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Hi,

I have two Objekts in same coordinate System. I want to calculate the difference between object1 and object2 in yaw, pitch and roll by comparing the rotation matrix .

If the objects dont move and if it has almoast the same orientation I can calculate each position relative to the origin and compare the angles, this already works verry good.

But if the objcts move and the orientation differs a lot I get allways a wrong angle differnce on one of the axises.

I dont know hot two fix this Problem.

Is there any sollution to calculate the difference between Rotation Matrixes/Quaterions/Axis and Angle and get solid results without singularitys?

Greetings

Florian

Jim Riggs
on 12 Aug 2019

Edited: Jim Riggs
on 12 Aug 2019

You have two objects described in a common reference frame. Lets call the objects A and B, and the frame is the I frame. So if Direction cosine matrix [I -> A] represents the transformation from the I frame to body A frame, and [I -> B] is the DCM which transforms coordinates from I to body B, then the transformation from A to B is:

[A -> B] = [I -> B] [I -> A]^T (where [I -> A]^T is the transpose of [I -> A]

This is the same as [A -> B] = [I -> B] [A -> I].

Now you can extract the Euler angles from [A -> B] which represent the rotation to get from A to B.

Jim Riggs
on 12 Aug 2019

Check the order of multiplication. (I made an edit to my answer a few minutes after I posted it)

The first operation is to go from A to I. This is [I -> A]^T or transpose(A).

The result of this is in the I frame. This result is then transposed to the B frame by multiplying it by [I -> B]. (Using matrix pre-multiplication, the second operation preceeds the first, i.e, it pre-multiplies)

So it should be R = AB = [I -> B]*[I -> A]^T = B*transpose(A).

Next, it appears from your equations that you are performing a Z-Y-X rotation sequence. In this case, the correct calculation for the Euler angles is as follows:

Angle Y = asin(-R(1,3) (this is correct)

But, there is no need to use this angle to calculate X and Z; Siimply use the following:

Angle X = atan2(R(2,3), R(3,3))

Angle Z = atan2(-R(1,2), R(1,1))

(note the "-" sign in the Angle Z term)

Jim Riggs
on 12 Aug 2019

Also note that if it seems like things are going the wrong way, it is possible that the A and B matrix that you get from the rotationVectorToMatrix function are defined opposite what I have assumed, i.e. the A and B matrix might be [A -> I] (in stead of [I -> A] and [B -> I] (in stead of [I -> B]).

If this is the case, then [A -> B] is given by:

[A -> B] = [B -> I]^T [A -> I] = transpose(B) * A

Chris
on 12 Aug 2019

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