Sampling-Based Motion Planning with μ-Calculus Specifications Without Steering
Bibliographic record
Abstract
While using temporal logic specifications with motion planning has been heavily researched, the reliance on having an available steering function is impractical and often suited only to basic problems with linear dynamics. This is because a steering function is a solution to an optimal two-point boundary value problem (OBVP); to our knowledge, it is nearly impossible to find an analytic solution to such problems in many cases. Addressing this issue, we have developed a means of combining the asymptotically optimal and probabilistically complete kinodynamic planning algorithm SST* with a local deterministic μ-calculus model checking procedure to create a motion planning algorithm with deterministic μ-calculus specifications that does not rely on a steering function. The procedure involves combining only the most pertinent information from multiple Kripke structures in order to create one abstracted Kripke structure storing the best paths to all possible proposition regions of the state-space. A linear-quadratic regulator (LQR) feedback control policy is then used to track these best paths, effectively connecting the trajectories found from multiple Kripke structures. Simulations demonstrate that it is possible to satisfy a complex liveness specification for infinitely often reaching specified regions of state-space using only forward propagation.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".