exoskeleton/docs/calibration/CALIBRATION_AUDIT_2026-07-27.md

Calibration Audit — 2026-07-27

Scope and decision rule

This audit covers pre-prototype numerical and rigid-body simulation evidence only. It does not contain physical prototype, independent F/T, fixture, or human-subject results, and none of its values may be copied into the manuscript Results section.

The calibration code was first committed as 4503a12bf10886902e69d4be3874a76d3be577d6. All three reported v2 raw batches record that commit with dirty=false. The independent metric code and configs were tested with 98 passing tests and one explicitly unsupported legacy MuJoCo demo skipped.

The decision terms verified contract, provisional numerical setting, frozen setting, and not freeze-ready follow docs/calibration/CALIBRATION_POLICY.md.

The companion formula-linked audit workbook is outputs/calibration-20260727/calibration_audit_2026-07-27.xlsx. It contains 13 visually inspected worksheets and has SHA-256 24df38f67ba1aa428928348561b452db181f963ed30ae18a570aabc4bd8ad920.

Traceable batches

Study	Completed	Plan hash	Metric-config hash	Row hash	Source-data SHA-256
H1 calibration v2	60/60	e86b4aec90912954fdee97834dee08dd630647a89000a24402fa56f25b3aea83	2be0e67feda3f862c3510b3318af47437977c2b87a17ab810ce68a49212d5215	9e274b01db38c97112ecd1e7b50050d5c342cf316a22ea9b2d2c0ea4acf347d4	85110ad917d6b933656571b15c764b26d6f8215bea6d6baa338d759ed51fc0ee
H2 calibration v2	576/576	87f797edb5d2d6378a42b95616fca8ed733d0c81de5e22c422b006ead7071b12	caaf8c3b1c8180eb19afb98d986e8a54b8a897bd1ab706f78e39c41441932a31	fcac031716e967d3832d8eb6f770f580bd68bb6c8f715d55d04b5878f86f0fbf	e3a9bc29003193b559fbfc595ce2595b19a29a7135b9f14057128a8c5f504710
Bilateral energy/gain v2 Stage A	36/36	c10fa2cd84392f9dbf62809b0960bfb38d1e7aac4791ef0345a7353c45d8e062	37ca1e72ae55eb2a4594ef8e6395302d76ebfea87c4bca43615e86b3eeb89ec2	3f3f7f09387f02fe88c1b070815bd108f7e6bf63a091861ae62c1fac1dcdf421	H3 baa82701ea4c3e116657b9ef4d12aa795849957934f9dc5d58d5811405936da7; H4 47a9cc05f22724edf078a525e31ace6332b6048ab36ed72a005a50e8ecb79453; diagnostics a765cb6cc87c8fc89849c4d0a5d2560a768769169caa625baf41ddfd18f7af63

All batches validated with zero failed trials and no validator warnings.

H1 — SEW retargeting

Design corrections verified

• Five trajectory strata are now separate: nominal, wider valid reach, valid near-singularity, intentional upper-reach clipping, and master joint-limit stress.
• Each stratum has three genuinely different seeded trajectory instances. All four methods receive a bit-identical master trajectory within a pair. The audit found one trajectory hash per pair and 15 unique hashes across the 15 pairs.
• Reach clipping, active limits, geometry degeneracy, low manipulability, pose failure, and differential invalidity are distinct machine-readable fields. No invalid sample in v2 had an unexplained reason.

Calibration outcome

Method	Trials with C_r=1	Main observation
SEW	6/15	Passed nominal, wider valid reach, and valid near-singularity; failed the intentionally invalid reach-clip and joint-limit strata
Task-priority IK	6/15	Same trajectory-level composite outcomes as SEW in every pair
Bounded DLS IK	6/15	Same trajectory-level composite outcomes as SEW in every pair
Scaled joint-space map	15/15	Mapping branch remained numerically valid in several strata, but task-space error exceeded the locked calibration tolerances

The paired difference C_{r,\mathrm{SEW}}-C_{r,\mathrm{taskIK}} was zero in all 15 pairs. Every method had D_r=0, including all valid trajectories. Consequently, this calibration does not support the H1 superiority hypothesis and cannot calibrate or freeze the discontinuity threshold.

The valid near-singularity stratum is no longer mixed with reach clipping: SEW, task-priority IK, and bounded DLS had 100% valid samples and zero reach clips; the SEW slave-output low-manipulability fraction was approximately 0.502. The intentional upper-reach-clip stratum had a clip fraction of 1.0 and reach_clipped_upper as the primary invalid reason. The joint-limit stratum had no reach clipping and correctly reported joint_limit_active.

Runtime tails over all v2 samples were:

Method	P50	P95	P99	Maximum
Scaled joint-space	0.140 ms	0.159 ms	0.235 ms	0.475 ms
Bounded DLS IK	0.191 ms	1.693 ms	1.760 ms	5.156 ms
SEW	0.845 ms	10.290 ms	12.007 ms	15.643 ms
Task-priority IK	0.322 ms	10.139 ms	10.423 ms	10.713 ms

These are workstation numerical timings, not a hardware real-time claim.

H1 decision

Not freeze-ready. Before a locked H1 study:

1. add valid branch-transition and near-degeneracy trajectories that can actually exercise D_r;
2. declare a target control period and separate target construction, recovery, and differential-map timing;
3. tune both SEW and the primary task-priority baseline only on a new calibration split;
4. require a nonzero number of eligible increments in every continuity stratum; and
5. rerun with enough independent trajectories for a precision-based paired confidence interval.

H2 — residual-wrench inversion

Pairing and conditioning audit

The v2 plan contains 16 physical-data groups. Each group has 36 (\ell_c\times\lambda\times)method candidates and one unique seed hash. Independent array hashes confirmed that the wrench reference, joint velocity, truth Jacobian, estimator Jacobian, and sensor noise are identical across all 36 candidates within each group.

Numerical rank and operational ill-conditioning are now separate. No sample was numerically rank deficient, but the minimum scaled singular value reached approximately 9.83\times10^{-4}, and 39.9% of samples at the provisional candidate were below the preregistered operational threshold.

Parameter scan

For scaled DLS, trial-mean force/moment RMSE at the strongest candidates was:

\ell_c (m)	\lambda	Force mean / max (N)	Moment mean / max (Nm)
0.2	0.02	3.051 / 9.336	0.722 / 1.478
0.2	0.03	2.848 / 8.229	0.704 / 1.269
0.2	0.05	2.763 / 7.322	0.705 / 1.126
0.3	0.03	3.033 / 8.058	0.772 / 1.283
0.4	0.02	3.184 / 8.448	0.812 / 1.362

At \ell_c=0.2 m and \lambda=0.05:

Method	Force mean / max (N)	Moment mean / max (Nm)
Scaled DLS	2.763 / 7.322	0.705 / 1.126
Undamped SVD	6.064 / 25.502	1.248 / 4.281
No bias correction	3.132 / 7.512	0.786 / 1.140
No friction correction	2.965 / 7.091	0.759 / 1.153

The paired DLS-minus-undamped mean differences were -3.301 N and -0.544 Nm, but DLS was better in only 10 of 16 physical-data groups. It was deliberately worse in several well-modelled, low-noise cells and much better in the low-singular/model-error tail. This is a bias--variance result, not a universal accuracy result. The largest undamped retained outlier was 25.502 N / 4.281 Nm; it was not removed.

H2 decision

Provisional numerical setting: use scaled DLS with \ell_c=0.2 m and \lambda=0.05 only for the next synthetic pilot. Keep \ell_c=0.2,\lambda=0.03 and undamped SVD as sensitivity conditions.

Not a frozen physical calibration. The length scale must ultimately be anchored to robot geometry and physical calibration, and H2 cannot support a paper wrench-accuracy claim before independent six-axis F/T truth, TCP/F/T transforms, torque conversion, payload/friction calibration, timestamp alignment, and causal acceleration estimation are available.

H3/H4 — bilateral mapping and final-port energy supervision

Contracts already verified

The v1 stored-array audit verified:

• fixed-branch (A)-port virtual-work error at numerical precision;
• same-input proposed-versus-matched-wrench behavior, with their contact normalized-power-mismatch difference approximately zero;
• 96/96 tank trials passing the independent final-applied-port audit;
• maximum preclip floor deficit of zero;
• maximum accounting and software-preclip error of 6.94\times10^{-18} J; and
• zero downstream torque modification after the audited projection.

These are verified implementation contracts, not H3/H4 performance acceptance.

The v1 free-space power normalizer was only about 2\times10^{-4} J, so its normalized mismatch was not suitable as a primary endpoint. Metric schema v2 therefore always reports absolute mismatch and marks normalized H3 values invalid below a 1 mJ activity gate.

Stage A outcome

Stage A scanned feedback strength 0.2/0.35/0.5 and initial headroom 0.005/0.020/0.040 J at two wall stiffness levels.

• 36/36 independent H4 audits passed.
• Maximum accounting and software-preclip error was 1.39\times10^{-17} J.
• Downstream modification and projected floor deficit were both zero.
• D_{\mathrm{proj}} remained 0.756--0.905, with a mean of 0.837.
• Projection intervention occupied 0.328--0.531 of samples.
• Every trial reached the configured 80 N contact-force limit.
• Slave tracking RMSE was 0.807--1.035 rad.

The audit therefore verifies the final-port implementation, while the tested contact envelope is unsuitable for selecting a transparency setting. Choosing the numerically smallest D_{\mathrm{proj}} cell would merely freeze a force-limited, poorly tracked trajectory.

H3/H4 decision

• Verified contract: differential-dual virtual work and final-applied-port energy accounting.
• Not freeze-ready: feedback strength, energy bounds, H4 distortion threshold, contact envelope, network envelope, and H3 superiority margin.
• Stage B not executed: its configuration explicitly requires an accepted Stage A profile. Running it with the placeholder middle cell would violate the calibration policy.

The next bilateral calibration must first establish a stable fixture envelope without force limiting or large tracking error, then introduce a separate, controlled energy-challenging excitation. Contact stability and energy-budget excitation must not be forced by the same aggressive trajectory. Only after that gate passes should the directional network screen cover forward/return delay, jitter, and loss.

Freeze record

Item	Decision	Permitted use now
H1 thresholds and SEW superiority margin	Not freeze-ready	trajectory/debug development only
H2 scaled DLS \ell_c=0.2 m, \lambda=0.05	Provisional	next synthetic pilot only
A^\top virtual-work implementation	Verified contract	deterministic regression gate
Final-output energy accounting	Verified contract	deterministic regression gate
H3 normalized endpoint	Definition repaired; margin not frozen	use gated value plus absolute mismatch in calibration
Feedback gain and tank energy window	Not freeze-ready	continue calibration
Bilateral Stage B network matrix	Blocked by Stage A selection gate	do not execute as a locked or confirmatory study

Required next execution order

1. Redesign and rerun H1 continuity trajectories.
2. Run the H2 provisional setting on a larger held-out synthetic pilot while preserving the 16-group pairing contract.
3. Establish a stable, unsaturated fixture/contact envelope.
4. Design a distinct bounded energy-challenging excitation and rerun Stage A.
5. Replace Stage B placeholder haptic values only after Stage A passes.
6. Build the prototype measurement chain and complete physical calibration.
7. Freeze new locked JSON plans, metric configs, margins, exclusions, and a clean source commit before collecting confirmatory data.