Pith Number

pith:PQCKD4VB

pith:2026:PQCKD4VBLBFWRXBLFXZERHYM2Q

not attested not anchored not stored refs resolved

Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds

Jonathan Kelly, Phone Thiha Kyaw

A midpoint-based approximation of Riemannian geodesic distance achieves third-order accuracy for sampling-based robot motion planning.

arxiv:2602.00992 v2 · 2026-02-01 · cs.RO

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\usepackage{pith}
\pithnumber{PQCKD4VBLBFWRXBLFXZERHYM2Q}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We introduce a computationally efficient midpoint-based approximation of the Riemannian geodesic distance and prove that it matches the true Riemannian distance with third-order accuracy.

C2weakest assumption

That the third-order midpoint approximation combined with first-order retractions remains accurate enough during sampling in high-dimensional configuration spaces without accumulating unacceptable errors or requiring excessive samples.

C3one line summary

A sampling-based planner approximates Riemannian geodesic distances via midpoints with third-order accuracy and uses retractions plus natural gradients for local planning, producing lower-cost trajectories than Euclidean baselines on robotic arms and SE(2) systems.

References

56 extracted · 56 resolved · 1 Pith anchors

[1] Expert Systems with Applications p 2025

[2] The International Journal of Robotics Research42(10), 729–754 (2023) 2023

[3] Proceed- ings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science216(1), 47–60 (2002) 2002

[4] Physical Review E—Statistical, Nonlinear, and Soft Matter Physics83(3), 031927 (2011) 2011

[5] Journal of Neuroscience 27(48), 13045–13064 (2007) 2007

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:16.468995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c04a1f2a1584b68dc2b2df2489f0cd4102bb6c12a9968998db36aa5c2e526ec

Aliases

arxiv: 2602.00992 · arxiv_version: 2602.00992v2 · doi: 10.48550/arxiv.2602.00992 · pith_short_12: PQCKD4VBLBFW · pith_short_16: PQCKD4VBLBFWRXBL · pith_short_8: PQCKD4VB

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Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PQCKD4VBLBFWRXBLFXZERHYM2Q \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7c04a1f2a1584b68dc2b2df2489f0cd4102bb6c12a9968998db36aa5c2e526ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "803d9336546758c675f1c057c0448c9a485ac991d8f70d2278cd4d9ea93ee2fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2026-02-01T03:14:46Z",
    "title_canon_sha256": "c494933bcc17e9a10a27292235ef21c98fc3174e91b31e552b5d31ffef715a75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.00992",
    "kind": "arxiv",
    "version": 2
  }
}