Kinematic Modeling of Robotic Manipulators

Review
  • 273 Downloads

Abstract

This paper presents the exhaustive review on the kinematic modeling of robotic manipulators in a systematic manner. A lot of techniques are available in the literature for kinematic modeling of robotic manipulators, however the ambiguity lies with the user to select the most appropriate method. This paper presents the comparative study of different kinematic modeling techniques in terms of complexity, applicability of the method to a particular class of robots and number of parameters or variables required to define the robot. Determination of the correct kinematic parameters, required to develop accurate kinematic models, using different methods has been demonstrated by considering the case study of a five degrees-of-freedom (DOFs) articulated manipulator. Moreover, a seven-DOFs manipulator is considered to highlight and address the inconsistencies of popular methods, while dealing with spatial hybrid manipulators. In this article, a review of 100 research papers is presented to investigate the kinematic study of robotic manipulators with a variety of modeling techniques, which are evolved or refined during the last sixty-odd years (1955–2016).

Keywords

Robotic manipulators D–H parameters Kinematic modeling Open- and closed-loop chains 

References

  1. 1.
    Denavit J, Hartenberg RS (1955) A kinematic notation for lower pair mechanisms based on matrices. ASME J Appl Mech 6:215–221MathSciNetMATHGoogle Scholar
  2. 2.
    Craig JJ (1986) Introduction to robotics: mechanics and control. Addison-Wesley, ReadingGoogle Scholar
  3. 3.
    Kahn ME, Roth B (1971) The near minimum-time control of open-loop articulated kinematic chains. ASME J Dyn Syst Meas Control 93(3):164–172CrossRefGoogle Scholar
  4. 4.
    Featherstone R (1982) A program for simulating robot dynamics, working paper 155, Department of Artificial Intelligence, University of Edinburgh, EdinburghGoogle Scholar
  5. 5.
    Rocha CR, Tonetto CP, Dias A (2011) A comparison between the Denavit–Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators. J Robot Comput Integr Manuf 27(4):723–728CrossRefGoogle Scholar
  6. 6.
    Lipkin H (2005) A note on Denavit–Hartenberg notation in robotics. In: Proceedings of ASME international design engineering technical conferences and computers and information in engineering conference (IDETC/CIE) 921–926, Long Beach, CaliforniaGoogle Scholar
  7. 7.
    Paul RP (2005) Robot manipulators mathematics, programming and control. MIT Press, CambridgeGoogle Scholar
  8. 8.
    Shilling RJ (2008) Fundamentals of robotics analysis and control, 3rd impression. Prentice Hall, Saddle RiverGoogle Scholar
  9. 9.
    Pennock GR, Yang AT (1985) Application of dual-number matrices to the inverse kinematics problem of robot manipulators. ASME J Mech Transm Autom Design 107(2):201–208CrossRefGoogle Scholar
  10. 10.
    Bergamasco M, Allotta B, Bosio L, Ferretti L, Parrini G, Prisco GM, Salsedo F, Sartini G (1994) An arm exoskeleton system for teleoperation and virtual environments applications. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), San Diego, pp 1449–1454Google Scholar
  11. 11.
    Zollo L, Siciliano B, Laschi C, Teti G, Dario P (2003) An experimental study on compliance control for a redundant personal robot arm. J Robot Auton Syst 44(2):101–129CrossRefGoogle Scholar
  12. 12.
    Zanchettin AM, Rocco P, Bascetta L, Symeonidis I, Peldschus S (2011) Kinematic analysis and synthesis of human arm during a manipulation task. In: Proceedings of the IEEE international conference of robotics and automation (ICRA), Shanghai, pp 2692–2697Google Scholar
  13. 13.
    Aspragathos NA, Dimitros JK (1998) A comparative study on three methods for robot kinematics. IEEE Trans Man Cybern Syst 28:135–145CrossRefGoogle Scholar
  14. 14.
    Cleary K, Brooks T (1993) Kinematic analysis of a novel six-DOF parallel manipulator. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Atlanta, pp 708–713Google Scholar
  15. 15.
    Sheth PN, Uicker JJ (1971) A generalized symbolic notation for mechanisms. ASME J Eng Ind 93(1):102–112CrossRefGoogle Scholar
  16. 16.
    Thomas U, Maciuszek I, Wahl FM (2002) A Unified Notation for Serial, parallel and hybrid kinematic structures. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Washington, DC, pp 2868–2873Google Scholar
  17. 17.
    Khalil W, Kleinfinger JF (1986) A new geometric notation for open and closed-loop robots. In: Proceedings of the IEEE international conference on robotics and automation (ICRA) vol 3, San Francisco, pp 1174–1179Google Scholar
  18. 18.
    Siciliano B, Sciavicco L, Villani L, Oriolo G (2009) Robotics, modeling, planning and control. In: Advanced textbooks in control and signal processing, Springer, London LimitedGoogle Scholar
  19. 19.
    Sahu S, Biswal BB, Subudhi B (2008) A novel method for representing robot kinematics using quaternion theory. In: Proceedings of the IEEE international conference on computational intelligence, control and computer vision in robotics and automation, NIT Rourkela, pp 76–82Google Scholar
  20. 20.
    Vandervaart RH, Cipra RJ (1984) The kinematics of open-loop manipulators using IMP (Integrated Mechanisms Program). In: Proceedings of the IEEE in American control conference, San Diego, pp 1870–1875Google Scholar
  21. 21.
    Muir PF, Neuman CP (1987) Kinematic modeling of wheeled mobile robots. J Robot Syst 4(2):281–340CrossRefGoogle Scholar
  22. 22.
    Bongardt B (2011) CAD-2-SIM—Kinematic modeling of mechanisms based on the Sheth–Uicker convention. Int Conf Intell Robot Appl 7101:465–477Google Scholar
  23. 23.
    Dutta PS, Wong TL (1989) Inverse kinematic analysis of moving base robot with redundant degree of freedom. CAD/CAM Robot Factor Future Robot Plant Autom 3:139–143Google Scholar
  24. 24.
    Goswami A, Quaid A, Peshkin M (1993) Identifying robot parameters using partial pose information. IEEE J Control Syst 13(5):6–14CrossRefGoogle Scholar
  25. 25.
    Baigunchekov Z, Nurakhmetov B, Absadykov B, Sartayev K, Izmambetov M, Baigunchekov N (2007) The new parallel manipulator with 6-degree-of-freedom. In: Proceedings of 12th IFToMM world congress in mechanism and machine science, vol 5, Besancon, France, pp 641–646Google Scholar
  26. 26.
    Megahed SM (1990) Human hand modeling by homogeneous transformation. Proc IEEE Int Conf Med Biol Soc 12:2122–2123Google Scholar
  27. 27.
    Megahed SM (1993) Efficient robot arm modeling for computer control. J Robot Syst 10(8):1095–1109CrossRefMATHGoogle Scholar
  28. 28.
    Acaccia GM, Bruzzone L, Michelini RC, Molfino RM, Calligari M (2001) Mobile robots: kinematics of non-holonomic path-planning. In: Proceeding of the IASTED international conference on modeling, identification and control, Innsbruck, Austria, pp 714–717Google Scholar
  29. 29.
    Megahed SM, Renaud M (1983) Dynamic modeling of robot manipulators containing closed kinematic chains. In: Proceedings of advanced software conference in robotics, Liege, BelgiumGoogle Scholar
  30. 30.
    Roth B (1985) Overview on advanced robotics: manipulation. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Tokyo, Japan, pp 559–570Google Scholar
  31. 31.
    Reichenbach T, Kovacic Z (2005) Collision free path planning in robot cells using virtual 3D sensors. In: Kordic V, Lazinica A, Meran M (eds) Cutting edge robotics. Pub: Pro Literatur Verlag, GermanyGoogle Scholar
  32. 32.
    Flückiger L, Baur C, Clavel R (1998) CINEGEN: A rapid prototyping tool for robot manipulators. In: The 4th international conference on motion and vibration control (MOVIC), vol 1, Zurich, pp 129–134Google Scholar
  33. 33.
    Flückiger L (1998) A robot kinematics using virtual reality and automatic kinematics generator. In: Proceedings of the 29th international symposium on robotics, Birmingham, pp, 123–126Google Scholar
  34. 34.
    Khalil W, Chevallereau C (1987) An efficient algorithm for the dynamic control of robots in Cartesian space. In: Proceedings of the IEEE the 28th conference on decision and control, Los Angeles, California, pp 582–588Google Scholar
  35. 35.
    Gautier M, Khalil W (1988) A direct determination of minimum inertial parameters of robots. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Philadelphia, pp 1682–1687Google Scholar
  36. 36.
    Khalil W, Guegan S (2004) Inverse and direct dynamic modeling of Gough–Stewart robots. IEEE Trans Robot Autom 20(4):754–761CrossRefGoogle Scholar
  37. 37.
    Khalil W, Ibrahim O (2007) General solution for dynamic modeling of parallel robots. J Intell Rob Syst 49(1):19–37CrossRefGoogle Scholar
  38. 38.
    Ibrahim O, Khalil W (2007) Kinematic and dynamic modeling of 3-RPS parallel manipulator. In: Proceedings of 12th IFToMM world congress, BesanconGoogle Scholar
  39. 39.
    Guegan S, Khalil W, Lemoine P (2003) Identification of dynamic parameters of the orthoglide. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), vol 3, Taipei, Taiwan, pp 3272–3277Google Scholar
  40. 40.
    Gautier M (1990) Numerical Calculation of the base inertial parameters of robots. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Cincinnati, pp 1020–1025Google Scholar
  41. 41.
    Khalil W, Besnard S, Lemoine P (2000) Comparison study of the parametric calibration methods 15:56–67Google Scholar
  42. 42.
    Bennis F, Khalil W (1991) Minimum inertial parameters of robots with parallelogram closed loops. IEEE Trans Syst Man Cybern 21:318–326CrossRefGoogle Scholar
  43. 43.
    Khalil W Garcia G Delagrade JF (1995) Calibration of geometric parameters of robots without external sensors. In: Proceedings of the IEEE, international conference on robotics and automation (ICRA), vol 3, Nagoya, pp 3039–3044Google Scholar
  44. 44.
    Perrin B, Chevallerau C, Verdier C (1997) Calculation of direct dynamic model of walking robots: comparison between two methods. In: Proceedings of the IEEE, international conference on robotics and automation (ICRA), vol 2, Albuquerque, New Mexico, pp 1088–1093Google Scholar
  45. 45.
    Khalil W, Lemoine P, Gautier M (1996) Autonomous calibration of robots using planar points. In: World automation congress, robotic and manufacturing systems, vol 3, Montpellier, FranceGoogle Scholar
  46. 46.
    Khalil W (2010) Dynamic modeling of robots using recursive Newton–Euler techniques. In: International conference on informatics in control, automation and robotics, PortugalGoogle Scholar
  47. 47.
    Khalil W, Restrepo PP (1996) An efficient algorithm for calculation of filtered dynamic models of robots. In: Proceedings of the IEEE, international conference on robotics and automation (ICRA), vol 1, Minneapolis, Minnesota, pp 323–328Google Scholar
  48. 48.
    Ma L, Zhang W, Chablat D, Bennis F, Guillaume F (2009) Multi-objective optimization method for posture prediction and analysis with consideration of fatigue effect and its application case. J Comput Ind Eng 57(4):1235–1246CrossRefGoogle Scholar
  49. 49.
    Khalil W, Boyer F (1995) An efficient calculation of computed torque control of flexible manipulators. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), vol 1, Nagoya, pp 609–614Google Scholar
  50. 50.
    Venture G, Khalil W, Guatier M, Bodson P (2002) Dynamic modeling and identification of a car. In: Proceedings of the world congress of international federation of automatic control, Barcelona, SpainGoogle Scholar
  51. 51.
    Khalil W, Kleinfinger JF (1987) Minimum operations and minimum parameters of the dynamic models of tree structure robots. IEEE J Robot Autom 3(6):517–526CrossRefGoogle Scholar
  52. 52.
    Khalil W, Guatier M, Lemoine P (2007) Identification of the payload inertial parameters of industrial manipulators. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Rome, pp 4943–4948Google Scholar
  53. 53.
    Bessonnet G, Sardain P (2005) Optimal dynamics of actuated kinematic chains. Part-1: dynamic modeling and differentiations. Eur J Mech A/Solids 24(3):452–471MathSciNetCrossRefMATHGoogle Scholar
  54. 54.
    Poignet P, Guatier M, Khalil W, Pham MT (2002) Modeling simulation and control of high speed machine tools using robotics formalism. J Mechatron 12(3):461–487CrossRefGoogle Scholar
  55. 55.
    Pham MT, Guatier M, Poignet P (2001) Identification of joint stiffness with bandpass filtering. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), vol 3, Seoul, Korea, pp 2867–2872Google Scholar
  56. 56.
    Belifiore NP, Benedetto AD (2000) Connectivity and redundancy in spatial robots. Int J Robot Res 19(12):1245–1261CrossRefGoogle Scholar
  57. 57.
    Corke PI (2007) A simple and systematic approach to assigning D–H parameters. IEEE Trans Robot 23(3):590–594CrossRefGoogle Scholar
  58. 58.
    Liarokapis MV, Artemiadis PK, Kyriakopoulos KJ (2013) Quantifying anthromorphism of robot hands. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Karlsruhe, pp 2041–2046Google Scholar
  59. 59.
    Chou JCK, Kamel M (1988) Quaternions approach to solve the kinematic equation of rotation \( {\text{A}}_{\text{a}} {\text{A}}_{\text{x}} = {\text{A}}_{\text{x}} {\text{A}}_{\text{b}} \), of a sensor-mounted robotic manipulator. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), Philadelphia, pp 656–662Google Scholar
  60. 60.
    Shoemake K (1985) Animating rotation with quaternion curves. In: Association for computing machinery’s special interest group (ACM SIGGRAPH) on computer graphics, vol 19(3), San Francisco, pp 245–254Google Scholar
  61. 61.
    Gouasmi M, Ouali M, Brahim F (2012) Robot kinematics using dual quaternions. Int J Robot Autom 1(1):13–30Google Scholar
  62. 62.
    Yang AT, Freudenstein F (1964) Application of dual-number quaternion algebra to the analysis of spatial mechanisms. Trans ASME J Appl Mech 31(2):300–308MathSciNetCrossRefMATHGoogle Scholar
  63. 63.
    Crane CD III, Duffy J (2008) Kinematic analysis of robot manipulators. Cambridge University Press, CambridgeMATHGoogle Scholar
  64. 64.
    Clifford W (1873) Preliminary sketch of bi-quaternion. In: Proceedings of London Mathematical SocietyGoogle Scholar
  65. 65.
    Rooney J, Clifford WK (1845–1879) (2007) Distinguished figures in mechanism and machine science: their contributions and legacies. In: Ceccarelli M (ed). History of mechanism and machine science, Springer, Dordrecht, pp 79–116Google Scholar
  66. 66.
    Pervin E, Webb JA (1982) Quaternions in computer vision and robotics. Carnegie-Mellon University, Department of Computer Science, PittsburghGoogle Scholar
  67. 67.
    Taylor RH (1979) Planning and execution of straight line manipulator trajectories. IBM J Res Dev 23(4):424–436CrossRefGoogle Scholar
  68. 68.
    Dooley JR, McCarthy JM (1991) Spatial rigid body dynamics using dual quaternion components. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Sacramento, pp 90–95Google Scholar
  69. 69.
    Azariadis P, Aspragathos N (2001) Computer graphics representation and transformation of geometric entities using dual unit vectors and line transformations. Comput Graph 25(2):195–209CrossRefGoogle Scholar
  70. 70.
    Perez A, McCarthy JM (2004) Dual quaternion synthesis of constrained robotic systems. ASME J Mech Des 126(3):425–435CrossRefGoogle Scholar
  71. 71.
    Yuanxin W, Hu X, Hu D, Li T, Lian J (2005) Strapdown inertial navigation system algorithms based on dual quaternions. Trans IEEE Aerosp Electron Syst 41(1):110–132ADSCrossRefGoogle Scholar
  72. 72.
    Salamin E (1979) Application of quaternions to computation with rotations. Working paper Stanford AI LabGoogle Scholar
  73. 73.
    Walker MW, Shao L, Volz RA (1991) Estimating 3-D location parameters using dual number quaternions. CVGIP Image Underst 54(3):358–367CrossRefMATHGoogle Scholar
  74. 74.
    Konstantinos D (1999) Hand-eye calibration using dual quaternions. Int J Robot Res 18(3):286–298CrossRefGoogle Scholar
  75. 75.
    Bottema O, Roth B (1979) Theoretical kinematics. North Holland Publishing, Amsterdam, pp 518–525MATHGoogle Scholar
  76. 76.
    Study E (1903) Geometrie der Dynamen: die Zusammensetzung von Kräften und verwandte Gegenstände der Geometrie. Cornell University Library, IthacaMATHGoogle Scholar
  77. 77.
    Funda J, Taylor RH, Paul RP (1990) On homogeneous transforms, quaternions, and computational efficiency. IEEE Trans Robot Autom 6(3):382–388CrossRefGoogle Scholar
  78. 78.
    Blaschke W (1982) Gesammelte Werke. Thales-Verlag, EssenMATHGoogle Scholar
  79. 79.
    Keat JE (1977) Analysis of least-squares attitude determination routine DOAOP, Technical report CSC/TM–77/6034, Computer Sciences CorpGoogle Scholar
  80. 80.
    Grace W (1966) A least squares estimate of satellite altitude Problem 65.1. Soc Ind Appl Math (SIAM) Rev 8(3):384–386Google Scholar
  81. 81.
    Horn BKP (1987) Closed-form solution of absolute orientation using unit quaternions. J Opt Soc Am (JOSA) 4(4):629–642ADSCrossRefGoogle Scholar
  82. 82.
    Gan D, Liao Q, Wei S, Dai JS, Qiao S (2008) Dual quaternion-based inverse kinematics of the general spatial 7R mechanism. Proc Inst Mech Eng Part C J Mech Eng Sci 222(8):1593–1598CrossRefGoogle Scholar
  83. 83.
    Wang X, Yu C (2011) Unit-dual-quaternion-based PID control scheme for rigid-body transformation. In: Proceedings of 18th world congress international federation of automatic control, Milano, Italy, pp 9296–9301Google Scholar
  84. 84.
    Gilmore R (2008) Lie groups, physics, and geometry: an introduction for physicists, engineers and chemists, 1st edn. Published in the United States of America by Cambridge University Press, New YorkCrossRefMATHGoogle Scholar
  85. 85.
    Iserles A, Munthe-Kaas H, Nørsett SP, Zanna A (2000) Lie-group methods. Acta Numer 9:215–365MathSciNetCrossRefMATHGoogle Scholar
  86. 86.
    Murray RM, Li Z, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC Press, Boca RatonMATHGoogle Scholar
  87. 87.
    Thomas F, Torras C (1988) A group-theoretic approach to the computation of symbolic part relations. IEEE J Robot Autom 4(6):622–634CrossRefGoogle Scholar
  88. 88.
    Jonghoon P, Chung WK (2005) Geometric integration on Euclidean group with application to articulated multi-body systems. IEEE Trans Robot 21(5):850–863CrossRefGoogle Scholar
  89. 89.
    Herve JM (1978) Analyse structurelle des mécanismes par groupe des déplacements. Mech Mach Theory 13(4):437–450CrossRefGoogle Scholar
  90. 90.
    Herve JM, Sparacino F (1991) Structural synthesis of parallel robots generating spatial translation. In: Proceedings of the IEEE international conference on advanced robotics, Pise, pp 808–813Google Scholar
  91. 91.
    Nordkvist N, Sanyal AK (2010) A Lie group variational integrator for rigid body motion in SE (3) with applications to underwater vehicle dynamics. In: The 49th IEEE conference on decision and control (CDC), Atlanta, pp 5414–5419Google Scholar
  92. 92.
    Park FC, Bobrow JE (1994) A recursive algorithm for robot dynamics using Lie groups. In: Proceedings of the IEEE international conference on robotics and automation (ICRA), San Diego, pp 1535–1540Google Scholar
  93. 93.
    Gu YL (1988) Analysis of orientation representations by Lie algebra in robotics. In Proceedings of the IEEE international conference on robotics and automation (ICRA), Philadelphia, pp 874–879Google Scholar
  94. 94.
    Selig JM (2004) Lie groups and Lie algebras in robotics. Computational non-commutative algebra and applications. Springer, Netherlands, pp 101–125Google Scholar
  95. 95.
    Rico JM, Gallardo J, Ravani B (2003) Lie algebra and the mobility of kinematic chains. J Robot Syst 20(8):477–499CrossRefMATHGoogle Scholar
  96. 96.
    Coelho P, Nunes U (2003) Lie algebra application to mobile robot control: a tutorial. Robotica 21:483–493CrossRefGoogle Scholar
  97. 97.
    Sparacino F, Herve JM (1993) Synthesis of parallel manipulators using Lie-groups Y-star and H-robot. Can robots contribute to preventing environmental deterioration? In: Proceedings of the IEEE international workshop on advanced robotics, Tsukuba, pp 75–80Google Scholar
  98. 98.
    Dekret A, Jan B (2001) Applications of line objects in robotics. Journal of Acta Universitatis Matthiae Belii Math 9:29–42MathSciNetMATHGoogle Scholar
  99. 99.
    Singh A, Singla A, Soni S (2014) D–H parameters augmented with dummy frames for serial manipulators containing spatial links. In: The 23rd IEEE international symposium on robot and human interactive communication (RO-MAN 2014), Edinburgh, Scotland, pp 975–980Google Scholar
  100. 100.
    Singh A, Singla A, Soni S (2015) Extension of D–H parameter method to hybrid manipulators used in robot-assisted surgery. Proc Inst Mech Eng Part H J Eng Med 229(10):703–712CrossRefGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThapar UniversityPatialaIndia

Personalised recommendations