAutomation Science and Engineering,Seoul,20-24 August 2012,1173-1178.5 Yan,F.,Zhuang,Y.and Xiao,J.(2012)3D PRM Based Real-Time Path Planning forUAV in Complex Environment.IEEE International Conference on Robotics and Biomimetics,Guangzhou,11-14 December 2012,1135-1140.6 Guo,Z.T.,Hu,H.J.and Feng,F.(2018)3D Path Planning for Multi-UAV Base on ArtificialPotential Field Method.DEStech Publications,Lancaster.7 Liu,S.,Wei,Y.and Gao,Y.(2012)3D path Planning for AUV Using Fuzzy Logic.2012International Conference on Computer Science and Information Processing(CSIP),Xian,24-26 August 2012,599-603.8 Volkan Pehlivanoglu,Y.,Baysal,O.and Hacioglu,A.(2007)Path Planning for AutonomousUAV via Vibrational Genetic Algorithm.Aircraft Engineering and Aerospace Technology,79,352-359.https:/doi.org/10.1108/000226607107582229 Xi,Q.-B.,Li,K.and Liu,H.-X.(2014)Research on UAV Path Planning Based on VibrationalGenetic Algorithm in 3D.Fire Control and Command Control,No.10,30-35.10 o.uA*|?:n;5yJ.C?,2018,56(12):62-66.11 Chen,X.and Ai,Y.-D.(2018)Application of Improved Neural Network in 3D Path Planningof UAVs.Electronics Optics and Control,25,7-11.12 Yu,J.,Zhang,Q.,Kroumov,V.,et al.(2008)Path Planning Algorithm for Robot in 3D En-vironment Based on Neural Network.In:Xiong,C.,Huang,Y.,Xiong,Y.and Liu,H.,Eds.,International Conference on Intelligent Robotics and Applications,Springer,Berlin,Heidel-berg,1081-1088.https:/doi.org/10.1007/978-3-540-88513-9 11513?.uV8NE?YefE,2022.14,.un6?Da?Sink;J.DaE?,2021,34(8):1117-1122.15?,+,?.u6Y;?n?1,2015,22(10):1-6.DOI:10.12677/aam.2024.1341161272A?