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A survey of efficient computational methods for manipulator inverse dynamics

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Abstract

In this paper, we present an up-to-date survey of various numerically efficient methods for solving the problem of computing manipulator inverse dynamics. The literature on this subject is extensive. However, in this paper, we review only those algorithms which have been derived based on the Euler—Lagrange, Newton—Euler and Kane's formulations of the dynamic equations of motion and are applicable to rigid-link open-chain robot manipulators. In particular, for each of these formulations we present a chronological account of the development of the most important algorithms which compute manipulator inverse dynamics. In this process some ‘classical’ algorithms are given and a number of issues which make it possible to reduce their computational complexity are emphasized. Also, the most efficient algorithms currently available are compared in terms of their computational complexity.

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References

  1. Khatib, O., Dynamic control of manipulators in operational space,6th IFTOMM Congress on Theory of Machines and Mechanisms, New Delhi, Dec. 15–20, 1983, pp. 1–10.

  2. Yoshikawa, T., Dynamic hybrid position/force control of robot manipulators, description of hand constraints and calculation of joint driving force,Proc. 1986 IEEE Int. Conf. Robot. Automat., San Francisco, CA, Apr. 1986, pp. 1393–1398.

  3. Misra, P., Patel, R. V. and Balafoutis, C. A., Robust control of robot manipulators using linearized dynamic models, in M. Jamshidi, J. Y. S. Luh and M. Shahinpoor (eds),Recent Trends in Robotics: Modeling, Control and Education, North-Holland, New York, 1986.

    Google Scholar 

  4. Misra, P., Patel, R. V. and Balafoutis, C. A., Robust control of robot manipulators in Cartesian space,Proc. American Control conf., Atlanta, Georgia, June 15–17, 1988, pp. 1351–1356.

  5. Spong, M. W., Thorp, J. S. and Kleinwaks, J. M., The control of robot manipulators with bounded input,IEEE Trans. Automat. Control AC-31(6), 483–490 (1986).

    Google Scholar 

  6. Shin, K. G. and McKay, N. D., A dynamic programming approach to trajectory planning of robotic manipulators,IEEE Trans. Automat. Control AC-31(6), 491–500 (1986).

    Google Scholar 

  7. Tan, H. H. and Potts, R. B., Minimum-time trajectory planner for the discrete dynamic robot model with dynamic constraints,IEEE J. Robot. Automat. RA-4(2), 174–185 (1988).

    Google Scholar 

  8. Hollerbach, J. M., Dynamic scaling of manipulator trajectories,ASME J. Dynam. Systems, Meas. Control 106 102–106 (1984).

    Google Scholar 

  9. Yoshikawa, T., Dynamic manipulability of robot manipulators,J. Robotic Systems, Vol. 2(1), 113–124 (1985).

    Google Scholar 

  10. Wittenburg, I. J.,Dynamics of Systems of Rigid Bodies, B. G. Teubner, Stuttgart, 1977.

    Google Scholar 

  11. Goldstein, H.,Classical Mechanics. 2nd edn. Addison-Wesley, Reading, MA, 1980.

    Google Scholar 

  12. Kane, T. R., Likins, P. W. and Levinson, D. A.,Spacecraft Dynamics, McGraw-Hill, New York, 1983.

    Google Scholar 

  13. REDUCE, The Rand Corporation, Santa Monica, CA, 1985.

  14. MACSYMA Reference Manual,The Mathlab Group Laboratory for Computer Science, MIT, 545 Technology Square, Cambridge, MA 02139, 1983.

  15. Paul, B., Analytical dynamics of mechanisms; a computer oriented overview,Mechanism and Machine Theory 10 481–507 (1975).

    Google Scholar 

  16. Newman, C. P. and Murray, J. J., Computational robot dynamics: Foundations and applications,J. Robot. Systems 2(4), 425–452 (1985).

    Google Scholar 

  17. Murray, J. J. and Neuman, C. P., ARM: An Algebraic Robot Dynamic Modeling Program,Proc. 1st Int. IEEE Conf. on Robotics, Atlanta, GA, Mar. 13–15, 1984, pp. 103–114.

  18. Kircanski, M.et al. A New Program Package for the Generation of Efficient Manipulator Kinematic and Dynamic Equations in Symbolic Form,Robotica 6 311–318 (1988).

    Google Scholar 

  19. Tzes, A. P., Yurkovich, S. and Langer, F. D., A symbolic manipulation package for modeling of rigid or flexible manipulators,Proc. 1986 IEEE Int. Conf. Robot. Automat., Philadelphia, PA, Apr. 1988, pp. 1526–1531.

  20. Ju, M. S. and Mansour, J. M., Comparison of methods for developing the dynamics of rigid-body systems,The Int. J. Robot. Res. 8(6), 19–27 (1989).

    Google Scholar 

  21. Bottema, O. and Roth, B.,Theoretical Kinematics, North-Holland, Amsterdam, 1978.

    Google Scholar 

  22. Paul, R. P.,Robot Manipulator: Mathematics, Programming and Control, MIT Press, Cambridge, MA, 1981.

    Google Scholar 

  23. Craig, J. J.,Introduction to Robotics: Mechanics and Control, Addison-Wesley, Reading, MA: 1986.

    Google Scholar 

  24. Wolovich, W. A.,Robotics: Basic Analysis and Design, Holt, Rinehart and Winston, New York, 1987.

    Google Scholar 

  25. Balafoutis, C. A. and Patel, R. V.,Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach, Kluwer Academic Publishers, Boston, MA, 1991.

    Google Scholar 

  26. Renaud, M., Quasi-minimal computation of the dynamic model of a robot manipulator utilizing the Newton—Euler formalism and the notion of augmented body,Proc. 1987 IEEE Int. Conf. Robot. Automat., Raleigh, NC, Apr. 1987, pp. 1677–1682.

  27. Uicker, J. J.,On the Dynamic Analysis of Spatial Linkages using 4 × 4Matrices, PhD dissertation, Northwestern University, August 1965.

  28. Kahn, M. E.,The Near Minimum-Time Control of Open Articulated Kinematic Chains, PhD thesis, Stanford University, 1969.

  29. Hollerbach, J. M., A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity,IEEE Trans. Systems Man Cybernet. SMC-10(11), 730–736 (1980).

    Google Scholar 

  30. Paul, R., Modeling, trajectory calculation, and servoing of a computer controlled arm,A.I. Memo. 177, Stanford Artificial Intelligence Lab., Sept., 1972.

  31. Bejczy, A. K., Robot arm dynamics and control, Memo. 33-669, Jet Propulsion Labs. Tech. Feb. 1974.

  32. Brady, M.et al., (eds),Robot Motion: Planning and Control, MIT Press, Cambridge, MA, 1982.

    Google Scholar 

  33. Albus, J. S., A new approach to manipulator control: The cerebellar model articulation controller (CMAC),ASME J. Dynam. Systems Meas. Control 97 270–277 (1975).

    Google Scholar 

  34. Raibert, M. H., Analytical equations vs. table look-up for manipulation: A unifying concept,Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1977, pp. 576–579.

  35. Horn, B. K. P. and Raibert, M. H., Configuration space control,The Industrial Robot, 69–73 (June 1978).

  36. Waters, R. C., Mechanical arm control, MIT Artificial Intelligence Lab. Memo. 549, Oct. 1979.

  37. Fischer, D.,Theoretical Foundation for the Mechanics of Living Mechanisms (in German), Teubner, Leipzig, 1906.

    Google Scholar 

  38. Renaud, M., An efficient iterative analytical procedure for obtaining a robot manipulator dynamic model,Proc. 1st Int. Symp. Robot. Res., Bretton Woods, New Hampshire, 1983, pp. 749–762.

  39. Vucobratovic, M., Li, S. and Kircanski, N., An efficient procedure for generating dynamic manipulator models,Robotica 3(3), 147–152 (1985).

    Google Scholar 

  40. Li, C. J., A new method of dynamics for robot manipulators,IEEE Trans. Systems Man Cybernet. 18(1), 105–114 (1988).

    Google Scholar 

  41. Hooker, W. W. and Margulies, G., The dynamical attitude equations for ann-body satellite,J. Astronaut. Sci. 12(4), 123–128 (1965).

    Google Scholar 

  42. Stepanenko, Y. and Vucobratovic, M., Dynamics of articulated open-chain active mechanisms,Math. Biosci. 28 137–170 (1976).

    Google Scholar 

  43. Vucobratovic, M., Dynamics of active articulated mechanisms and synthesis of artificial motion,Mechanism and Machine Theory 13 1–56 (1978).

    Google Scholar 

  44. Ho, J. Y. L., Direct path method for flexible multibody spacecraft dynamics,AIAA J. Spacecraft and Rockets 14(2), 102–110 (1977).

    Google Scholar 

  45. Hughes, P. C., Dynamics of a chain of flexible bodies,J. Astronaut. Sci. 27(4), 359–380 (1979).

    Google Scholar 

  46. Orin, D. E., McGhee, R. B., Vucobratovic, M. and Hartoch, G., Kinematic and kinetic analysis of open-chain linkages utilizing Newton—Euler methods,Math. Biosci. 43(1/2), 107–130 (1979).

    Google Scholar 

  47. Luh, J. Y. S., Walker, M. W. and Paul, R. P., On-line computational scheme for mechanical manipulators,ASME J. Dynam. Systems Meas. Control 102 69–79 (1980).

    Google Scholar 

  48. Silver, W. M., On the equivalence of Lagrangian and Newton—Euler dynamics for manipulators,Int. J. Robotics Research 1 60–70 (1982).

    Google Scholar 

  49. Balafoutis, C. A., Patel, R. V. and Misra, P., Efficient modeling and computation of manipulator dynamics using orthogonal Cartesian tensors,IEEE J. Robot. Automat. 4(6), 665–676 (1988).

    Google Scholar 

  50. Balafoutis, C. A., Patel, R. V. and Angeles, J., A comparative study of Lagrange, Newton—Euler and Kane's formulations for robot manipulator dynamics, in M. Jamshidi, J. Y. S. Luh, H. Seraji and G. P. Starr (eds),Robotics and Manufacturing: Recent Trends in Research, Education, and Applications, ASME Press, New York, 1988.

    Google Scholar 

  51. Featherstone, R.,Robot Dynamics Algorithms, Kluwer Academic Publishers, Boston, MA, 1987.

    Google Scholar 

  52. Rodriguez, G., Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics,IEEE J. Robot. Automat. RA-3(6), 624–639 (1987).

    Google Scholar 

  53. Rodriguez, G. and Kreutz, K., Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics,JPL Publication 88-11, March 15, 1988.

  54. Kane, T. R., Dynamics of holonomic systems,ASME J. Appl. Mech. 28 574–578 (1961).

    Google Scholar 

  55. Kane, T. R. and Wang, C. F., On the derivation of equations of motion,J. Soc. Ind. Appl. Math.,13 487–492 (1965).

    Google Scholar 

  56. Huston, R. L., Passerello, C. E. and Harlow, M. W., Dynamics of multirigid-body systems,ASME J. Appl. Mech. 45 889–894 (1978).

    Google Scholar 

  57. Huston, R. L. and Kelly, F. A., The development of equations of motion of single-arm robots,IEEE Trans. Systems Man Cybernet. SMC-12(3), 259–266 (1982).

    Google Scholar 

  58. Faessler, H., Computer-assisted generation of dynamical equations for multi-body systems,Int. J. Robot. Res. 5(3), 129–141 (1986).

    Google Scholar 

  59. Kane, T. R. and Levinson, D. A., The use of Kane's dynamical equations in robotics,Int. J. Robot. Res. 2(3), 3–21 (1983).

    Google Scholar 

  60. Angeles, J., Ma, O. and Rojas, A., An algorithm for the inverse dynamics ofn-axis general manipulators using Kane's equations,Computers Math. Appl. 17(12), 1545–1561 (1989).

    Google Scholar 

  61. Neuman, C. P. and Murray, J. J., The complete dynamic model and customized algorithms of the PUMA robot,IEEE Trans. Systems Man Cybernet. SMC-17(4), 635–644 (1987).

    Google Scholar 

  62. Murray, J. J. and Neuman, C. P., Organizing customized robot dynamics algorithms for efficient numerical evaluation,IEEE Trans. Systems, Man, Cybernet. SMC-18(1), 115–125 (1988).

    Google Scholar 

  63. Khosla, P. K. and Neuman, C. P., Computational requirements of customized Newton—Euler algorithms,J. Robot. Systems 2(3), 309–327 (1985).

    Google Scholar 

  64. Khalil, W., Kleinfinger, J. F. and Gautier, M., Reducing the Computational Burden of the Dynamic Models of Robots,Proc. 1986 IEEE Int. Conf. Robot. Automat. San Francisco, CA, Apr. 1986, pp. 525–531.

  65. Khalil, W. and Kleinfinger, J. F., Minimum operations and minimum parameters of the dynamic models of tree structure robots,IEEE J. Robot. Automat. RA-3(6), 517–526 (1987).

    Google Scholar 

  66. Burdick, J. W., An algorithm for generation of efficient manipulator dynamic equations,Proc. 1986 IEEE Int. Conf. Robot. Automat. San Francisco, CA, Apr. 1986, pp. 212–218.

  67. Armstrong, B., Khatib, O. and Burdick, J., The explicit dynamic model and inertia parameters of the PUMA 560 Arm,Proc. 1986 IEEE Int. Conf. Robot. Automat., San Francisco, CA, Apr. 1986, pp. 510–518.

  68. Leahy, M. B. Jr., Nugent, L. M., Valavanis, K. P. and Saridis, G. N., Efficient dynamics for a PUMA-600,Proc. 1986 IEEE Int. Conf. Robotics and Automation, San Francisco, CA, Apr. 1986, pp. 519–524.

  69. Youcef-Toumi, K. and Asada, H., The design of open-loop manipulator arms with decoupled and configuration-invariant inertia tensors,Proc. 1986 IEEE Int. Conf. Robot. Automat. San Francisco, CA, Apr. 1986, pp. 2018–2026.

  70. Yang, D. C. H. and Tzeng, S. W., Simplification and linearization of manipulator dynamics by the design of inertia distribution,Int. J. Robot. Res. 5(3), 120–128 (1986).

    Google Scholar 

  71. Ramos, S. and Khosla, P. K., Scheduling parallel computation of inverse dynamics formulation, in M. Jamshidi, J. Y. S. Luh, H. Seraji and G. P. Starr (eds),Robotics and Manufacturing: Recent Trends in Research, Education, and Applications, ASME Press, New York, 1988.

    Google Scholar 

  72. Kasahara, H. and Narita, S., Parallel processing of robot-arm control computation on a multimicroprocessor system,IEEE J. Robot. Automat. RA-1(2), 104–113 (1985).

    Google Scholar 

  73. Nigam, R. and Lee, C. S. G., A multiprocessor-based controller for the control of mechanical manipulators,IEEE J. Robot. Automat. RA-1(4), 173–182 (1985).

    Google Scholar 

  74. Lee, C. S. G. and Chang, P. R., Efficient parallel algorithm for robot inverse dynamics computation,IEEE Trans. Systems Man Cybernet. SMC-16(4) 532–542 (1986).

    Google Scholar 

  75. Vucobratovic, M., Kircanski, N. and Li, S. G., An approach to parallel processing of dynamic robot models,Int. J. Robot. Res. 7(2), 64–71 (1988).

    Google Scholar 

  76. Kazerounian, K. and Gupta, K. C., Manipulator dynamics using the extended zero reference position description,IEEE J. Robot. Automat. RA-2(4), 221–224 (1986).

    Google Scholar 

  77. Wang, L. T. and Ravani, B., Recursive computations of kinematics and dynamics equations for mechanical manipulators,IEEE J. Robot. Automat. RA-1(3) 124–131 (1985).

    Google Scholar 

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This research was supported by a postdoctoral fellowship funded from NSERC of Canada Grant OGP0001345 and a grant from the Institute of Robotics and Intelligent Systems (IRIS), both awarded to Dr. R. V. Patel.

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Balafoutis, C.A. A survey of efficient computational methods for manipulator inverse dynamics. J Intell Robot Syst 9, 45–71 (1994). https://doi.org/10.1007/BF01258313

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