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...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 57; H. 11; S. 1615 - 1641 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Chichester, UK
John Wiley & Sons, Ltd
21.07.2003
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| ISSN: | 0029-5981, 1097-0207 |
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| 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. |
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| 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 |
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| 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 |
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| 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 |
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| 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... |
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| 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 |
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