FA-12116 / Robotics frame conventions / Open access

A shifted velocity reference omits angular motion of the lever arm · case 01

A shifted velocity reference omits angular motion of the lever arm.

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

ROOT CAUSE

Linear velocity at the body origin is copied to an offset point.

THE FAILURE

Linear velocity at the body origin is copied to an offset point.

Unsuccessful approach: Adding the cross term with reversed sign computes the opposite offset.

Case contract

In a shared planar frame, v is origin velocity, w is signed angular velocity, r goes from origin to target point. Return target velocity v+[-w*ry,w*rx].

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(v,w,r):
    return v
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('forward lever', solve([0,0],2,[N,0]), [0,2*N])
check('left lever', solve([0,0],2,[0,N]), [-2*N,0])
check('translation and rotation', solve([N,N],-1,[N,2*N]), [3*N,0])
check('zero angular', solve([N,-N],0,[N,N]), [N,-N])
check('zero lever', solve([N,-N],3,[0,0]), [N,-N])
check('negative lever', solve([0,0],-2,[-N,-N]), [-2*N,2*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
forward lever	`[0, 0]`	`[0, 2]`	Failed
left lever	`[0, 0]`	`[-2, 0]`	Failed
translation and rotation	`[1, 1]`	`[3, 0]`	Failed
zero angular	`[1, -1]`	`[1, -1]`	Passed
zero lever	`[1, -1]`	`[1, -1]`	Passed
negative lever	`[0, 0]`	`[-2, 2]`	Failed

SHA-256 / 8a01c9fa8ea7057d6de979b8c98c70fb12da58c2a5a6b33576b6456e5d413b04

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(v,w,r):
    return [v[0]+w*r[1],v[1]-w*r[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('forward lever', solve([0,0],2,[N,0]), [0,2*N])
check('left lever', solve([0,0],2,[0,N]), [-2*N,0])
check('translation and rotation', solve([N,N],-1,[N,2*N]), [3*N,0])
check('zero angular', solve([N,-N],0,[N,N]), [N,-N])
check('zero lever', solve([N,-N],3,[0,0]), [N,-N])
check('negative lever', solve([0,0],-2,[-N,-N]), [-2*N,2*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
forward lever	`[0, -2]`	`[0, 2]`	Failed
left lever	`[2, 0]`	`[-2, 0]`	Failed
translation and rotation	`[-1, 2]`	`[3, 0]`	Failed
zero angular	`[1, -1]`	`[1, -1]`	Passed
zero lever	`[1, -1]`	`[1, -1]`	Passed
negative lever	`[2, -2]`	`[-2, 2]`	Failed

SHA-256 / 18c9d6e96295ce3bd798ddfb5c3ba34491b0ccce036bedec4c2b065694c8c18f

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:38:54.028531+00:00.

Case digest / 6ebf71dd8841b25345ac83e8b2a1d980d313ef31c4d56f9ea24c9546fe2d1fb8