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A Simple Approach to Kinematic Inversion of Redundant Mechanisms

[+] Author Affiliations
Alessandro Fumagalli, Gabriella Gaias, Pierangelo Masarati

Politecnico di Milano, Milano, Italy

Paper No. DETC2007-35285, pp. 1931-1939; 9 pages
doi:10.1115/DETC2007-35285
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

This work addresses the problem of kinematic inversion of complex redundant mechanisms. The inverse problem for redundant mechanisms is known to be ill-posed. Using the multibody formalism and the capability to automatically write the equations of motion of mechanisms provided by general multibody software, a simple algorithm is proposed for the solution of the inverse kinematics problem for redundant robotic systems. The algorithm, in its basic form, is equivalent to the classical Moore-Penrose pseudo-inverse applied to the Jacobian matrix of the constraints. The inverse solution is found in a least squares sense: among the infinite admissible solutions, the one with minimum norm is chosen. Little extra effort allows the computation of optimized inverse kinematics. In this case, the solution is found in a weighted least squares sense. Weights can be automatically chosen by an optimization algorithm in order to minimize a given cost function, or assigned by the user based on engineering judgment. Among the advantages of the proposed approach, it is worth mentioning its simplicity and the possibility to be used within generic multibody software with very limited effort.

Copyright © 2007 by ASME
Topics: Mechanisms

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