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Article #71Solution of matrix Equation AX=XB
From: Stewart Moorehead
Date: Thu, 12 Nov 1992 14:38
Date: Thu, 12 Nov 1992 14:38
18 lines
1448 bytes
1448 bytes
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