Trajectory-planning through interpolation by overlapping cubic arcs and cubic splines
A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end‐effector of th...
Uložené v:
| Vydané v: | International journal for numerical methods in engineering Ročník 57; číslo 11; s. 1615 - 1641 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Chichester, UK
John Wiley & Sons, Ltd
21.07.2003
|
| Predmet: | |
| ISSN: | 0029-5981, 1097-0207 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end‐effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time‐domain. Further user‐specified information is used to determine how the end‐effector orientation angle should vary along the specified curve. The proposed trajectory‐planning methodology is embodied in a computer‐algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time‐domain. If a varying end‐effector orientation angle is specified, the OCAS‐algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time‐domain. The trajectory‐planning capabilities of the OCAS‐algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non‐linear functions, as well as for nodal points specified along a non‐analytical (free‐form) test‐curve. The proposed trajectory‐planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free‐form curves. Copyright © 2003 John Wiley & Sons, Ltd. |
|---|---|
| AbstractList | A new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end-effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time-domain. Further user-specified information is used to determine how the end-effector orientation angle should vary along the specified curve. The proposed trajectory-planning methodology is embodied in a computer-algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time-domain. If a varying end-effector orientation angle is specified, the OCAS-algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time-domain. The trajectory-planning capabilities of the OCAS-algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non-linear functions, as well as for nodal points specified along a non-analytical (free-form) test-curve. The proposed trajectory-planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free-form curves. A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end‐effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time‐domain. Further user‐specified information is used to determine how the end‐effector orientation angle should vary along the specified curve. The proposed trajectory‐planning methodology is embodied in a computer‐algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time‐domain. If a varying end‐effector orientation angle is specified, the OCAS‐algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time‐domain. The trajectory‐planning capabilities of the OCAS‐algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non‐linear functions, as well as for nodal points specified along a non‐analytical (free‐form) test‐curve. The proposed trajectory‐planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free‐form curves. Copyright © 2003 John Wiley & Sons, Ltd. A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end‐effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time‐domain. Further user‐specified information is used to determine how the end‐effector orientation angle should vary along the specified curve. The proposed trajectory‐planning methodology is embodied in a computer‐algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time‐domain. If a varying end‐effector orientation angle is specified, the OCAS‐algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time‐domain. The trajectory‐planning capabilities of the OCAS‐algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non‐linear functions, as well as for nodal points specified along a non‐analytical (free‐form) test‐curve. The proposed trajectory‐planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free‐form curves. Copyright © 2003 John Wiley & Sons, Ltd. |
| Author | du Plessis, L. J. Snyman, J. A. |
| Author_xml | – sequence: 1 givenname: L. J. surname: du Plessis fullname: du Plessis, L. J. organization: Multidisciplinary Design Optimization Group, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa – sequence: 2 givenname: J. A. surname: Snyman fullname: Snyman, J. A. email: jan.snyman@eng.up.ac.za organization: Multidisciplinary Design Optimization Group, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa |
| BookMark | eNp90F1LwzAUBuAgCs4p_oVeqSCdJ-naNJeicwp-3Dh2GdL0VKNdUpNO3b-3c0NQ1KvD4Ty8cN4dsmmdRUL2KQwoADuxMxzwRGyQHgXBY2DAN0mvu4g4FTndJjshPAFQmkLSI5N7r55Qt84v4qZW1hr7ELWP3s0fHiNjW_SNq1VrnI2KReRe0deqaZZIzwujI-V1iJQt12toamMx7JKtStUB99azTyYXo_uzy_j6bnx1dnod6ySjIsYhKC5YlRdYoQJeiVQjpghVWQk2TJBBmlKsKC8KNeRZnhVlXiLkZVkUOlNJnxyschvvXuYYWjkzQWPdPYJuHiTLgWWMiQ4e_Qsp5IwKxmnW0cMV1d6F4LGSjTcz5RcdksuGZdew7BruZPxDatN-dtV6Zepf_PHKv5kaF3_Fytub0bd0E1p8_9LKP8uMJzyV09uxzM_5FLKhkNPkA4k7nrs |
| CitedBy_id | crossref_primary_10_1017_S0263574714000393 crossref_primary_10_1016_j_mechmachtheory_2005_05_007 crossref_primary_10_1016_j_mechmachtheory_2009_04_005 crossref_primary_10_1002_cmm4_1049 crossref_primary_10_1016_j_mechmachtheory_2005_05_006 crossref_primary_10_1108_01439911011063263 crossref_primary_10_1002_asjc_203 crossref_primary_10_1177_0954406220969734 crossref_primary_10_1016_j_euromechsol_2013_05_007 crossref_primary_10_1016_j_robot_2016_09_008 crossref_primary_10_1002_mma_4790 crossref_primary_10_1016_j_endm_2018_05_004 |
| Cites_doi | 10.1016/S0094-114X(01)00030-1 10.1115/1.2919211 10.1016/S0736-5845(97)00021-5 10.1016/S0166-3615(01)00087-2 10.1016/S0094-114X(97)00095-5 |
| ContentType | Journal Article |
| Copyright | Copyright © 2003 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: Copyright © 2003 John Wiley & Sons, Ltd. |
| DBID | BSCLL AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D H8D |
| DOI | 10.1002/nme.739 |
| DatabaseName | Istex CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Aerospace Database |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Aerospace Database |
| DatabaseTitleList | Civil Engineering Abstracts Aerospace Database CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering Mathematics |
| EISSN | 1097-0207 |
| EndPage | 1641 |
| ExternalDocumentID | 10_1002_nme_739 NME739 ark_67375_WNG_8D7W0649_W |
| Genre | article |
| GroupedDBID | -~X .3N .DC .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACRPL ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GNP GODZA H.T H.X HBH HGLYW HHY HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K RNS ROL RX1 SUPJJ TN5 UB1 V2E VOH W8V W99 WBKPD WIB WIH WIK WLBEL WOHZO WQJ WXSBR WYISQ XG1 XPP XV2 ZZTAW ~02 ~A~ ~IA ~WT AAYXX CITATION O8X 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D H8D |
| ID | FETCH-LOGICAL-c3619-e40a792f8befea07f95cee5e0fdf9243e20551ef17bba47686bd8de08ddbbc6a3 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 12 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000184196400006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0029-5981 |
| IngestDate | Fri Jul 11 11:34:06 EDT 2025 Fri Jul 11 15:53:51 EDT 2025 Sat Nov 29 01:43:46 EST 2025 Tue Nov 18 21:36:27 EST 2025 Sun Sep 21 06:26:15 EDT 2025 Sun Sep 21 06:18:46 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Language | English |
| License | http://onlinelibrary.wiley.com/termsAndConditions#vor |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c3619-e40a792f8befea07f95cee5e0fdf9243e20551ef17bba47686bd8de08ddbbc6a3 |
| Notes | istex:55956E2B054579AA971D1E670D2058CD76DBBEC8 ark:/67375/WNG-8D7W0649-W ArticleID:NME739 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1082192716 |
| PQPubID | 23500 |
| PageCount | 27 |
| ParticipantIDs | proquest_miscellaneous_28026229 proquest_miscellaneous_1082192716 crossref_primary_10_1002_nme_739 crossref_citationtrail_10_1002_nme_739 wiley_primary_10_1002_nme_739_NME739 istex_primary_ark_67375_WNG_8D7W0649_W |
| PublicationCentury | 2000 |
| PublicationDate | 21 July 2003 |
| PublicationDateYYYYMMDD | 2003-07-21 |
| PublicationDate_xml | – month: 07 year: 2003 text: 21 July 2003 day: 21 |
| PublicationDecade | 2000 |
| PublicationPlace | Chichester, UK |
| PublicationPlace_xml | – name: Chichester, UK |
| PublicationTitle | International journal for numerical methods in engineering |
| PublicationTitleAlternate | Int. J. Numer. Meth. Engng |
| PublicationYear | 2003 |
| Publisher | John Wiley & Sons, Ltd |
| Publisher_xml | – name: John Wiley & Sons, Ltd |
| References | Bahr B, Xiao X, Krishnan K. A real-time scheme of cubic parametric curve interpolations for CNC systems. Computers in Industry 2001; 45:309-317. Granville WA, Smith PF, Longley WR. Elements of Differential and Integral Calculus. New Revised Edition. Blaisdell Publishing Company: Massachusetts, 1962. Kim J-H, Ryuh B-S, Pennock GR. Development of a trajectory method for a five-axis NC machine. Mechanism and Machine Theory 2001; 36:983-996. Wolovich WA. Robotics: Basic Analysis and Design. CBS College Publishing: New York, 1987. Dasgupta B, Mruthyunjaya TS. Singularity-free path planning for the Stewart platform manipulator. Mechanism and Machine Theory 1998; 33:711-725. Buchanan JL, Turner PR. Numerical Methods and Analysis. McGraw-Hill: New York, 1992. Gosselin CM, Hadj-Messaoud A. Automatic planning of smooth trajectories for pick-and-place operations. Transactions of the ASME: Journal of Mechanical Design 1993; 115:450-456. Burden RL, Faires JD. Numerical Analysis, 6th edn. Brooks/Cole Publishing Company: Pacific Grove, USA, 1997. Zhang QG, Greenway RB. Development and implementation of a NURBS curve motion interpolator. Robotics and Computer-Integrated Manufacturing 1998; 14:27-36. 1987 1997 1962 1992 2002 2000 2001; 45 1993; 115 2001; 36 1998; 33 1998; 14 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 Wolovich WA (e_1_2_1_5_2) 1987 Burden RL (e_1_2_1_11_2) 1997 e_1_2_1_2_2 e_1_2_1_3_2 Buchanan JL (e_1_2_1_12_2) 1992 e_1_2_1_10_2 Granville WA (e_1_2_1_13_2) 1962 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – reference: Gosselin CM, Hadj-Messaoud A. Automatic planning of smooth trajectories for pick-and-place operations. Transactions of the ASME: Journal of Mechanical Design 1993; 115:450-456. – reference: Bahr B, Xiao X, Krishnan K. A real-time scheme of cubic parametric curve interpolations for CNC systems. Computers in Industry 2001; 45:309-317. – reference: Wolovich WA. Robotics: Basic Analysis and Design. CBS College Publishing: New York, 1987. – reference: Buchanan JL, Turner PR. Numerical Methods and Analysis. McGraw-Hill: New York, 1992. – reference: Dasgupta B, Mruthyunjaya TS. Singularity-free path planning for the Stewart platform manipulator. Mechanism and Machine Theory 1998; 33:711-725. – reference: Zhang QG, Greenway RB. Development and implementation of a NURBS curve motion interpolator. Robotics and Computer-Integrated Manufacturing 1998; 14:27-36. – reference: Burden RL, Faires JD. Numerical Analysis, 6th edn. Brooks/Cole Publishing Company: Pacific Grove, USA, 1997. – reference: Granville WA, Smith PF, Longley WR. Elements of Differential and Integral Calculus. New Revised Edition. Blaisdell Publishing Company: Massachusetts, 1962. – reference: Kim J-H, Ryuh B-S, Pennock GR. Development of a trajectory method for a five-axis NC machine. Mechanism and Machine Theory 2001; 36:983-996. – volume: 45 start-page: 309 year: 2001 end-page: 317 article-title: A real‐time scheme of cubic parametric curve interpolations for CNC systems publication-title: Computers in Industry – year: 1997 – start-page: 126 year: 2000 end-page: 134 – start-page: 24 year: 2000 end-page: 33 – volume: 33 start-page: 711 year: 1998 end-page: 725 article-title: Singularity‐free path planning for the Stewart platform manipulator publication-title: Mechanism and Machine Theory – year: 1962 – volume: 115 start-page: 450 year: 1993 end-page: 456 article-title: Automatic planning of smooth trajectories for pick‐and‐place operations publication-title: Transactions of the ASME: Journal of Mechanical Design – year: 1992 – year: 2002 – year: 1987 – volume: 36 start-page: 983 year: 2001 end-page: 996 article-title: Development of a trajectory method for a five‐axis NC machine publication-title: Mechanism and Machine Theory – volume: 14 start-page: 27 year: 1998 end-page: 36 article-title: Development and implementation of a NURBS curve motion interpolator publication-title: Robotics and Computer‐Integrated Manufacturing – volume-title: Numerical Methods and Analysis year: 1992 ident: e_1_2_1_12_2 – volume-title: Numerical Analysis year: 1997 ident: e_1_2_1_11_2 – volume-title: Robotics: Basic Analysis and Design year: 1987 ident: e_1_2_1_5_2 – ident: e_1_2_1_6_2 – ident: e_1_2_1_9_2 doi: 10.1016/S0094-114X(01)00030-1 – volume-title: Elements of Differential and Integral Calculus year: 1962 ident: e_1_2_1_13_2 – ident: e_1_2_1_2_2 doi: 10.1115/1.2919211 – ident: e_1_2_1_10_2 – ident: e_1_2_1_7_2 doi: 10.1016/S0736-5845(97)00021-5 – ident: e_1_2_1_8_2 doi: 10.1016/S0166-3615(01)00087-2 – ident: e_1_2_1_3_2 doi: 10.1016/S0094-114X(97)00095-5 – ident: e_1_2_1_4_2 |
| SSID | ssj0011503 |
| Score | 1.765018 |
| Snippet | A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar... A new path‐planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar... A new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar... |
| SourceID | proquest crossref wiley istex |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1615 |
| SubjectTerms | Acceleration Automation cubic spline interpolation Interpolation machine tool orientation Machine tools Mathematical analysis Methodology non-uniform rational B-splines (NURBS) Orientation overlapping cubic arcs planar industrial robot Splines trajectory-planning |
| Title | Trajectory-planning through interpolation by overlapping cubic arcs and cubic splines |
| URI | https://api.istex.fr/ark:/67375/WNG-8D7W0649-W/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnme.739 https://www.proquest.com/docview/1082192716 https://www.proquest.com/docview/28026229 |
| Volume | 57 |
| WOSCitedRecordID | wos000184196400006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library Full Collection 2020 customDbUrl: eissn: 1097-0207 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011503 issn: 0029-5981 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NbtQwEB6VXQ5woKWAWGiLkareQrPOJraPVdulh3aFENX2ZtnxGC2UtNp0Eb3xCDwjT8I48UZboUpInCIrYyWaH8-MPf4GYDfzxHmnTIICVTKS6BIj3DApCme9R-ukayR9KiYTeXGhPqy0-mrxIboNt2AZzXodDNzYen8FNPQbvhOZegB9Tlqb96B_9HF8ftodIVCkky3rO3Ilh-2N2TB5P06944r6gas_7sSZq9Fq427G6__xoxvwJMaY7KBViqewhtUmrMd4k0Vrrjfh8QoYIY3OOgTX-hlMyYl9aXb0b3___HUdWxux2NaHzdr2XG0hHbO3LFSCXpoA9vCZlQs7KxlZUM1M5eKwDld_sX4O5-PjT4cnSWzCkJQZJVcJjlIjFPfSokeTCq9y8qs5pt55yt0y5CkFXeiHwlozouSlCPLFVDpnbVmY7AX0qqsKXwKj7M5TekKLCsVtFqXNS0XpnrBcWJOPigHsLeWhy4hQHhplXOoWW5lrYqUmVg6AdYTXLSjH3yR7jUC792b-NdSwiVxPJ--1PBJTCsaUng7g7VLimiwrHJeYCq8WdYBOpeWcU0I5gDf30HBJOSzn9LndRgXu-x09OTumx6t_I3sNj5qawVQkfLgFvZv5ArfhYfn9ZlbPd6Ki_wFZ2AYA |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwEB5BFwk4UCgglleNVPUWmnUedo6IdiliN0Ko1fZm2fEYLZS02nQRvfET-I38EsaJN9oKVULiFFkZK9E8PDP2-BuAncQR522hIxRYRKlEG2lhR1GeW-McGittK-mJKEt5clJ8DFWV_i5Mhw_Rb7h5y2jXa2_gfkN6bw019Bu-FklxEwYpKRFp92D_0_h40p8hUKiTrAo8skKOuiuzfvJemHrFFw08W39cCTTXw9XW34w3_-dP78O9EGWyN51aPIAbWG_BZog4WbDnZgvursER0mjaY7g2D2FGbuxLu6d_-fvnr_PQ3IiFxj5s3jXo6krpmLlkvhb0VHu4h8-sWpp5xciGGqZrG4aNv_yLzSM4Hh8cvT2MQhuGqEoovYowjbUouJMGHepYuCIjz5ph7Kyj7C1BHlPYhW4kjNEppS-5lzDG0lpjqlwnj2GjPqvxCTDK7xwlKLSsUORmUJqsKijhE4YLo7M0H8LuSiCqChjlvlXGqerQlbkiVipi5RBYT3jewXL8TbLbSrR_rxdffRWbyNSsfKfkvphROFao2RBerUSuyLb8gYmu8WzZePBUWtA5pZRD2L6GhkvKYjmnz-20OnDd76hyekCPp_9Gtg23D4-mEzV5X354BnfaCsJYRHz0HDYuFkt8Abeq7xfzZvEyaP0f9UwJ8A |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1fb9MwED9BixA8MBhDlH8z0rS3sDT_HD9OdAVEF02IqXuz7PiMCiOrmhWxNz7CPuM-yc6JG3VCk5B4iqyclejOZ__OPv8OYCe2pHkjVIAcRZDkaALFzTDIMqOtRW1y01h6wosiPzkRRz6r0t2Fafkhug035xnNfO0cHOfG7q2xhv7EdzwWd6GfuBIyPeiPvoyPJ90ZAkGdeJXgkYp82F6ZdZ33fNcba1HfqfX3DaC5Dleb9Wa88T9_-hgeeZTJ9tth8QTuYLUJGx5xMu_P9SY8XKMjpNZhx-FaP4UpLWPfmz39i6s_l3Nf3Ij5wj5s1hboalPpmL5gLhf0VDm6h2-sXOpZyciHaqYq45u1u_yL9RYcjw--vv8Y-DIMQRlTeBVgEiouIptrtKhCbkVKK2uKoTWWorcYo5BgF9oh11olFL5kzsIY5sZoXWYqfga96qzC58AovrMUoNC0QshNY67TUlDAx3XEtUqTbAC7K4PI0nOUu1IZp7JlV44kqVKSKgfAOsF5S8vxt8huY9HuvVr8cFlsPJXT4oPMR3xKcEzI6QDerkwuybfcgYmq8GxZO_JUmtAjCikHsH2LTJRTFBtF9LmdZgzc9juyODygx4t_E9uG-0ejsZx8Kj6_hAdNAmHIg2j4CnrniyW-hnvlr_NZvXjjB_01dHEJaw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Trajectory-planning+through+interpolation+by+overlapping+cubic+arcs+and+cubic+splines&rft.jtitle=International+journal+for+numerical+methods+in+engineering&rft.au=du+Plessis%2C+L+J&rft.au=Snyman%2C+J+A&rft.date=2003-07-21&rft.issn=0029-5981&rft.volume=57&rft.issue=11&rft.spage=1615&rft.epage=1641&rft_id=info:doi/10.1002%2Fnme.739&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-5981&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-5981&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-5981&client=summon |