FA-88081 / Inverse kinematics solvers / Open access

First wrist angle is read from the bottom row instead of the last column · case 01

The first angle equals a function of the last angle, so a and g appear swapped.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The matrix is indexed as if stored column-major, reading R21,R20 instead of R12,R02.

THE FAILURE

The matrix is indexed as if stored column-major, reading R21,R20 instead of R12,R02.

Unsuccessful approach: Swapping the atan2 arguments still reads the right entries but measures from the y axis.

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.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    R,flip=x
    sb=math.hypot(R[0][2],R[1][2])
    if sb<1e-9:
        if R[2][2]>0: return [0.0,0.0,round(math.degrees(math.atan2(R[1][0],R[0][0])),4)]
        return [0.0,180.0,round(math.degrees(math.atan2(R[0][1],-R[0][0])),4)]
    if flip:
        b=math.atan2(-sb,R[2][2])
        a=math.atan2(-R[1][2],-R[0][2])
        g=math.atan2(-R[2][1],R[2][0])
    else:
        b=math.atan2(sb,R[2][2])
        a=math.atan2(R[2][1],-R[2][0])
        g=math.atan2(R[2][1],-R[2][0])
    return [round(math.degrees(v),4) for v in (a,b,g)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['large tilt flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], True]], [120.0, -130.0, -160.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]]], [['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]], ['exact inverted', [[[[-0.766044443118978, 0.6427876096865393, 1.2246467991473532e-16], [0.6427876096865393, 0.766044443118978, 0.0], [-9.381338752702731e-17, 7.871877887341985e-17, -1.0]], True]], [0.0, 180.0, 40.0]], ['negative angles', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], False]], [-120.0, 75.0, -150.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]]], [['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]], ['exact inverted', [[[[-0.766044443118978, 0.6427876096865393, 1.2246467991473532e-16], [0.6427876096865393, 0.766044443118978, 0.0], [-9.381338752702731e-17, 7.871877887341985e-17, -1.0]], True]], [0.0, 180.0, 40.0]], ['negative angles', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], False]], [-120.0, 75.0, -150.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]], ['tilt 90', [[[[0.49999999999999994, -0.49999999999999994, 0.7071067811865476], [-0.49999999999999994, 0.5000000000000001, 0.7071067811865475], [-0.7071067811865476, -0.7071067811865475, 6.123233995736766e-17]], False]], [45.0, 90.0, -45.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]], ['inverted with roll', [[[[0.49999999999999983, -0.8660254037844387, 1.2246467991473532e-16], [-0.8660254037844387, -0.49999999999999983, 0.0], [6.123233995736764e-17, -1.0605752387249069e-16, -1.0]], False]], [0.0, 180.0, -120.0]]], [['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]], ['tilt 90', [[[[0.49999999999999994, -0.49999999999999994, 0.7071067811865476], [-0.49999999999999994, 0.5000000000000001, 0.7071067811865475], [-0.7071067811865476, -0.7071067811865475, 6.123233995736766e-17]], False]], [45.0, 90.0, -45.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]], ['inverted with roll', [[[[0.49999999999999983, -0.8660254037844387, 1.2246467991473532e-16], [-0.8660254037844387, -0.49999999999999983, 0.0], [6.123233995736764e-17, -1.0605752387249069e-16, -1.0]], False]], [0.0, 180.0, -120.0]], ['small tilt flip', [[[[0.34136939837363944, -0.9398073646785109, 0.015134435901338627], [0.9360020627702564, 0.34136939837363944, 0.08583165117743129], [-0.08583165117743129, -0.01513443590133862, 0.9961946980917455]], True]], [-100.0, -5.0, 170.0]]], [['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['large tilt flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], True]], [120.0, -130.0, -160.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
generic no flip	`[50.0, 40.0, 50.0]`	`[30.0, 40.0, 50.0]`	Failed
generic flip	`[-150.0, -40.0, -130.0]`	`[-150.0, -40.0, -130.0]`	Passed
large tilt no flip	`[20.0, 130.0, 20.0]`	`[-60.0, 130.0, 20.0]`	Failed
large tilt flip	`[120.0, -130.0, -160.0]`	`[120.0, -130.0, -160.0]`	Passed
near upright singular	`[0.0, 0.0, 60.0]`	`[0.0, 0.0, 60.0]`	Passed
near inverted singular	`[0.0, 180.0, 60.0]`	`[0.0, 180.0, 60.0]`	Passed
exact upright	`[0.0, 0.0, 40.0]`	`[0.0, 0.0, 40.0]`	Passed

SHA-256 / 5236a0f2a548fc94c557958befe35bb4bb4ded6c3c1337922fe2f3f2b397ac4d

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    R,flip=x
    sb=math.hypot(R[0][2],R[1][2])
    if sb<1e-9:
        if R[2][2]>0: return [0.0,0.0,round(math.degrees(math.atan2(R[1][0],R[0][0])),4)]
        return [0.0,180.0,round(math.degrees(math.atan2(R[0][1],-R[0][0])),4)]
    if flip:
        b=math.atan2(-sb,R[2][2])
        a=math.atan2(-R[1][2],-R[0][2])
        g=math.atan2(-R[2][1],R[2][0])
    else:
        b=math.atan2(sb,R[2][2])
        a=math.atan2(R[0][2],R[1][2])
        g=math.atan2(R[2][1],-R[2][0])
    return [round(math.degrees(v),4) for v in (a,b,g)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['large tilt flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], True]], [120.0, -130.0, -160.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]]], [['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]], ['exact inverted', [[[[-0.766044443118978, 0.6427876096865393, 1.2246467991473532e-16], [0.6427876096865393, 0.766044443118978, 0.0], [-9.381338752702731e-17, 7.871877887341985e-17, -1.0]], True]], [0.0, 180.0, 40.0]], ['negative angles', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], False]], [-120.0, 75.0, -150.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]]], [['exact upright', [[[[0.766044443118978, -0.6427876096865393, 0.0], [0.6427876096865393, 0.766044443118978, 0.0], [-0.0, 0.0, 1.0]], False]], [0.0, 0.0, 40.0]], ['exact inverted', [[[[-0.766044443118978, 0.6427876096865393, 1.2246467991473532e-16], [0.6427876096865393, 0.766044443118978, 0.0], [-9.381338752702731e-17, 7.871877887341985e-17, -1.0]], True]], [0.0, 180.0, 40.0]], ['negative angles', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], False]], [-120.0, 75.0, -150.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]], ['tilt 90', [[[[0.49999999999999994, -0.49999999999999994, 0.7071067811865476], [-0.49999999999999994, 0.5000000000000001, 0.7071067811865475], [-0.7071067811865476, -0.7071067811865475, 6.123233995736766e-17]], False]], [45.0, 90.0, -45.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]], ['inverted with roll', [[[[0.49999999999999983, -0.8660254037844387, 1.2246467991473532e-16], [-0.8660254037844387, -0.49999999999999983, 0.0], [6.123233995736764e-17, -1.0605752387249069e-16, -1.0]], False]], [0.0, 180.0, -120.0]]], [['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['negative angles flip', [[[[-0.3209407678712127, -0.8147047612756303, -0.482962913144534], [0.44411428382689044, 0.3209407678712125, -0.8365163037378079], [0.8365163037378079, -0.4829629131445341, 0.25881904510252074]], True]], [60.0, -75.0, 30.0]], ['tilt 90', [[[[0.49999999999999994, -0.49999999999999994, 0.7071067811865476], [-0.49999999999999994, 0.5000000000000001, 0.7071067811865475], [-0.7071067811865476, -0.7071067811865475, 6.123233995736766e-17]], False]], [45.0, 90.0, -45.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]], ['inverted with roll', [[[[0.49999999999999983, -0.8660254037844387, 1.2246467991473532e-16], [-0.8660254037844387, -0.49999999999999983, 0.0], [6.123233995736764e-17, -1.0605752387249069e-16, -1.0]], False]], [0.0, 180.0, -120.0]], ['small tilt flip', [[[[0.34136939837363944, -0.9398073646785109, 0.015134435901338627], [0.9360020627702564, 0.34136939837363944, 0.08583165117743129], [-0.08583165117743129, -0.01513443590133862, 0.9961946980917455]], True]], [-100.0, -5.0, 170.0]]], [['generic no flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], False]], [30.0, 40.0, 50.0]], ['generic flip', [[[[0.04341204441673269, -0.8295983733257066, 0.5566703992264194], [0.9096158864219903, 0.26325835480968696, 0.32139380484326957], [-0.4131759111665348, 0.49240387650610395, 0.766044443118978]], True]], [-150.0, -40.0, -130.0]], ['large tilt no flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], False]], [-60.0, 130.0, 20.0]], ['large tilt flip', [[[[-0.005813254051503125, 0.9237208365458508, 0.3830222215594891], [0.6941091380258464, 0.2794538206643772, -0.6634139481689384], [-0.7198463103929542, 0.2620026302293849, -0.6427876096865394]], True]], [120.0, -130.0, -160.0]], ['near upright singular', [[[[0.5, -0.8660254037844386, 1.5818054920253123e-10], [0.8660254037844386, 0.5, 7.376080146430387e-11], [-1.429690024728532e-10, 1.0010797326181444e-10, 1.0]], False]], [0.0, 0.0, 60.0]], ['near inverted singular', [[[[-0.5, 0.8660254037844385, 1.718814073341628e-10], [0.8660254037844385, 0.5, 3.030732959515473e-11], [-5.969378631680947e-11, 1.6400732998718326e-10, -1.0]], False]], [0.0, 180.0, 60.0]], ['back quadrant', [[[[-0.08550503583141712, 0.515076844803523, -0.8528685319524432], [-0.984923155196477, 0.08550503583141716, 0.15038373318043521], [0.15038373318043524, 0.8528685319524432, 0.5000000000000001]], False]], [170.0, 60.0, 100.0]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
generic no flip	`[60.0, 40.0, 50.0]`	`[30.0, 40.0, 50.0]`	Failed
generic flip	`[-150.0, -40.0, -130.0]`	`[-150.0, -40.0, -130.0]`	Passed
large tilt no flip	`[150.0, 130.0, 20.0]`	`[-60.0, 130.0, 20.0]`	Failed
large tilt flip	`[120.0, -130.0, -160.0]`	`[120.0, -130.0, -160.0]`	Passed
near upright singular	`[0.0, 0.0, 60.0]`	`[0.0, 0.0, 60.0]`	Passed
near inverted singular	`[0.0, 180.0, 60.0]`	`[0.0, 180.0, 60.0]`	Passed
exact upright	`[0.0, 0.0, 40.0]`	`[0.0, 0.0, 40.0]`	Passed

SHA-256 / aff2783bec4567b0cd65f3d3eb9f9bf0ead737222c345accb9ea1a0f26de11fc

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Deterministic planar or low-dimensional teaching model with a stipulated convention; not a general robotics library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:04.906687+00:00.

Case digest / f6f8fb7ba9324e42df9b0b182adc53384042cc5aace22a5cdb0beeeb27962c08