🚀 go-pugleaf

In article <6611@dciem.dciem.dnd.ca> sjm@dciem.dciem.dnd.ca (Stewart Moorehead) writes:
>
> 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

The problem as you stated it may or may not be well defined.
First of all, as stated, there may be many solutions for X
analogous to finding a set of eigenfunctions for X.  To see this,
consider A=B.  In this case X=0 is a solution as well as X equal
to the identity matrix.  This is one example of multiple solutions
to the equation.

Next, consider the problem definition.  Since you want to estimate
X, try a statistical estimation approach.  Formulate the problem
by doubling the number of measurements (assumming that they are
noisey) and then figure how to use this information to estimate
X.  A similar category of problem is in photogrammetry where one
estimates the location and orientation of a camera given the 
photograph and some measured points in the "true" scene.


-- 
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- John Heimbold  -  heimbold@cerf.net - -
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