FA-12101 / Robotics frame conventions / Open access

An inverse sensor pose negates translation in the wrong frame · case 01

An inverse sensor pose negates translation in the wrong frame.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Translation is negated without applying the inverse orientation.

VERIFIED REPAIR

Use inverse rotation on both coordinates and negated origin.

Unsuccessful approach: Rotating the negative translation by the forward orientation only works at some headings.

Case contract

Pose maps child to parent by p_parent=R(q)*p_child+t. Return inverse translation for integer t and quarter-turn q.

Why this case matters

Robot adapters must preserve the declared frame, reference point, and representation conventions across interfaces.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

def rot(v, q):
    x,y = v
    return [(x,y),(-y,x),(-x,-y),(y,-x)][q%4]

N = 1
observations = []
def solve(t, q):
    return [-t[0],-t[1]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('quarter turn', solve([N,2*N],1), [-2*N,N])
check('negative quarter', solve([N,2*N],-1), [2*N,-N])
check('identity', solve([N,2*N],0), [-N,-2*N])
check('half turn', solve([N,2*N],2), [N,2*N])
check('origin', solve([0,0],1), [0,0])
check('full turns', solve([N,-N],5), [N,N])
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
quarter turn	`[-1, -2]`	`[-2, 1]`	Failed
negative quarter	`[-1, -2]`	`[2, -1]`	Failed
identity	`[-1, -2]`	`[-1, -2]`	Passed
half turn	`[-1, -2]`	`[1, 2]`	Failed
origin	`[0, 0]`	`[0, 0]`	Passed
full turns	`[-1, 1]`	`[1, 1]`	Failed

SHA-256 / 271434660dde3e375e2dd475fdf709ec21acee8513b58a19553b5a2bc6f8b4a5

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

def rot(v, q):
    x,y = v
    return [(x,y),(-y,x),(-x,-y),(y,-x)][q%4]

N = 1
observations = []
def solve(t, q):
    return list(rot([-t[0],-t[1]],q))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('quarter turn', solve([N,2*N],1), [-2*N,N])
check('negative quarter', solve([N,2*N],-1), [2*N,-N])
check('identity', solve([N,2*N],0), [-N,-2*N])
check('half turn', solve([N,2*N],2), [N,2*N])
check('origin', solve([0,0],1), [0,0])
check('full turns', solve([N,-N],5), [N,N])
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
quarter turn	`[2, -1]`	`[-2, 1]`	Failed
negative quarter	`[-2, 1]`	`[2, -1]`	Failed
identity	`[-1, -2]`	`[-1, -2]`	Passed
half turn	`[1, 2]`	`[1, 2]`	Passed
origin	`[0, 0]`	`[0, 0]`	Passed
full turns	`[-1, -1]`	`[1, 1]`	Failed

SHA-256 / 090c364a99aca2fbcc3f13b86dadc5a3170abf388cd3f8edf9fc7b6bfb6de1c5

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

def rot(v, q):
    x,y = v
    return [(x,y),(-y,x),(-x,-y),(y,-x)][q%4]

N = 1
observations = []
def solve(t, q):
    return list(rot([-t[0],-t[1]],-q))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('quarter turn', solve([N,2*N],1), [-2*N,N])
check('negative quarter', solve([N,2*N],-1), [2*N,-N])
check('identity', solve([N,2*N],0), [-N,-2*N])
check('half turn', solve([N,2*N],2), [N,2*N])
check('origin', solve([0,0],1), [0,0])
check('full turns', solve([N,-N],5), [N,N])
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
quarter turn	`[-2, 1]`	`[-2, 1]`	Passed
negative quarter	`[2, -1]`	`[2, -1]`	Passed
identity	`[-1, -2]`	`[-1, -2]`	Passed
half turn	`[1, 2]`	`[1, 2]`	Passed
origin	`[0, 0]`	`[0, 0]`	Passed
full turns	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / c7d8caf0a640864b82a91dd32bc70ef04a65325a8a1923be30e01638e66ad766

Verification & scope

Small exact offline frame model; not a robot middleware implementation or continuous pose estimator. 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 2026-09-29T14:38:53.733618+00:00.

Case digest / 86b8b2281b199258c9b5cc20057f52107e1190f85141919652322ac7c59ded19