Why Does dcm2angle Work Like This?

Suppose I have a direction cosine matrix, brought to my attention by a colleague

C = round(angle2dcm(-pi/2,-pi/2,0,'ZYX'))

C = 3x3

0 0 1 1 0 0 0 1 0

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Extract the angles with @doc:dcm2angle (Aerospace Toolbox) using the Default option

[a1,a2,a3] = dcm2angle(C,'ZYX','Default');[a1,a2,a3]

ans = 1x3

0 -1.5708 0

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Because the middle angle is -pi/2, the extracted angle triplets have multiple solutions, but the default result isn't one of them.

Sometime after R2019b and before or at R2022a, an additonal optional argument can be specified, though I could find nothing about this new argument in the release notes nor the bug fixes.

[a1,a2,a3] = dcm2angle(C,'ZYX','Robust');[a1,a2,a3]

ans = 1x3

-1.5708 -1.5708 0

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Now we get a correct answer.

Trying with @doc:rotm2eul that's used in other toolboxes (Robotics, Navigation, UAV) we see that it returns a correct result without any optional arguments.

eul = rotm2eul(C.','ZYX')

eul = 1x3

0 -1.5708 -1.5708

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round(angle2dcm(eul(1),eul(2),eul(3),'ZYX'))

ans = 3x3

0 0 1 1 0 0 0 1 0

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@doc:dcm2angle with the Robust option actually computes two sets of angles, then computes the DCM with each set, and then compares the recomputed DCMs to the input DCM, and then returns the set of angles that result in a DCM that's closest to the input. @doc:rotm2eul uses a different approach altogether, though is limited to only three axes sequences.

To be sure, the Default option with @doc:dcm2angle is considerably faster than Robust, but Robust appears to take the same amout of time as @doc:rotm2eul

timeit(@() dcm2angle(repmat(C,1,1,1e5),'ZYX','Default'),3)

ans = 0.0065

timeit(@() dcm2angle(repmat(C,1,1,1e5),'ZYX','Robust'),3)

ans = 0.0101

timeit(@() rotm2eul(repmat(C.',1,1,1e5),'ZYX'),1)

ans = 0.0110

Does anyone have a thought as to why dcm2angle is implemented as it is with Default and forces the user to use Robust? And why wouldn't that same reason apply to rotm2eul?

Once MathWorks realized that dcm2angle Default was returning incorrect results in some cases, why patch it with Robust and keep Default instead of just fixing the bug?

[William Rose]

@Paul,

I think Mathworks places a very high value on code returning the same results when the user migrates to the next version. Maybe some user uses dcm2angle() in a critical process, and they have adapted to the incorrect operation of dcm2angle(). The user doesn't want to find that their controller is broken when they migrated to the newest version of Matlab.

[Paul]

Hi William,

As to the first part, If you haven't see it already, check out this answer from @Steven Lord (in his personal capacity).

Following this logic, it would be difficult for MathWorks to address any bug, for which a user has found their own workaround, without implementing the correction through some other means, like an optional argument as in the case of dcm2angle.

I might be able to be convinced otherwise, but the Default implementation is a bug and the way to fix a bug is to fix the bug. Users with critical processes should always check the release notes for bug fixes and behavior changes, though in this case the Robust option wasn't captured as either for R2021b, where it first shows up in the doc page.

[William Rose]

@Paul, good points. And thanks for the link.