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Article #71

Solution of matrix Equation AX=XB

#71
From: Stewart Moorehead
Date: Thu, 12 Nov 1992 14:38
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 I am recording the 6D position (x,y,z,roll,pitch,yaw) of an object
 using two independant devices. Since these devices have different
 reference frames a transformation matrix, call it X, must be
 calculated. To calculate X, the equation AX=XB must be solved, with A
 and B being known 4x4 matrices. I have found two methods which claim to
 solve for X. They were proposed by Roger Tsai and Reimar Lenz (June
 1989 IEEE Transactions on Robotics and Automation) and by C. C. Wang
 (April 1992). Both of these methods work if I pre-define X and create
 some 'cooked' data around it, however when I use actual data that was
 recorded using teh devices I get an incorrect answer. The devices being
 used are any two of : Northern Digital's Optotrak, Logitech's 3D mouse,
 and Polhemus Fastrak. I feel that the inherent error in these devices
 may be too great for the methods being used.
 I would appreciate it if anyone has information regarding these methods
 or the devices being used. If anyone has solved a similar problem
 please respond.
 You can send mail to sjm.dretor.dciem.dnd.ca
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Path: arc1-ca.pugleaf.net!sparky!uunet!utcsri!torn!utzoo!dciem!sjm
From: sjm@dciem.dciem.dnd.ca (Stewart Moorehead)
Newsgroups: sci.engr.control
Subject: Solution of matrix Equation AX=XB
Message-ID: <6611@dciem.dciem.dnd.ca>
Date: 12 Nov 92 14:38:27 GMT
Distribution: na
Organization: Defence and Civil Institute of Environmental Medicine
Lines: 19