Safe Flow Expansion for Static Obstacles

This repository is the compact, source-grounded record of the current method: SafeMPPI demonstrations, a conditional flow model, and verifier-guided flow expansion in a static 2-D obstacle scene. Historical Phase A/B/C result bundles have been removed; the only promoted result is B1_current_best.

Current result

The canonical OOD scene starts at (0.3, 0.3), ends at (4.7, 4.7), and replaces the unseen center geometry by one radius-1.0 obstacle. Evaluation is raw, untilted, temperature-1 sampling with a disjoint M=50 seed bank for each of seven safety levels.

checkpoint	SR	CR	timeout	V-safe	V-full	successful U/R	min clearance, all
pretrained r0	57.43%	42.57%	0%	18.29%	13.14%	94/107	0.0171 m
B1 r19	96.00%	4.00%	0%	86.29%	49.71%	174/162	0.0557 m

The round-19 checkpoint was selected by the declared M10 screen before the disjoint M50 holdout was opened. The recovered delivery is scientifically complete and hash-validated, but remains marked RECOVERED_NONCANONICAL because a foreign GPU process violated the original artifact-assembly exclusivity gate after training and evaluation had completed.

1. Static scene and SafeMPPI teacher

The in-distribution scene is a 5 m x 5 m workspace with radius-0.2 static disks on the 4 x 4 integer grid and static boundary-wall disks. The robot is a point double integrator with dt=0.1, |u|<=1, and a planning horizon H=10. The obstacle, planner, and extra barrier margins are all exactly zero.

Exact teacher settings

setting	value
MPPI samples / horizon / temperature	512 / 10 / 0.1
Gaussian proposal sigma	0.5 sqrt(3) = 0.8660 per axis
sensing and barrier range	2.0 m
use_polytope_barrier / warm_start	true / true
use_goal_nominal	false
centroid gain / temporal smoothing / epsilon	0.2 / 0.25 / 0.15
centroid anisotropy / urgency floor	2.5 / 0.02
control-sequence smoothness cost	0.12
safety / extra barrier / planning margin	0 / 0 / 0
robot radius	0

These values are frozen in configs/safemppi_static_teacher.json.

Important correction: centroid sampling is active

The teacher loads best_area_mode4.json, then mode1_config changes the proposal to Gaussian mode, sets the range, action limits, and noise. It does not zero the centroid parameters. With the current robot-centered nominal polytope, SafeMPPI computes

[ \rho_t=\max!\left(0,\frac{R-s_t}{s_t+\epsilon}\right),\qquad \tilde p_t=\operatorname{clip}(0.2\rho_t,0.02,1), ]

and, after the first replan,

[ p_t=(1-0.25)\tilde p_t+0.25p_{t-1}. ]

Here s_t is the current nominal-polytope minimum face margin. Mode B samples toward the polytope opening/centroid with probability p_t. Static obstacles only imply zero obstacle velocity; the robot moves, so its robot-centered polytope and s_t change. Therefore centroid_gain, centroid_smooth, and centroid_eps remain active during demonstration gathering. The separate smooth_weight=0.12 is an MPPI control-sequence cost and must not be confused with centroid_smooth=0.25.

At every state SafeMPPI exposes its cost-selected weighted-mean plan and internal-best plan. Both exact H=10 plans are passed to the full verifier. Among certified cost-selected plans, the data collector executes the first action of the plan with the greatest verified progress. No raw debug rollout is executed or used as a training target.

2. Demonstration data and pretraining

The goal is fixed at (4.7,4.7). Starts are a jittered 32 x 32 grid over [0.1,4.9]^2, filtered to free space with zero initial velocity; there is no diagonal exclusion. The frozen bank has 881 starts. Collection uses gamma in {0.1,0.2,0.3,0.4,0.5,0.7,1.0}, up to three deterministic retries, and T<=800. It produced 878 successful trajectories per gamma and 341,968 verified planned windows in total.

The conditional flow predicts an acceleration window U in R^(10 x 2). Its condition contains

• five raw values: relative goal, velocity, and gamma;
• a two-dimensional closest-obstacle-boundary vector, averaged only on a numerical nearest-obstacle tie;
• a 32-dimensional CNN encoding of the nominal-polytope field.

The resulting context has dimension 39. The velocity network has input 91, hidden widths 160 -> 96 -> 32, and a 20-dimensional output. Pretraining uses reflection-paired data, no equivariance penalty, and exact x/y reflection group averaging at inference. Each trajectory has equal total loss mass, preventing long low-gamma trajectories from dominating solely through window count.

The 4.38 GB tensor is not committed. Its authenticated path and digest are in DATA_POINTER.json; on Helios run:

./scripts/link_helios_data.sh

3. Safe Flow Expansion (B1_current_best)

For round n, eight replicas per gamma advance synchronously. At each context, the current flow generates K=16 plans. An RBF posterior over the current-model representation z=phi_s(U,c), s=0.9, scores

[ k(z,z')=\exp!\left(-\frac{\lVert z-z'\rVert^2}{2\ell^2}\right), \qquad \sigma_n^2(z)=k(z,z)-k_z^\top(K_n+\lambda I)^{-1}k_z, ]

with ell=0.2003239429, lambda=0.01, and at most 512 positive support points from the current and previous round (W=2). Embeddings and the RBF state are rebuilt at each round and frozen during that round's gathering.

The verifier queries B=4 candidates sequentially without replacement using

[ \pi_j\propto\exp(\sigma_n(z_j)/\beta_n), ]

where one beta per gamma is calibrated to normalized ESS=0.25. Every solved selected-B query enters cumulative D; only full-H positives enter cumulative D+. SOCP errors enter neither. Execution first applies the nominal one-step H_P eligibility gate, then selects the eligible full-H-positive plan with the minimum exact SafeMPPI execution cost and executes only its first action. If no such plan exists, that replica terminates as NVP; there is no expert fallback.

Training replays full-H positives from W=2. Every eligible positive is used exactly once per round. Loss mass is equalized hierarchically over

[ \gamma;\rightarrow;(\text{round},\text{episode}) ;\rightarrow;\text{context};\rightarrow;\text{positive query}. ]

The batch size is 128, learning rate is 1e-5, the number of Adam steps is ceil(|D_W^+|/128), and the visual encoder is frozen. At NVP contexts the selected-B population supplies the signed negative gradient

[ g=g_+-\rho g_-,\qquad \rho=0.01\frac{\lVert g_+\rVert_2}{\lVert g_-\rVert_2}. ]

The complete generated recipe is configs/b1_current_best_recipe.json.

4. Reproduction entry points

The files below preserve their original safeMPPI-relative paths under source_snapshot/; copy the snapshot into a clean checkout of the parent safeMPPI project or use the original source commit shown below.

stage	entry point
static scene and teacher configuration	overnight_run_07_06/grid_scene.py, overnight_run_2026-06-28/best_area_mode4.json
SafeMPPI implementation	cfm_mppi/safegpc_adapter/safemppi.py
endpoints, expert collection, combine, visualization	overnight_run_07_06/rev_expansion/codex_challenging/afe_restart/stage2_low7_randomized.py
low7 CFM pretraining	.../afe_restart/stage3_low7_pretrain.py
balanced reflection-paired r0 launcher	.../afe_restart/run_low7_reflection_pretrain_pair.sh
RBF expansion trainer	overnight_run_07_06/rev_expansion/codex_overnight/grid_expand_afe_rbf.py
RBF, beta, execution, negative update	afe_rbf_core.py, afe_adaptive.py, afe_execution.py, afe_signed_update.py
exact B1 sweep/selection launcher	run_low7_b1_balanced_sweep.sh, analysis/low7_b1_balanced_sweep_driver.py
raw temperature-1 M50 evaluation	paper_results/low7_raw_m50_eval.py

Canonical identities:

• algorithm source: 63ebefa7877c0b923c1c7cdea19228302dd6a0ca;
• dataset SHA-256: 4b8e2d9be794584fad232bcc46cf78c2c4f422efb3e0642f503c8a77fcd2e8ec;
• balanced pretrained checkpoint: 524c9c0a4fd071221ac509b9d8e6fbbfb85fdf1811aa04160317f2a9e2d3ef90;
• selected r19 checkpoint: 60c155472f5ed0e4a1d53581857f09aead7924f8ce11e8e3adf890d5a57fc079;
• scene SHA-256: 356d6d48b3af2b017b529562b530f35285c86f9107da512a73de6ef664b03e72.

Verify this repository with:

python scripts/verify_package.py
python -m pytest tests/test_workbook_contract.py -q

Scope and blind spots

• RBF variance is a novelty score in the learned representation, not a safety probability or certificate.
• A verified finite-H window does not prove recursive closed-loop viability; NVP remains possible.
• The closest-boundary vector compresses multi-obstacle geometry to two numbers; the nominal-polytope grid carries the remaining local geometry.
• minimum_clearance is the minimum over every state and obstacle/wall, then averaged over all episodes, including failures. At r20, gamma 0.1 is 0.0491 m over all episodes and 0.0549 m over successes only.
• The current result is established on static circular obstacles and should not be presented as a dynamic-obstacle guarantee.