Validate the residual
Estimate the payload contribution, then check the compensated momentum-observer residual on separate challenge poses.
Calibration + trust gate SIMULATION REPLAY / 0.9 KG SUSPENDED LOAD
CONTACT LOCALIZATION · SIMULATION STUDY
Preserve
ambiguity.
Move to
resolve it.
Ambiguity-Preserving Contact Localization
Where did contact happen? A robot keeps the possibilities open, then changes its view to find out.
A contact point.
No object model.
Joint states + commanded torques.
No joint-torque, F/T or tactile measurements.
Geometry in the renderer.
Unknown to the estimator.
01 / THE CENTRAL IDEA
One view gives a line.
A new view gives a point.
A single configuration cannot distinguish contact points along the force line of action. A narrow particle cloud can look certain while missing the true contact.
Keep the ambiguity that the measurement cannot remove.
APCL restores hypotheses along the unresolved direction. Reorienting the grasped object then changes the force direction in the object frame, making the contact point identifiable across views.
(p + αf) × f = p × f
The same force and moment can correspond to an entire line of contact points.
TRY A SECOND VIEW
Different directions resolve the contact; a wider angle improves conditioning.
Idealized geometry illustration. The shaded region is schematic, not a measured confidence interval.
02 / SEE THE MECHANISM
A hanging load.
An unknown attachment.
A 0.9 kg weight pulls on the grasped object through a cable. Two robots tilt the object and estimate the attachment point. Compare CPF and APCL side by side, with close-ups of their estimates.
Earlier development implementation, seed 17. Left: CPF without recovery. Right: APCL. The revised benchmark is reported below. Both begin from the same state and independently select the same next orientation in this example. The load settles before each measurement.Download film
01
Measure
One view leaves a direction unresolved.
02
Preserve
Recovery restores support along that direction.
03
Move
Tilt the object while keeping the cable attached.
04
Localize
Earlier development episode: CPF 22.5 mm; APCL 8.7 mm position error.
How to read this replay
Coral shows CPF without recovery; mint shows APCL. A colored diamond marks the estimated attachment point, and the gold dot marks the true point on the grasped object. The close-ups use the actual 3D positions. Marker symbols are enlarged for visibility; their positions are not displaced. The two robots replay paired trials, with matching camera views.
The suspended weight and cable tension are simulated physically. The estimated quantity is the attachment point on the object. The fixture is calibrated before connecting the weight, and its geometry and the attachment position are not supplied to the estimator.
The particle plots show saved distributions in object coordinates; the gold dot is the true point and the white cross is the weighted estimate. Each plot keeps the same scale throughout. Playback slows the motion and retimes waiting periods. The final 22.5 mm and 8.7 mm errors describe this single example; the updated 1,200-trial study below uses the revised MH and recovery implementation.
Transcript: A hanging weight pulls at an unknown attachment point. The first measurement leaves a direction unresolved. APCL restores candidate positions along that direction. The robot tilts the object, lets the load settle, and measures again. The final close-ups compare the recorded CPF and APCL estimates.
03 / THE METHOD
Measure what is observable.
Preserve what is not.
APCL combines residual validation, ambiguity-preserving contact inference, and active measurement. The object geometry and contact location are unknown.
Preserve hypotheses
The core recovery rule, D3, re-supplies hypotheses along the unresolved force line. Metropolis–Hastings moves and auxiliary recovery rules support the particle estimate.
Line-of-action recoveryChoose the next view
Score feasible orientations with profile Fisher information. Change orientation while regulating the tool position, then update the estimate.
Active reorientationPreserve the alternatives.
Then separate them.
The comparison isolates what recovery adds to a CPF that already uses Metropolis–Hastings (MH) moves. Recovery reduces confident but wrong estimates; active view selection resolves ambiguity with fewer measurements.
04 / SIMULATION EVIDENCE
What does recovery add?
The completed 1,200-trial study compares APCL with a CPF that already uses Metropolis–Hastings moves. Recovery improves the error tail and reduces estimates that look certain but are wrong.
Simulation reruns are complete. Hardware validation is pending.
95th-percentile position error
Lower is better · mmConfident but wrong
Lower is better · % of trials| Method | Median error | 95th-percentile error | Confident but wrong | 95% ellipsoid coverage | 95% particle-ball coverage |
|---|---|---|---|---|---|
| Regularized PF / no recovery | 9.0 mm | 145.8 mm | 216 / 1,200 | 69.6% | 69.6% |
| CPF + MH / no recovery | 6.7 mm | 24.9 mm | 35 / 1,200 | 76.1% | 78.0% |
| CPF + MH / D3 only | 5.4 mm | 20.6 mm | 0 / 1,200 | 83.9% | 88.7% |
| APCL | 5.5 mm | 20.8 mm | 0 / 1,200 | 84.3% | 88.2% |
Confident but wrong (CBW): reported 95% particle radius < 10 mm while true position error > 20 mm. All methods select views actively. The regularized PF uses kernel roughening; the other variants use MH moves and differ in recovery. All variants were rerun with the same seeds and calibration states. Ellipsoid coverage uses the covariance-based region; particle-ball coverage checks whether the true error is within the reported radius.
Errors above 20 mm: 8.1% without recovery and 5.9% with APCL.
APCL: 0 CBW events in 1,200 trials. The exact 95% interval is 0.00–0.31%; zero observed events do not establish zero risk.
The threshold fixed on a separate derivation set (c ≤ 1.15) accepts 675 / 1,200 main-study trials. On the held-out gate study, 3 / 456 invalid models and 25 / 44 valid models were admitted. Trial records: TBD.
Uncertainty still needs calibration. APCL’s 95% ellipsoid covered the truth in 84.3% of all trials; its 95% particle ball covered 88.2%. Both remain below the nominal 95% level. Hardware validation is pending.
What the additional studies test.
Across all 1,200 trials, line-of-action recovery alone (D3) reached a p95 error of 20.6 mm with 0 CBW events, similar to the complete method. D1 and D2 are auxiliary rules; these results do not establish an additional accuracy gain from combining all three.
Active measurement
24.4 vs 35.1 mmp95 after two views · active vs random
With recovery on in 1,200 paired trials, active selection used 4.15 views on average, compared with 4.88 for random selection.
Physical contact in simulation
7.1 mm / 19.8 mmmedian / p95 position error
A following spherical pusher generated force through MuJoCo contact dynamics. Rotating about the tool center point gave 0 CBW events in 300 trials; rotating about the estimated contact gave 2 in 300.
Parameter sensitivity
17.5–18.9 mmp95 across tested parameter settings
300 matched trials per setting varied the re-supply fraction, information threshold, and persistence. 0 CBW events across the tested settings.
A known load as a reference.
A second completed study attaches a steel disc after payload calibration: eight mounting positions, three masses (0.5, 1.0, and 1.5 kg), four repetitions, and three simulated robot instances — 288 trials.
The target is the disc’s center of mass, where its weight acts as an equivalent point force. This tests the measurement chain against a known reference; it does not model a surface-contact experiment.
| Method | Median error | 95th-percentile error | Confident but wrong | 95% ellipsoid coverage | 95% particle-ball coverage |
|---|---|---|---|---|---|
| CPF + MH / no recovery | 9.9 mm | 31.9 mm | 0 / 288 | 93.4% | 88.2% |
| APCL / active views | 9.6 mm | 30.7 mm | 0 / 288 | 95.5% | 88.2% |
| APCL / random views | 12.5 mm | 39.7 mm | 0 / 288 | 96.9% | 94.1% |
| APCL / gate-accepted subset | 17.1 mm | 36.2 mm | 0 / 97 | 88.7% | 66.0% |
Recovery and no recovery have similar position accuracy in this protocol, and neither produced a CBW event. The varied contact geometries in the main study provide the evidence for recovery’s benefit.
The gate admits 97 / 288 reference trials. Their median error is 17.1 mm and particle-ball coverage is 66.0%. Passing the contact-free residual check does not guarantee lower position error or calibrated coverage in this protocol.
05 / RESOURCES
Paper & supporting materials.
The current anonymous manuscript includes the updated simulation studies and Appendix A. Red hardware values are planned, not measured. Code and data: TBD.
Paper
Anonymous draft with completed simulation reruns and Appendix A. Red text marks planned hardware results.
Study code
Python / MuJoCo implementation and experiment runner.
Simulation data
Trial records, trajectories, and weighted particle snapshots.
Current scope
A rigidly grasped payload, a single object-fixed contact point, approximately world-fixed force across views, quasi-static measurement windows, and regulated tool position.
Validation status
The main, physical-contact, added-mass, gate, and sensitivity simulation studies have been rerun. Real-robot validation is pending.