Computing a Minimal Set of t-Spanning Motion Primitives for Lattice\n Planners
Bibliographic record
Abstract
In this paper we consider the problem of computing an optimal set of motion\nprimitives for a lattice planner. The objective we consider is to compute a\nminimal set of motion primitives that t-span a configuration space lattice. A\nset of motion primitives t-span a lattice if, given a real number t greater or\nequal to one, any configuration in the lattice can be reached via a sequence of\nmotion primitives whose cost is no more than t times the cost of the optimal\npath to that configuration. Determining the smallest set of t-spanning motion\nprimitives allows for quick traversal of a state lattice in the context of\nrobotic motion planning, while maintaining a t-factor adherence to the\ntheoretically optimal path. While several heuristics exist to determine a\nt-spanning set of motion primitives, these are presented without guarantees on\nthe size of the set relative to optimal. This paper provides a proof that the\nminimal t-spanning control set problem for a lattice defined over an arbitrary\nrobot configuration space is NP-complete, and presents a compact mixed integer\nlinear programming formulation to compute an optimal t-spanner. We show that\nsolutions obtained by the mixed integer linear program have significantly fewer\nmotion primitives than state of the art heuristic algorithms, and out perform a\nset of standard primitives used in robotic path planning.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".