A Function which measures "error"

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The discussion centers on the evaluation of a non-symmetric error function e(x,y) used to compare two positions and orientations of a drill, represented as elements of SE(3). The suitability of this function depends on the intended application, particularly whether it effectively captures the nuances of error in practical scenarios. While norms and symmetry can simplify proofs, they are not strictly necessary for demonstrating that the error is bounded. The asymmetry in the function can be justified, as certain errors may have significantly different implications, such as "drill too low" versus "drill too high." Ultimately, the effectiveness of the error measure hinges on its alignment with the specific context of its use.
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I have an error, denoted e(x,y) for example. It's not a norm and it isn't symmetric, that is to say: e(x,y)\neq e(y,x).

My question is simply this: With such properties, is the choice of such a function a good one?
 
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I suppose that depends on what you want to do with it.
If your goal is to show that the error is bounded, then you should not need the properties of norms and symmetry, although those properties can simplify your proof.
 
I'm not worried about showing it's bounded but if it's a good measure of error with it being non-symmetric.
 
What defines "good"? What do you want to do with this number?
Also, what are x and y?
 
Okay, I am trying to compare two different positions and orientations of a drill. The x and y are elements of SE(3).
 
Something like expected and real position? Then I don't see anything wrong with an asymmetry - as an example, "drill too low" could be much worse/better than "drill too high".
 

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