FA-88064 / Inverse kinematics solvers / Member archive

Inverted wrist singularity reuses the upright roll formula · case 04

At b=180 the returned g has the wrong sign relation to the rotation.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [R, flip]: R is a 3x3 wrist rotation R = Rz(a) Ry(b) Rz(g). Return [a,b,g] in degrees rounded to 4. With flip false b is in [0,180]; with flip true b is negative and a,g are shifted by 180 degrees. When hypot(R02,R12) < 1e-9 the wrist is singular: a=0 and b=0 (R22>0, g=atan2(R10,R00)) or b=180 (g=atan2(R01,-R00)).

Why this case matters

Inverse kinematics code turns task-space goals into joint commands; a wrong branch, sign, limit or update order sends a real arm to the wrong pose.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
near inverted singular	`[0.0, 180.0, 120.0]`	`[0.0, 180.0, 60.0]`	Failed

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