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Optimum Kinematics Error Allocation in Robotic Manipulators Using Geometric Programming

[+] Author Affiliations
Hami Golbayani, Kazem Kazerounian

University of Connecticut, Storrs, CT

Paper No. DETC2008-49764, pp. 1241-1248; 8 pages
doi:10.1115/DETC2008-49764
From:
  • ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B
  • Brooklyn, New York, USA, August 3–6, 2008
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4326-0 | eISBN: 0-7918-3831-5
  • Copyright © 2008 by ASME

abstract

In this paper, a simple and efficient formulation is presented to optimize the kinematic error mapping from the Cartesian space of the end-effector position and orientation to the inputs space. The results are optimized allocation of the joints’ errors for the accepted end-effector positioning errors. The linearized relation (Jacobian) between the end-effector position and the joints’ errors is used. Upper bounds of the error are developed so that the error function is defined in the form of posinomials of joint errors. An optimization problem is set up to find the optimum error allocation at each joint. The problem is then formulated as a zero degree-of-difficulty geometric programming. It is shown that the weight of each term in the total cost function is constant and independent of manipulator’s design. As a result, the solution to the error optimization is readily available. Explicit solutions to these weight factors are presented.

Copyright © 2008 by ASME

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