NDLI: High speed computation of the inverse Jacobian matrix and of servo inputs for robot arm control

Content Provider	IEEE Xplore Digital Library
Author	Melouah, H. Andre, P.
Copyright Year	1982
Description	Author affiliation: CNRS, ENSMM, Besancon Cedex, France (Melouah, H.; Andre, P.)
Abstract	For controlling in real time robot arms having six degrees of freedom, the most efficient way is to use an incremental method which consists in deriving the variations of the six variables si associated to the degrees of freedom from those of the six variables xj representing the position and the orientation of the end effector, using the inverse jacobian matrix J-1. We have developed a method avoiding the inversion of the 6×6 jacobian matrix J. We show that in all cases it is possible to derive, and often very easily, the mathematical expressions of the 36 terms of J-1 from those of the terms of J and from the inverse of a 3×3 sub-matrix whose choice is arbitrary and usually directed by simplicity of inversion. The computations involve only 3×3 matrices and consist in multiplications and only 2 inversions. Moreover it is sufficient to determine only the 9 terms of a 3×3 sub-matrix of J-1 for computing directly the sis, then the computing time is significantly reduced. We demonstrate the use of this method for controlling our hydraulic telethesis: the time needed for computing the inputs of the servos associated to the actuators, from the true positions of the joints delivered by transducers, is less than 8 milliseconds using a Texas Instruments TMS 9900 microprocessor.
Starting Page	89
Ending Page	94
File Size	393714
Page Count	6
File Format	PDF
DOI	10.1109/CDC.1982.268406
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1982-12-08
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Jacobian matrices Servomechanisms Robot control Microprocessors Tellurium Assembly
Content Type	Text
Resource Type	Article

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