Application of Nonlinear Receding Horizon Control for Ship Maneuvering

Abstract

Recently, maritime works, such as ocean observation or cable laying works, become efficient with the dynamic positioning control of the vessels. The conventional PID control is still useful but the performance is not enough for precise positioning or multiple waypoints tracking. In this paper, we present the application of real-time non-linear Receding Horizon control for route tracking problem and control allocation problem for vessels equipped with azimuth thrusters. The performance and usefulness of the proposed method is verified with the actual cable laying works. Key Words: nonlinear receding horizon control, dynamic positioning system, maritime working vessel 1.‚Í ‚ ¶ ‚ß ‚É ƒ^ ƒOƒ{ •[ ƒg‚â ƒt ƒF ƒŠ•[ ‚ ‚é ‚¢ ‚Í ŠC-m ŠÏ 'ª 'D‚â •ì ‹AE'D ‚È ‚Ç‚Ì 'D"• ‚Í,-£ '…ŠÝŽž ‚â ƒ~ ƒb ƒVƒ ‡ ƒ"•ì ‹AEŽž‚Ì '€ 'D•« ‚â 'Ï OEÌ•á •« ‚ð •‚ ‚ß ‚é ‚½‚ß ‚É'D Žñ ‚â 'D"ö ‚É ƒT ƒC ƒhƒXƒ‰ ƒX ƒ^ ‚ð "‹ •Ú ‚µ,‚³ ‚ç ‚É OE´"®‹@‚â ƒv ƒ• ƒy ƒ‰‚à •¡ •" Šî ‚Ì •\ •¬ ‚É ‚È ‚é •ê • ‡ ‚à '¿ ‚µ ‚-‚È ‚¢. ‚µ ‚© ‚µ,‚± ‚ê ‚ç •¡ •" ‚Ì •" •i ‹@ ‚ð OE •Ê ‚É '€ •ì ‚µ ‚Ä'D'Ì ‚ð •Š-] ‚Ì ˆÊ 'u ‚É'€ •c ‚· ‚é ‚É ‚Í ‚© ‚È ‚è ‚Ì •n-û‚ð-v‚µ,1980"N 'ã "¼‚Î ‚© ‚ç '€ 'D ‚ð •â •• ‚· ‚é '• 'u ‚AE‚µ ‚Ä ƒWƒ ‡ ƒCƒXƒe ƒB ƒb ƒN‚AE‰ñ "ª ƒ_ ƒC ƒ" ƒ‹ ‚ð-p‚¢ ‚ÄŠe •" •i ‹@‚ðˆê‹@‚ðˆê Š ‡ '€ •c ‚· ‚é '€ 'D '• 'u ‚ª Žg ‚í ‚ê Žn ‚ß ‚½.‚± ‚ê ‚Í ƒI ƒy ƒOE•[ ƒ^ ‚ª '€ •ì ‚µ ‚½ ƒWƒ ‡ ƒCƒXƒe ƒBƒb ƒN‚Ì •û OEü‚É •"-Í‚ð "-• ¶ ‚³ ‚¹,‰ñ "ª ƒ_ ƒCƒ" ƒ‹ ‚ð ‰ñ‚µ ‚½•û OEü‚É ‰ñ "ª ƒ‚ •[ ƒ• ƒ" ƒg‚ð "-• ¶ ‚³ ‚¹ ‚é '€ 'DŽx‰ ‡'• 'u ‚Å‚ ‚é ‚ª,‚± ‚ê ‚ÉGPS(Global Positioning System)‚É 'ã •\ ‚³ ‚ê ‚é 'ª ˆÊ ƒVƒXƒe ƒ€ ‚AEƒWƒƒ ƒC ƒ• ƒR ƒ"ƒp ƒX ‚ð-p‚¢ ‚Ä'D ˆÊ •E'DŽñ •û ˆÊ ‚ð Ž©"®• § OEä‚· ‚é ƒVƒXƒe ƒ€ ‚ª DPS(Dynamic Positioning System)‚Å ‚ ‚è,‹ß "N,DGPS (DifFerential Global Positioning System)‚È ‚Ç‚Ì 'ª ˆÊ ƒVƒXƒe ƒ€ ‚Ì •‚ •¸ "x ‰»‚É "º ‚Á‚Ä ŠC-m •ì ‹AE'D ‚È ‚Ç‚Ö ‚Ì "‹ •Ú ‚ª '…ŽÀ‚É'• ‚¦ ‚Ä‚¢ ‚é.•]-ˆ‚Ì ŠC-m •ì ‹AE‚Å ‚Í,‚½ ‚AE‚¦ ‚Î ŠC'ê ƒP•[ ƒu ƒ‹ ‚Ì •z •Ý •ì ‹AE‚Ì •ê • ‡,•ì ‹AE'D ‚ÌˆÊ‚ÌˆÊ 'u OEˆ‚ß ‚ð •s ‚È ‚¤ ‚½‚ß ‚É•¡ •" ‚Ì ƒAƒ" ƒJ •[ ‚ÅOEW-¯ ‚µ,'€ ˆê ƒAƒ" ƒJ •[ ‚ð 'Å ‚¿ •Ï ‚¦ ‚ÄOEW-¯•õ ‚ð ŽèOEJ ‚è Šñ‚¹ ‚È ‚ª ‚ç 'D ‚ð •i ‚ß ‚Ä•z •Ý‚· ‚é •H-@‚ª ‚AE‚ç ‚ê ‚Ä ‚« ‚½‚ª,‚± ‚ÌDPS‚ð Žg-p ‚· ‚é ‚± ‚AE‚É ‚ae ‚Á ‚Ä,1)-Ú •W ƒ‹ •[ ƒg‚Ö ‚Ì •‚ •¸ "x •z •Ý,2)•z •Ý•ì ‹AE‚Ì •‚ '¬ ‰»,'‹-é ˜A'± •ì ‹AE‚Ì ŽÀOE»‚É ‚ae ‚é •HŠú ‚Ì 'Z •k,3)ƒA ƒ" ƒJ •[ OEW-¯‚ª "ï ‚µ ‚¢ 'å •[ "x ‚Å‚Ì •ì ‹AE‚ª ‰Â "\ ‚É ‚È ‚é ‚È ‚Ç ‚³ ‚Ü ‚´ ‚Ü‚È-˜"_ ‚ª • ¶ ‚Ü‚ê,•¡ OEãˆê 'w•L ‚Ü‚Á‚Ä‚¢ ‚-‚à ‚Ì ‚AEŽv ‚í ‚ê ‚é. DPS‚Ì-ð Š" ‚Í,ŠC-m •ã ‚Ì-Ú•W'è "_ ‚Ö ‚Ì "C ˆÓŽp •¨ ‚Å‚Ì 'â 'D, ‚Ü‚½‚Í-Ú•W•q •s ƒ‹ •[ ƒg•ã ‚ð •Ý'è 'D'¬ ‚Å'Ç •](ƒ‹ •[ ƒg ƒgƒ‰ƒbƒL ƒ" ƒO)‚³ ‚¹ ‚é ‚à ‚Ì ‚Å ‚ ‚é.ƒI •[ ƒgƒp ƒC ƒ• ƒb ƒg‚Í Žå ‚É•‚ '¬ •q •s ‚Å'Ç ‚ð '€ •ì ‚µ ‚Ä'DŽñ •û ˆÊ ‚ð • § OEä‚· ‚é ‚Ì ‚É'Î ‚µ ‚Ä,DPS‚͈ê DPS‚͈ê "Ê "I ‚É'á '¬ ˆae ‚É ‚¨‚¢‚¨‚¢ ‚Ä'D 'Ì 'O OEã •E• ¶ ‰E-Í‚¨‚ae‚ÑÍ‚¨‚ae‚Ñ•ù ‰ñ ƒ‚ •[ ƒ• ƒ" ƒg ‚ð '€ •ì-Ê‚AE‚µ,'D ˆÊ ‚AE'DŽñ •û ˆÊ Šp ‚ð Ž© "®• § OEä‚· ‚é.‚» ‚Ì • § OEä Žè-@‚Í,'D 'Ì 'OOEã,• ¶ ‰E,•ù ‰ñ ‚» ‚ê ‚¼ ‚ê ‚É"AE-§‚ÌPID• § OEä‚ð •s ‚È ‚¤ ‚Ì ‚ª Žå-¬‚Å ‚ ‚é ‚ª,-¬ 'Ì-Í‚É ‚ae ‚é •¡ ŽG‚È"ñ •ü OE`"Á•« ‚Ì ‚½‚ß ‚É ‚ ‚Ü ‚èƒn ƒCƒQƒC ƒ" ‚É‚· ‚é ‚± ‚AE‚ª ‚Å ‚« ‚¸,ˆÀ 'è ‰»‚Í •} ‚ê ‚é ‚à ‚Ì ‚Ì • § OE䕸 "x ‚É ‚Í ‰ü 'P ‚Ì-]'n ‚ª Žc ‚³ ‚ê ‚Ä‚¢ ‚½.‚³ ‚ç ‚É,‚± ‚ê ‚Ü‚Å ‚Í 'è "_ •Û Ž• ‹@"\ ‚É•d "_ ‚ª 'u ‚© ‚ê ‚Ä ‚¢ ‚½‚ª,ŠC-m •HŽ-‚â ŠC-m '² •¸ "™‚Å ƒ‹ •[ ƒg ƒgƒ‰ƒbƒL ƒ" ƒO‹@"\ ‚Ì Žù-v ‚ª '• ‚¦ ‚Ä ‚« ‚½‚½ ‚ß,-¬ 'Ì-Í‚É‹NˆöÍ‚É‹Nˆö ‚· ‚é "®"Á•« ‚Ì 'å ‚« ‚È•Ï ‰» ‚Ö ‚Ì 'Î ‰ž‚â,ƒ• ƒ{ ƒb ƒg‚Ì ‹O"¹ 'Ç •] • § OEä ‚AE"¯ ‚ ¶ ‚ae ‚¤ ‚É ƒ‹ •[ ƒg‚Ì •Ï •j "_(Waypoint; WP)‚Å ‚Ì • § OEä•Î •· ‚Ì ‰ü'P ‚â '€ •ì-Ê ‚Ì ‹} •Ï ‚Ì ŠÉ˜aŠÉ˜a ‚È ‚Ç ‚à ‹• ‚ß ‚ç ‚ê ‚é ‚ae ‚¤ ‚É ‚È ‚Á‚Ä ‚« ‚½."Á ‚ÉŠµ•« ‚Ì 'å ‚« ‚È'D ‚Å ‚Í,WP‚Ì Žè'O ‚© ‚ç 'D ‚Ì "®•ì ‚ð-\'ª ‚µ ‚Ä•Ï •j "®•ì ‚É"ü ‚é ƒAƒ‹ ƒS ƒŠƒYƒ€ ‚ð •l ‚¦ ‚é •K-v ‚ª ‚ ‚é. ‚± ‚ê ‚ç ‚Ì-v ‹• ‚É'Î ‚µ ‚Ä,‹ß "N"ñ •ü OE`OEn‚Ö ‚Ì "K-p‚ª •· ‚ñ ‚ÉOE¤ ‹ †1)‚³ ‚ê ‚Ä‚¢ ‚é "ñ •ü OE`Receding Horizon(RH)• § OEä‚Í,Še Žž•• ‚É ‚¨‚¢‚¨‚¢ ‚Ä-L OEÀ Žž ŠÔ-¢-ˆ‚Ü‚Å‚Ì ‹" "® ‚ð-\'ª ‚µ ‚È ‚ª ‚ç •Å"K ‚È '€ •ì-Ê‚ð OEˆ'è ‚· ‚é • § OEäŽè-@‚Å ‚ ‚é ‚± ‚AE‚© ‚ç,•ó ‹µ •Ï ‰»‚ɉž‚ ¶ ‚½•Å"K ‚È• § OE䂪 ‰Â "\ ‚AE‚È ‚è,•]-ˆ"K-p‚ª •¢ "ï ‚Å ‚ ‚Á‚½•¡ ŽG‚È ƒVƒXƒe ƒ€ ‚Å ‚à • § OEä•« "\ ‚Ì OEü•ã ‚ð •} ‚é ‚± ‚AE‚ª Šú 'Ò ‚Å ‚« ‚é.-{ •e ‚Å ‚Í,‚± ‚Ì "ñ •ü OE`RH• § OEä‚ð "K-p‚µ ‚½DPS‚Ì • § OEä'¥,‚¨‚ae ‚¨‚ae ‚Ñ‚» ‚Ì ‹@"\ ‚ð "‹ •Ú ‚µ ‚½ŠC'ê ƒP •[ ƒu ƒ‹ •z •Ý•ì ‹AE'D ‚Ì ŠC-m •HŽ-‚Ö ‚Ì "K-pŽ-á‚É‚Â ‚¢ ‚Ä•q ‚× ‚é. *•ì •è •d •H‹AEƒVƒXƒe ƒ€‹Z •p ŠJ"-ƒZƒ" ƒ^•[-¾•Î Žs •ì •è '¬1-1