A near Minimum Iterative Analytical Procedure for Obtaining a Robot-Manipulator Dynamic Model
The dynamic control synthesis of robot manipulators requires a great number of arithmetic operations, and it cannot be effected in real time unless this number is reduced. This paper presents a systematic analytical procedure for obtaining the dynamic model necessary for the dynamic control synthesis. This procedure which uses a Lagrangian formulation is applicable to all manipulators having a simple kinematic chain structure with revolute and/or prismatic joints.
An example shows that the calculation of the dynamic model requires 368 multiplications and 271 additions for a particular 6 revolute joint manipulator using the systematic procedure. The examination of the results shows that only a few simpliciations are a fortiori possible and proves that the procedure is near-minimum.
KeywordsGeneralize Link Robot Manipulator Multi Body System Prismatic Joint Homogeneous Transformation Matrix
Unable to display preview. Download preview PDF.
- [l]A. K. Bejczy, 1974, “Technical memorandum 33–669”, Pasadena J.P.L. California Institute of Technology.Google Scholar
- O. Fischer, 1906, “Einführung in die mechanik lebender Mechanismen”, Leipzig.Google Scholar
- J.M. Hollerbach, 1980, “A.I. Memo n°533”, Boston, MITGoogle Scholar
- J.M. Hollerbach and G. Sahar, 1983, “Partitioned inverse kinematic accelerations and manipulator dynamics”, The International Journal of Robotics Research, vol.2, n°4.Google Scholar
- M.E. Kahn, The near minimum time control of open loop articulated kinematic chains“, Ph.D. thesis, Stanford University. 1970.Google Scholar
- A.G. Leskov and V.S. Medvedev, 1974, “Analysis of dynamics and synthesis of movement control of robot manipulator functional organs”, Engineering Cybernetics, vol.12, n°6, pp. 56–65.Google Scholar
- P.W. Likins, 1971, October, “Passive and semi-active attitude stabilizations-flexible space-craft”, AGARD.Google Scholar
- S. Megahed and M. Renaud, 1982, “Minimization of the computation time necessary for the dynamic control of robot manipulators”, 12th ISIR, Paris.Google Scholar
- M. Renaud, 1980, “Contribution à la modélisation et à la commande dynamique des robots manipulateurs”, Thèse d’Etat, Université Paul Sabatier, Toulouse, France.Google Scholar
- M. Renaud, 1983, “An efficient iterative analytical procedure for obtaining a robot manipulator dynamic model”, 1st Int. Symposium of Robotics Research, B.Woods.Google Scholar
- W.M. Silver, 1982, “On the equivalence of Lagrangian and Newton-Euler dynamics for manipulators”, The International Journal of Robotics Research, vol.1, n°2.Google Scholar
- J.J. Uicker, 1968, “Dynamic behaviour of spatial linkages”, ASME, Mech. 5, n°68, pp. 1–15.Google Scholar
- M. Vukobratovie and V. Potkonjak, 1982, “Dynamics of manipulation robots”, Berlin, Heidelberg, New-York, Springer-Verlag.Google Scholar
- M.W. Walker and D.E. Orin, 1981, “Efficient dynamic’ computer simulation of robotic mechanisms”, JACC, Charlotteville.Google Scholar