FA-93436 / Solar tracker geometry / Open access
Dual-axis azimuth cable-wrap slew: shortest move metric · case 01
The drive always prefers the most counterclockwise wrap, however far away.
ROOT CAUSE
The move is ranked by signed distance instead of magnitude.
VERIFIED REPAIR
Rank candidates by |c - cur_az|.
Unsuccessful approach: Taking the distance modulo 360 makes every wrap look equally near.
Case contract
The azimuth drive has a continuous mechanical range [min_az, max_az] (may exceed 360 span). target_az is 0..359. Candidates are target + 360k inside the range; pick the smallest |move| from cur_az, ties to the candidate nearest the range centre, then the smaller. If none is in range, go to the limit with the smaller angular distance (mod 360) to the target, ties to min_az, status 'limit'. Return [position, move, status].
Why this case matters
Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cur_az, target_az, min_az, max_az):
cands = []
k0 = math.floor((min_az - target_az) / 360)
for k in range(k0, k0 + 4):
c = target_az + 360 * k
if min_az <= c <= max_az:
cands.append(c)
center = (min_az + max_az) / 2
if not cands:
def ang(a):
d = (a - target_az) % 360
return min(d, 360 - d)
lim = min_az if ang(min_az) <= ang(max_az) else max_az
return [lim, lim - cur_az, 'limit']
best = min(cands, key=lambda c: (c - cur_az, abs(c - center), c))
return [best, best - cur_az, 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [450, 90, -90, 450], [450, 0, 'ok']],
['regression: shortest move metric (partial repair)', [225, 225, -270, 270], [225, 0, 'ok']],
['control 1', [180, 0, -90, 450], [0, -180, 'ok']],
['control 2', [180, 315, 0, 360], [315, 135, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [180, 90, -270, 270], [90, -90, 'ok']],
['regression: shortest move metric (partial repair)', [225, 180, -270, 270], [180, -45, 'ok']],
['control 1', [45, 225, -90, 450], [225, 180, 'ok']],
['control 2', [180, 180, -90, 450], [180, 0, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [360, 90, -90, 450], [450, 90, 'ok']],
['regression: shortest move metric (partial repair)', [360, 0, -90, 450], [360, 0, 'ok']],
['control 1', [0, 45, -90, 450], [45, 45, 'ok']],
['control 2', [360, 45, 0, 360], [45, -315, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [90, 180, -270, 270], [180, 90, 'ok']],
['regression: shortest move metric (partial repair)', [180, 180, -270, 270], [180, 0, 'ok']],
['control 1', [315, 135, 45, 315], [135, -180, 'ok']],
['control 2', [45, 135, 45, 315], [135, 90, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [135, 90, -270, 270], [90, -45, 'ok']],
['regression: shortest move metric (partial repair)', [-270, 90, -270, 270], [-270, 0, 'ok']],
['control 1', [45, 315, 0, 180], [0, -45, 'limit']],
['control 2', [315, 180, 0, 360], [180, -135, 'ok']]]]
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 |
|---|---|---|---|
| boundary: target exactly at max stop | [-90, -90, 'ok'] | [-90, -90, 'ok'] | Passed |
| normal: short way through north | [10, -340, 'ok'] | [10, -340, 'ok'] | Passed |
| boundary: target outside narrow range | [90, -90, 'limit'] | [90, -90, 'limit'] | Passed |
| regression: shortest move metric | [90, -360, 'ok'] | [450, 0, 'ok'] | Failed |
| regression: shortest move metric (partial repair) | [-135, -360, 'ok'] | [225, 0, 'ok'] | Failed |
| control 1 | [0, -180, 'ok'] | [0, -180, 'ok'] | Passed |
| control 2 | [315, 135, 'ok'] | [315, 135, 'ok'] | Passed |
SHA-256 / db5f41b6c84c44c0f51b856aa68a96c73717b148329a69964d178cdb066ec8a1
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cur_az, target_az, min_az, max_az):
cands = []
k0 = math.floor((min_az - target_az) / 360)
for k in range(k0, k0 + 4):
c = target_az + 360 * k
if min_az <= c <= max_az:
cands.append(c)
center = (min_az + max_az) / 2
if not cands:
def ang(a):
d = (a - target_az) % 360
return min(d, 360 - d)
lim = min_az if ang(min_az) <= ang(max_az) else max_az
return [lim, lim - cur_az, 'limit']
best = min(cands, key=lambda c: (abs(c - cur_az) % 360, abs(c - center), c))
return [best, best - cur_az, 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [450, 90, -90, 450], [450, 0, 'ok']],
['regression: shortest move metric (partial repair)', [225, 225, -270, 270], [225, 0, 'ok']],
['control 1', [180, 0, -90, 450], [0, -180, 'ok']],
['control 2', [180, 315, 0, 360], [315, 135, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [180, 90, -270, 270], [90, -90, 'ok']],
['regression: shortest move metric (partial repair)', [225, 180, -270, 270], [180, -45, 'ok']],
['control 1', [45, 225, -90, 450], [225, 180, 'ok']],
['control 2', [180, 180, -90, 450], [180, 0, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [360, 90, -90, 450], [450, 90, 'ok']],
['regression: shortest move metric (partial repair)', [360, 0, -90, 450], [360, 0, 'ok']],
['control 1', [0, 45, -90, 450], [45, 45, 'ok']],
['control 2', [360, 45, 0, 360], [45, -315, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [90, 180, -270, 270], [180, 90, 'ok']],
['regression: shortest move metric (partial repair)', [180, 180, -270, 270], [180, 0, 'ok']],
['control 1', [315, 135, 45, 315], [135, -180, 'ok']],
['control 2', [45, 135, 45, 315], [135, 90, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [135, 90, -270, 270], [90, -45, 'ok']],
['regression: shortest move metric (partial repair)', [-270, 90, -270, 270], [-270, 0, 'ok']],
['control 1', [45, 315, 0, 180], [0, -45, 'limit']],
['control 2', [315, 180, 0, 360], [180, -135, 'ok']]]]
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 |
|---|---|---|---|
| boundary: target exactly at max stop | [-90, -90, 'ok'] | [-90, -90, 'ok'] | Passed |
| normal: short way through north | [10, -340, 'ok'] | [10, -340, 'ok'] | Passed |
| boundary: target outside narrow range | [90, -90, 'limit'] | [90, -90, 'limit'] | Passed |
| regression: shortest move metric | [90, -360, 'ok'] | [450, 0, 'ok'] | Failed |
| regression: shortest move metric (partial repair) | [-135, -360, 'ok'] | [225, 0, 'ok'] | Failed |
| control 1 | [0, -180, 'ok'] | [0, -180, 'ok'] | Passed |
| control 2 | [315, 135, 'ok'] | [315, 135, 'ok'] | Passed |
SHA-256 / 498640a7047ea36dff8e7e83cc52b976a32ee17793f723d263ce54666fae23c0
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cur_az, target_az, min_az, max_az):
cands = []
k0 = math.floor((min_az - target_az) / 360)
for k in range(k0, k0 + 4):
c = target_az + 360 * k
if min_az <= c <= max_az:
cands.append(c)
center = (min_az + max_az) / 2
if not cands:
def ang(a):
d = (a - target_az) % 360
return min(d, 360 - d)
lim = min_az if ang(min_az) <= ang(max_az) else max_az
return [lim, lim - cur_az, 'limit']
best = min(cands, key=lambda c: (abs(c - cur_az), abs(c - center), c))
return [best, best - cur_az, 'ok']
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [450, 90, -90, 450], [450, 0, 'ok']],
['regression: shortest move metric (partial repair)', [225, 225, -270, 270], [225, 0, 'ok']],
['control 1', [180, 0, -90, 450], [0, -180, 'ok']],
['control 2', [180, 315, 0, 360], [315, 135, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [180, 90, -270, 270], [90, -90, 'ok']],
['regression: shortest move metric (partial repair)', [225, 180, -270, 270], [180, -45, 'ok']],
['control 1', [45, 225, -90, 450], [225, 180, 'ok']],
['control 2', [180, 180, -90, 450], [180, 0, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [360, 90, -90, 450], [450, 90, 'ok']],
['regression: shortest move metric (partial repair)', [360, 0, -90, 450], [360, 0, 'ok']],
['control 1', [0, 45, -90, 450], [45, 45, 'ok']],
['control 2', [360, 45, 0, 360], [45, -315, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [90, 180, -270, 270], [180, 90, 'ok']],
['regression: shortest move metric (partial repair)', [180, 180, -270, 270], [180, 0, 'ok']],
['control 1', [315, 135, 45, 315], [135, -180, 'ok']],
['control 2', [45, 135, 45, 315], [135, 90, 'ok']]],
[['boundary: target exactly at max stop', [0, 270, -270, 270], [-90, -90, 'ok']],
['normal: short way through north', [350, 10, -270, 270], [10, -340, 'ok']],
['boundary: target outside narrow range', [180, 0, 90, 270], [90, -90, 'limit']],
['regression: shortest move metric', [135, 90, -270, 270], [90, -45, 'ok']],
['regression: shortest move metric (partial repair)', [-270, 90, -270, 270], [-270, 0, 'ok']],
['control 1', [45, 315, 0, 180], [0, -45, 'limit']],
['control 2', [315, 180, 0, 360], [180, -135, 'ok']]]]
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 |
|---|---|---|---|
| boundary: target exactly at max stop | [-90, -90, 'ok'] | [-90, -90, 'ok'] | Passed |
| normal: short way through north | [10, -340, 'ok'] | [10, -340, 'ok'] | Passed |
| boundary: target outside narrow range | [90, -90, 'limit'] | [90, -90, 'limit'] | Passed |
| regression: shortest move metric | [450, 0, 'ok'] | [450, 0, 'ok'] | Passed |
| regression: shortest move metric (partial repair) | [225, 0, 'ok'] | [225, 0, 'ok'] | Passed |
| control 1 | [0, -180, 'ok'] | [0, -180, 'ok'] | Passed |
| control 2 | [315, 135, 'ok'] | [315, 135, 'ok'] | Passed |
SHA-256 / 7ababaa0c0eedbea61893211caf1ae9e0a36e1fada79c9f0d6f06d6d344772ca
Verification & scope
Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. 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 2026-09-29T14:51:55.071746+00:00.
Case digest / 11cc61afb1f1a50c3f3509b7ac2d65f16c9b354da487f00be87e694c38a316c3