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.

Paper mechanism result

The shared mechanism gallery juxtaposes the pretraining support, the raw pretrained OOD failure, the expanded policy, and two CFM--MPPI guidance settings. The fourth column uses a common close-up language: gray dashed Horizon-10 generative plans and, for CFM--MPPI, the goal and safety reward gradients. The displayed expanded row is the fixed B1 r15 policy used by the matched trend study below.

Vector PDF

Paper baseline assembly

The reusable baseline figure modules and their current preview are documented in PAPER_BASELINE_STUDY.md. They provide:

• a four-metric, four-gamma comparison interface for SafeMPPI, max-safety expansion, the pending SafeMPPI-cost expansion, and native-cost CFM--MPPI;
• a coefficient-pair sweep and trajectory-overlay interface for CFM--MPPI;
• an absolute (4\times4) CFM--MPPI guidance-scale screen at (\gamma\in{0.1,1.0});
• explicit JSON sidecars, without filling missing experimental results.

The preview is not yet a matched paper claim: max-safety uses its declared per-gamma evaluation temperatures, while the local baseline screens use native deployment. The final figure must use one common seed-bank, sample-count, and temperature contract after the running cost arm finishes.

Absolute Kazuki coefficient metrics and trajectory overlays show that the guidance response is non-monotone and gamma-dependent; the historical low/high coefficient rows were not calibrated optima.

The finer (\alpha,w_g,w_s) screen finds no coefficient that jointly restores high task success and verified trajectory validity. Its selected-mode figure and direction-conflict replay show a 20-step, 2.47-mm dwell interval at the unseen giant obstacle before collision. This is local-minimum-like evidence, not a claimed stable equilibrium: none of the (M=10) episodes timed out.

The subsequent high-(\alpha), high-(w_s) screen tests eight arms at (\gamma\in{0.1,0.5,1}). All have zero Validity, and six have zero success. A separate (M=50/\gamma) wall-route search finds only a weak bottom-wall segment, not a full wall-hugging route.

Indexed controller replay suite

All five videos retain the numbered PNG frames under the full Helios artifact root /data3/research1/b1_indexed_video_suite_f93a3ed. Blue contours are the actual nominal $H_P$ levels returned by SafeMPPI. Green contours are an offline, candidate-specific full-$H$ verifier audit; they never select the raw B1 action. Kazuki has no polytope overlay.

replay	fixed episode	evidence	video
SafeMPPI, in distribution	$\gamma=0.5$, SR	native nominal $H_P$ (blue)	MP4
SafeMPPI, giant-obstacle OOD	$\gamma=0.4$, lowest collision at index 82 in the declared M100 bank	native nominal $H_P$ (blue)	MP4
Expansion mechanism, giant-obstacle OOD	rounds 0/5/10/15, $\gamma\in{0.1,0.5,1.0}$	queried plans, uncertainty, positive/NVP traces	MP4
B1 r15, giant-obstacle OOD	successful parallel rollouts at $\gamma\in{0.1,0.5,1.0}$	offline full-$H$ verifier (green)	MP4
CFM--MPPI native-cost diagnostic, OOD	parallel failures at $\gamma\in{0.1,0.5,1.0}$	no polytope; goal_coef=0, safe_coef=0.1	MP4

The displayed Kazuki video is a diagnostic failure under the latest r19 model. All three refinement stages use the exact frozen B1 SafeMPPI plan cost. Its coefficient sweep is reported separately in PAPER_BASELINE_STUDY.md; no displayed coefficient is treated as an optimized final baseline.

SafeMPPI tutorial: hard rejection versus soft-cost MPPI

The local tutorial renderer scripts/build_safemppi_vs_vanilla_tutorial.py uses the same in-distribution scene and frozen teacher recipe as the first indexed replay. Its left panel evaluates all 512 SafeMPPI proposals per state and draws a deterministic 16-plan subset: accepted proposals are black dashed with a light glow, rejected proposals are red dashed, and the nominal polytope is always blue. In addition to the ten gamma-dependent levels, the explicit tangent-bounded (H_P=0) outer face is drawn; this keeps the (\gamma=0.1) geometry visible even when its ten inner levels remain far from the obstacle tangent.

The right panel is an explicitly non-certified, cost-only vanilla MPPI diagnostic. It retains the double-integrator, (H=10), action bounds, native task/control cost, and MPPI weighting, removes every feasibility mask, and uses only a smooth nearest-obstacle proximity cost. A fixed common-noise episode gives small/medium/large proposal standard deviations (\sigma={0.01,0.35,2.0}) with outcomes collision/success/collision. The displayed index is the first cell in a declared 20-seed diagnostic bank with interior-obstacle collisions in both failing arms. These three traces illustrate exploration starvation, a workable proposal scale, and high-variance saturation/averaging; they are not a performance estimate.

Tutorial MP4

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
indexed controller/polytope videos	paper_results/b1_indexed_video_suite.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.