Multi-Agent Path Finding Among Dynamic Uncontrollable Agents with Statistical Safety Guarantees

Eric Wang; Kegan J. Strawn; Lars Lindemann; Nora Ayanian; Sven Koenig; Thomy Phan

REVIEW 3 major objections 5 minor 38 references

Multi-Agent Path Finding Among Dynamic Uncontrollable Agents with Statistical Safety Guarantees

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read CP-Solver wraps a learned trajectory predictor in conformal prediction intervals and feeds them to a modified ECBS planner, guaranteeing that collisions with uncontrollable agents occur with probability at most a user-set δ for one-shot…

desk verdict A genuinely useful integration of conformal prediction into ECBS for MAPF with uncontrollable agents, but the stated statistical safety guarantee overclaims the horizon and ignores edge conflicts. read the letter →

arxiv 2507.22282 v1 pith:OUIIDV46 submitted 2025-07-29 cs.MA cs.RO

Kegan J. Strawn , Thomy Phan , Eric Wang , Nora Ayanian , Sven Koenig , Lars Lindemann This is my paper · ORCID

classification cs.MAcs.RO

keywords multi-agentpathfindingconformalpredictionuncertaintyquantificationdynamicobstaclesEnhancedConflict-BasedSearchstatisticalsafetyguaranteeslifelongMAPFtrajectory

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Multi-agent path finding (MAPF) solvers usually assume static environments and cooperative agents. This paper considers the harder setting where some agents are uncontrollable—humans, player-controlled characters, or other robots whose plans are unknown—and asks for paths that avoid them with a quantifiable safety margin. The authors propose CP-Solver, which combines a learned trajectory predictor, conformal prediction (CP) to convert prediction errors into statistically valid uncertainty intervals, and a modified Enhanced Conflict-Based Search (ECBS) planner that treats those intervals as moving obstacles. The central claim is that, for one-shot missions, this construction guarantees that the probability of any controlled agent colliding with any uncontrollable agent over the planning horizon is at most a user-specified δ. For lifelong missions, the method replans in a rolling horizon and reports competitive throughput with fewer collisions than baselines, though the formal guarantee is stated per windowed plan.

What carries the argument

The central machinery is the conformal prediction interval. For each uncontrollable agent and each future timestep, the algorithm forms a radius $C_{t+h}$ around the predicted position such that, with probability at least $1-\delta$ over the draw of the uncontrollable trajectory, the true position lies within that radius for every agent and every timestep in the horizon (equation (6)). The radii are the output of a conformal calibration step that normalizes errors across timesteps via linear complementarity programming, making the intervals less conservative than naive per-step calibration. These continuous intervals are projected onto the graph as 'CP interval vertex sets'—vertices within the ball of radius $C_{t+h}$ around a predicted position and reachable within $h$ edges—and the modified ECBS treats any path through those vertices as a conflict, adding constraints to keep controlled agents out.

What would settle it

Run CP-Solver in an environment where uncontrollable agents actively react to the controlled agents—for example, a pedestrian who steps out of the way of a robot—and count collisions over many trials; if the collision rate exceeds δ, the guarantee has broken under Assumption 2. A more direct check is to measure the empirical coverage of the CP intervals (equation (6)) on a held-out set of interacting trajectories; coverage significantly below 1−δ would falsify the statistical claim.

Watch

Extended reading notes

Core claim

CP-Solver replaces the unknown trajectories of uncontrollable agents with prediction intervals that, by conformal prediction, contain the true trajectory with probability at least 1−δ. The intervals are computed from a calibration dataset and normalized across prediction timesteps to keep them tight; they are then discretized onto the graph as sets of vertices the controlled agents must avoid. The modified ECBS planner resolves conflicts between controlled agents' paths and these avoided regions, and any conflict-free plan it returns therefore avoids the uncontrollable agents with probability at least 1−δ. This is the content of Corollary 1: equation (6) holds by construction of the intervals, and the planner's validity transforms that interval coverage into a collision-avoidance guarantee for the controlled agents.

Load-bearing premise

The guarantee holds only if the uncontrollable agents' trajectories are drawn from the same distribution that was used to calibrate the prediction intervals, i.e., if the controlled agents' actions do not change how the uncontrollable agents move.

Editorial extensions

If this is right

One-shot MAPF in warehouses, games, and other settings with human or non-cooperative agents can be given a quantitative safety guarantee: the user sets δ and the planner returns paths that collide with uncontrollable agents with probability at most δ.
The method is agnostic to the trajectory predictor: any learned forecaster can be wrapped with the conformal calibration step, so better predictors directly translate into tighter intervals and less conservative plans.
For lifelong operation, the same machinery applied in a rolling-horizon fashion yields collision counts below the δ bound in the paper's experiments while maintaining throughput competitive with planners that ignore or freeze the uncontrollable agents.
Because the conformal guarantee is distribution-free—it does not assume a Gaussian or other parametric noise model—it applies to arbitrary unpredictable agents as long as the calibration data are drawn independently from the same distribution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's Assumption 2—that controlled agents do not alter the distribution of uncontrollable trajectories—is strong in human-robot settings; a natural extension, which the authors mention but do not implement, is online re-calibration of the conformal intervals to adapt to detected distribution shifts.
The guarantee is per one-shot plan; composing it across rolling-horizon windows without re-calibration would require a union bound over windows (inflating δ) or periodic re-calibration, so the closed-loop results should be read as empirical rather than proven bounds.
The LCP normalization is a technical lever that trades interval tightness for computational cost; a simpler quantile-of-max-error calibration could be tested as a drop-in replacement to make the method easier to deploy without a linear-complementarity solver.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short take: this is a real new combination — conformal prediction intervals wrapped around a learned predictor, fed into ECBS as vertex constraints, for both one-shot and lifelong MAPF. The experiments show CP-Solver cuts collisions relative to the prediction-free baseline while keeping throughput competitive. That part is worth reading.

The core CP machinery is standard and the coverage result is sound under exchangeability. The LCP-based interval construction is from Cleaveland et al., and extending it with max-pooling over agents is straightforward but useful. The discretization to graph vertices is a sensible bridge. I believe the paper when it says the intervals cover 95% of prediction errors in the prediction window — Table 1 is consistent with that.

Where it breaks down is Corollary 1. Equation (6) bounds prediction errors only for h in [1,H]. Constraint (2i) demands collision avoidance for all t in [0,T]. Unless T=H, the solver has no CP interval information after H, so a collision after the prediction horizon is unprotected. The experiments dodge this by assuming the uncontrollable agent stays at its goal location, but that is not in the formal problem nor in Corollary 1. This is an internal proof gap, independent of distribution shift. It can be repaired by explicitly requiring T≤H or by adding a formal post-horizon assumption.

There is a second, smaller gap: avoiding the discretized vertex sets at each timestep prevents vertex conflicts at integer times, but not edge conflicts (two agents swapping positions along an edge between t and t+1). The CP guarantee is about positions at discrete times; edge conflict is a different event. The paper lists edge conflicts in the problem definition, so the guarantee does not cover its own collision definition.

Assumption 2 (controlled agents do not affect the uncontrolled agents' distribution) is acknowledged as approximate, and the paper points to robustness results for small shifts. That is fair, though a quantitative sensitivity analysis would help. The lack of released code/data and error bars on the main comparisons is a minor limitation; the method is reproducible in principle, but the paper does not ship it.

Who is this for: people working on MAPF with dynamic obstacles or human-robot shared spaces, and anyone applying conformal prediction inside planners. It is not a paradigm shift, but it is a useful step. I would send it to peer review, with the expectation of major revision to fix the horizon and edge-conflict claims. The core idea is solid enough to be worth refereeing.

Referee Report

3 major / 5 minor

Summary. The paper introduces the Multi-Agent Path Finding among Dynamic Uncontrollable Agents (MAPF-DUA) problem and proposes CP-Solver, an extension of Enhanced Conflict-Based Search (ECBS) that integrates a learned trajectory predictor with conformal prediction (CP) uncertainty intervals. CP-Solver has an open-loop variant for one-shot missions and a closed-loop variant for lifelong missions. The central formal claim is Corollary 1: a valid open-loop solution produced by Algorithm 2 avoids collisions with uncontrollable agents over the full horizon with probability at least 1-delta, where delta is user-specified. The paper reports experiments on warehouse and game maps comparing CP-Solver against baselines that ignore, treat as static obstacles, or use predictions without CP intervals, measuring throughput, runtime, and collisions.

Significance. The combination of conformal prediction with MAPF is timely and potentially useful: it replaces ad hoc safety margins with a statistical, distribution-free uncertainty quantification, and the algorithmic integration into ECBS is concrete and nontrivial. The paper's strengths are its explicit probabilistic problem formulation, the use of joint CP intervals that cover all uncontrolled agents and all prediction steps simultaneously, and an empirical section that verifies CP coverage above 1-delta and reports low violation counts. The central safety guarantee, however, currently has two load-bearing gaps: it does not cover time steps beyond the prediction horizon, and it does not address edge conflicts. These gaps must be repaired before the paper's main claim can be accepted; the empirical results are encouraging but do not by themselves close the formal gaps.

major comments (3)

[Open-Loop CP-Solver, Corollary 1 and Eq. (6)] The guarantee in Eq. (6) covers only h in lambda = [1,H], yet constraint (2i) is imposed for all t in [0,T]. Algorithm 2 computes CP interval sets only for times t+1 through t+H, so if T > H the solver has no uncertainty information after H and collisions in the interval (H,T] are not covered by the claimed 1-delta guarantee. The experimental sentence 'we assume the agent stays in this goal location' is a workaround, not part of the formal problem or of Corollary 1. The theorem should either require T = H, add a formal assumption about uncontrollable-agent behavior after H, or extend the CP construction to the full horizon.
[Preliminaries and Algorithm 2] Collisions in equations (2h)-(2i) include edge conflicts K_{(...),(...)}, where two agents traverse the same edge in opposite directions. The CP interval sets built in Algorithm 2 (line 3 and the discretization step) only restrict positions at integer timesteps, so avoiding those vertex sets does not rule out an edge conflict: two agents can be at different vertices at both t and t+1 while swapping edges between t and t+1. Corollary 1 therefore does not follow from the construction as written. Supporting the claim would require constraining edge traversals against all uncontrolled edge usages consistent with the CP intervals, or explicitly restricting the collision definition to vertex conflicts.
[Trajectory Prediction, Assumption 2] The 1-delta guarantee is valid only under Assumption 2, i.e. that controlled-agent trajectories do not change the distribution of uncontrollable-agent trajectories. The paper states this assumption and cites robust-CP work, but it provides no quantitative analysis of how much distribution shift is tolerable and no experimental validation that the assumption holds beyond the right-of-way setup in the experiments. The abstract and Corollary 1 are stated unconditionally, so the paper should explicitly qualify the safety guarantee as conditional on Assumption 2 and ideally provide a robustness bound or a practical test for the assumption.

minor comments (5)

[Problem Formulation, Eq. (2d) and Eq. (3d)] The notation for the one-shot horizon is inconsistent: Eq. (2d) uses \widehat{T} although the one-shot problem uses T, and Eq. (3d) contains a duplicated subscript in the uncontrolled goal sequence. Please correct these typographical issues.
[Algorithm 2, line 14] The condition 'if agent a, bin U' appears to be a typo for 'if agent a, b in U'. Please fix the pseudocode.
[Experimental Evaluation, Tables 2 and 3] Tables 2 and 3 report safety-violation counts for a small subset of configurations. Since the formal claim in Corollary 1 is about all configurations, please either report violation counts across all tested parameter combinations or clearly state that the tables are illustrative.
[Experimental Evaluation, prediction beyond the horizon] The sentence 'we assign the closest unassigned task spot to the final prediction as the goal vertex and assume the agent stays in this goal location' is a substantive modeling assumption. It should be moved from the experimental description into the formal problem statement or be explicitly identified as a limitation of the experiments.
[Figure 4] The caption 'averaged across all agent initialization, maps, and configuration parameters not specified' is vague; please specify exactly which parameters are averaged and which are held fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the statistical safety guarantee is a forward conformal-prediction statement calibrated on independent data; self-citations are supporting, not load-bearing.

full rationale

The paper's central derivation is not circular. Algorithm 1 trains a predictor on Dtrain and calibrates conformal intervals on a held-out Dcal; equation (6) is a standard CP validity statement conditional on exchangeability, and it is not fitted to the planner's collision outcomes or to any test result. Algorithm 2 then discretizes these intervals into sets of vertices and has ECBS avoid them; avoiding a superset that contains the true uncontrolled-agent trajectory with probability 1 − δ is a sound reduction, not an equivalence to the input. The cited CP framework (Cleaveland et al. 2024) is prior peer-reviewed work by a co-author, but the paper describes and modifies the algorithm, and the guarantee does not rest on an unverified uniqueness theorem from the same authors. Assumption 2 is an explicit modeling assumption; the reference to Strawn et al. 2023 is a robustness remark, not a load-bearing premise. One non-circular defect is a proof gap in Corollary 1: it claims collision avoidance for all t ∈ [0, T] ('guarantees that collision as per equations (2h)-(2i) are avoided with the user-specified confidence level of 1 − δ'), whereas equation (6) and the CP interval sets cover only h ∈ [1, H]; unless T = H or post-H dynamics are assumed known, the full-horizon guarantee is unsupported. This is a correctness concern and does not raise the circularity score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the conformal prediction exchangeability assumption and on the CP method from prior work. The learned predictor and calibration constants are fitted to data, but the statistical guarantee is distribution-free under exchangeability. The main unstated assumption is that vertex-level interval avoidance, not edge-level avoidance, is sufficient for the stated collision guarantee.

free parameters (3)

LSTM network weights = trained on Dtrain (final values not reported)
The trajectory predictor is trained on per-map datasets; its accuracy affects the size of the CP intervals and practical collision counts, though the distribution-free guarantee does not depend on predictor accuracy.
LCP normalization constants alpha_{t+h} = computed from Ccal1 in Algorithm 1
These constants rescale per-timestep prediction errors and are fitted to the first half of the calibration set; they directly set the size of the CP intervals.
CP quantile threshold = p-th smallest value of Ccal2
Computed from the second half of the calibration set; this is the conformal quantile that determines the interval radius.

assumptions (5)

domain assumption Calibration and training trajectories are independently drawn from the same distribution D_B~ (exchangeability)
Stated as Assumption 1 in Trajectory Prediction; required for conformal prediction validity.
domain assumption Controlled agents' actions do not affect the distribution of uncontrollable agent trajectories
Stated as Assumption 2; if false, the CP coverage guarantee may not hold at deployment. The paper acknowledges this.
standard math LCP conformal prediction procedure from Cleaveland et al. 2024 produces valid intervals under exchangeability
Invoked in Algorithm 1; the paper does not prove this theorem, relying on the cited AAAI paper.
standard math Avoiding vertices within radius C of the prediction prevents all vertex collisions when the true position lies within that radius
Geometric implication used in discretize(); straightforward but not stated as a formal lemma.
ad hoc to paper The CP intervals only need to cover vertex positions at integer timesteps, not edge traversal
Implicit in the discretization; edge conflicts are part of the collision definition (2i) but are not covered by the constructed sets.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Multi-Agent Path Finding Among Dynamic Uncontrollable Agents with Statistical Safety Guarantees." pith.science (2026). https://pith.science/paper/OUIIDV46

@misc{pith2026250722282,
  author       = {Pith},
  title        = {Pith review of: Multi-Agent Path Finding Among Dynamic Uncontrollable Agents with Statistical Safety Guarantees},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OUIIDV46}},
  note         = {Machine review of arXiv:2507.22282}
}

read the original abstract

Existing multi-agent path finding (MAPF) solvers do not account for uncertain behavior of uncontrollable agents. We present a novel variant of Enhanced Conflict-Based Search (ECBS), for both one-shot and lifelong MAPF in dynamic environments with uncontrollable agents. Our method consists of (1) training a learned predictor for the movement of uncontrollable agents, (2) quantifying the prediction error using conformal prediction (CP), a tool for statistical uncertainty quantification, and (3) integrating these uncertainty intervals into our modified ECBS solver. Our method can account for uncertain agent behavior, comes with statistical guarantees on collision-free paths for one-shot missions, and scales to lifelong missions with a receding horizon sequence of one-shot instances. We run our algorithm, CP-Solver, across warehouse and game maps, with competitive throughput and reduced collisions.

Figures

Figures reproduced from arXiv: 2507.22282 by the authors.

**Figure 2.** Three MAPF DUA warehouse instances (small, [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Game maps: (left) den201d and (right) arena. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Closed-loop CP-Solver averaged across all agent initialization, maps, and configuration parameters not specified: [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

38 extracted references · 31 canonical work pages

[1]

Alahi, A.; Goel, K.; Ramanathan, V.; Robicquet, A.; Fei-Fei, L.; and Savarese, S. 2016. Social lstm: Human trajectory prediction in crowded spaces. In Proc. of the IEEE Conf. on computer vision and pattern recognition, 961--971

work page 2016
[2]

D.; Coogan, S.; Egerstedt, M.; Notomista, G.; Sreenath, K.; and Tabuada, P

Ames, A. D.; Coogan, S.; Egerstedt, M.; Notomista, G.; Sreenath, K.; and Tabuada, P. 2019. Control barrier functions: Theory and applications. In 2019 18th European control Conf. (ECC), 3420--3431. IEEE

work page 2019
[3]

Andreychuk, A.; Yakovlev, K.; Surynek, P.; Atzmon, D.; and Stern, R. 2022. Multi-agent pathfinding with continuous time. A.I., 305: 103662

work page 2022
[4]

N.; Barber, R

Angelopoulos, A. N.; Barber, R. F.; and Bates, S. 2024. Theoretical Foundations of Conformal Prediction. arXiv preprint arXiv:2411.11824

arXiv 2024
[5]

N.; and Bates, S

Angelopoulos, A. N.; and Bates, S. 2021. A gentle introduction to conformal prediction and distribution-free uncertainty quantification. arXiv preprint arXiv:2107.07511

arXiv 2021
[6]

R.; and Koenig, S

Atzmon, D.; Stern, R.; Felner, A.; Sturtevant, N. R.; and Koenig, S. 2020. Probabilistic robust MAPF. In Proc. of the Int. Conf. on Automated Planning and Scheduling, volume 30, 29--37

work page 2020
[7]

Atzmon, D.; Stern, R.; Felner, A.; Wagner, G.; Bart \'a k, R.; and Zhou, N.-F. 2018. Robust MAPF. In Proc. of the Int. Sym. on Combinatorial Search, volume 9, 2--9

work page 2018
[8]

Bansal, S.; Chen, M.; Herbert, S.; and Tomlin, C. J. 2017. Hamilton-jacobi reachability: A brief overview and recent advances. In 2017 IEEE 56th Annual Conf. on Decision and Control (CDC), 2242--2253. IEEE

work page 2017

Show all 38 references

[9]

Barer, M.; Sharon, G.; Stern, R.; and Felner, A. 2014. Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem. In Proc. of the Int. Sym. on combinatorial Search, volume 5, 19--27

2014
[10]

Bellusci, M.; Basilico, N.; Amigoni, F.; et al. 2020. MAPF in configurable environments. In Proc. of the Intl. Joiint Conf. on Autonomous Agents and Multiagent Systems, 159--167. Int. Foundation for Autonomous Agents and Multiagent Sys

2020
[11]

Berkenkamp, F.; and Schoellig, A. P. 2015. Safe and robust learning control with Gaussian processes. In 2015 European Control Conf. (ECC), 2496--2501. IEEE

2015
[12]

Cauchois, M.; Gupta, S.; Ali, A.; and Duchi, J. C. 2023. Robust validation: Confident predictions even when distributions shift. Journal of the American Statistical Association, (just-accepted): 1--22

2023
[13]

D.; Li, J.; and Stuckey, P

Chen, Z.; Harabor, D. D.; Li, J.; and Stuckey, P. J. 2021. Symmetry breaking for k-robust MAPF. In Proc. of the AAAI Conf. on A.I., volume 35, 12267--12274

2021
[14]

J.; and Lindemann, L

Cleaveland, M.; Lee, I.; Pappas, G. J.; and Lindemann, L. 2024. Conformal prediction regions for time series using linear complementarity programming. In Proc. of the AAAI Conf. on A.I., volume 38, 20984--20992

2024
[15]

E.; Nilsson, N

Hart, P. E.; Nilsson, N. J.; and Raphael, B. 1968. A formal basis for the heuristic determination of minimum cost paths. IEEE Tran. on Sys. Science and Cybernetics, 4(2): 100--107

1968
[16]

Hochreiter, S. 1997. Long Short-term Memory. Neural Computation MIT-Press

1997
[17]

H \"o nig, W.; Kumar, T.; Cohen, L.; Ma, H.; Xu, H.; Ayanian, N.; and Koenig, S. 2016. MAPF with kinematic constraints. In Proc. of the Int. Conf. on Automated Planning and Scheduling, volume 26, 477--485

2016
[18]

LaValle, S. M. 2006. Planning algorithms. Cambridge U. Press

2006
[19]

W.; Kumar, T

Li, J.; Tinka, A.; Kiesel, S.; Durham, J. W.; Kumar, T. S.; and Koenig, S. 2021. Lifelong MAPF in large-scale warehouses. In Proc. of the AAAI Conf. on A.I., volume 35, 11272--11281

2021
[20]

Lindemann, L.; Cleaveland, M.; Shim, G.; and Pappas, G. J. 2023. Safe planning in dynamic environments using conformal prediction. IEEE Robo. and Auto. Letters

2023
[21]

J.; and Deshmukh, J

Lindemann, L.; Zhao, Y.; Yu, X.; Pappas, G. J.; and Deshmukh, J. V. 2024. Formal verification and control with conformal prediction. arXiv preprint arXiv:2409.00536

2024 arXiv
[22]

S.; and Koenig, S

Ma, H.; Li, J.; Kumar, T. S.; and Koenig, S. 2017. Lifelong MAPF for Online Pickup and Delivery Tasks. In Proc. of the 16th Conf. on Autonomous Agents and MultiAgent Systems, AAMAS '17, 837–845. Int. Foundation for Autonomous Agents and Multiagent Sys

2017
[23]

S.; and Sapp, B

Nayakanti, N.; Al-Rfou, R.; Zhou, A.; Goel, K.; Refaat, K. S.; and Sapp, B. 2022. Wayformer: Motion forecasting via simple & efficient attention networks. arXiv preprint arXiv:2207.05844

2022 arXiv
[24]

Okumura, K.; and Tixeuil, S. 2023. Fault-tolerant offline multi-agent path planning. In Proc. of the AAAI Conf. on A.I., volume 37, 11647--11654

2023
[25]

Padalkar, A.; Pooley, A.; Jain, A.; Bewley, A.; Herzog, A.; Irpan, A.; Khazatsky, A.; Rai, A.; Singh, A.; Brohan, A.; et al. 2023. Open x-embodiment: Robotic learning datasets and rt-x models. arXiv preprint arXiv:2310.08864

2023 arXiv
[26]

Phan, T.; Huang, T.; Dilkina, B.; and Koenig, S. 2024. Adaptive Anytime MAPF Using Bandit-Based Large Neighborhood Search. In Proc. of the AAAI Conf. on A.I., volume 38, 17514--17522

2024
[27]

Rawlings, J. B. 2000. Tutorial overview of model predictive control. IEEE control Sys. magazine, 20(3): 38--52

2000
[28]

M.; Sidrane, C.; Yel, E.; Everett, M.; Kochenderfer, M

Rober, N.; Katz, S. M.; Sidrane, C.; Yel, E.; Everett, M.; Kochenderfer, M. J.; and How, J. P. 2023. Backward reachability analysis of neural feedback loops: Techniques for linear and nonlinear systems. IEEE Open Journal of Control Sys

2023
[29]

Sharon, G.; Stern, R.; Felner, A.; and Sturtevant, N. R. 2015. Conflict-based search for optimal multi-agent pathfinding. A.I., 219: 40--66

2015
[30]

Stankeviciute, K.; M Alaa, A.; and van der Schaar, M. 2021. Conformal time-series forecasting. Adv. in Neural Info. Process. Sys., 34: 6216--6228

2021
[31]

R.; Felner, A.; Koenig, S.; Ma, H.; Walker, T

Stern, R.; Sturtevant, N. R.; Felner, A.; Koenig, S.; Ma, H.; Walker, T. T.; Li, J.; Atzmon, D.; Cohen, L.; Kumar, T. K. S.; Boyarski, E.; and Bartak, R. 2019. MAPF: Definitions, Variants, and Benchmarks. Sym. on Combinatorial Search (SoCS), 151--158

2019
[32]

Strawn, K.; and Ayanian, N. 2022. Byzantine fault tolerant consensus for lifelong and online multi-robot pickup and delivery. In Distributed Autonomous Robotic Systems: 15th Int. Sym., 31--44. Springer

2022
[33]

J.; Ayanian, N.; and Lindemann, L

Strawn, K. J.; Ayanian, N.; and Lindemann, L. 2023. Conformal Predictive Safety Filter for RL Controllers in Dynamic Environments. IEEE Robo. and Auto. Letters, 8(11): 7833--7840

2023
[34]

Thrun, S. 2002. Probabilistic robotics. Communications of the ACM, 45(3): 52--57

2002
[35]

Wan, Q.; Gu, C.; Sun, S.; Chen, M.; Huang, H.; and Jia, X. 2018. Lifelong MAPF in a dynamic environment. In 2018 15th Int. Conf. on Control, Auto., Robo. and Vision (ICARCV), 875--882. IEEE

2018
[36]

Yu, J.; and LaValle, S. M. 2016. Optimal multirobot path planning on graphs: Complete algorithms and effective heuristics. IEEE Tran. on Robo., 32(5): 1163--1177

2016
[37]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all...
[38]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Alahi, A.; Goel, K.; Ramanathan, V.; Robicquet, A.; Fei-Fei, L.; and Savarese, S. 2016. Social lstm: Human trajectory prediction in crowded spaces. In Proc. of the IEEE Conf. on computer vision and pattern recognition, 961--971

work page 2016

[2] [2]

D.; Coogan, S.; Egerstedt, M.; Notomista, G.; Sreenath, K.; and Tabuada, P

Ames, A. D.; Coogan, S.; Egerstedt, M.; Notomista, G.; Sreenath, K.; and Tabuada, P. 2019. Control barrier functions: Theory and applications. In 2019 18th European control Conf. (ECC), 3420--3431. IEEE

work page 2019

[3] [3]

Andreychuk, A.; Yakovlev, K.; Surynek, P.; Atzmon, D.; and Stern, R. 2022. Multi-agent pathfinding with continuous time. A.I., 305: 103662

work page 2022

[4] [4]

N.; Barber, R

Angelopoulos, A. N.; Barber, R. F.; and Bates, S. 2024. Theoretical Foundations of Conformal Prediction. arXiv preprint arXiv:2411.11824

arXiv 2024

[5] [5]

N.; and Bates, S

Angelopoulos, A. N.; and Bates, S. 2021. A gentle introduction to conformal prediction and distribution-free uncertainty quantification. arXiv preprint arXiv:2107.07511

arXiv 2021

[6] [6]

R.; and Koenig, S

Atzmon, D.; Stern, R.; Felner, A.; Sturtevant, N. R.; and Koenig, S. 2020. Probabilistic robust MAPF. In Proc. of the Int. Conf. on Automated Planning and Scheduling, volume 30, 29--37

work page 2020

[7] [7]

Atzmon, D.; Stern, R.; Felner, A.; Wagner, G.; Bart \'a k, R.; and Zhou, N.-F. 2018. Robust MAPF. In Proc. of the Int. Sym. on Combinatorial Search, volume 9, 2--9

work page 2018

[8] [8]

Bansal, S.; Chen, M.; Herbert, S.; and Tomlin, C. J. 2017. Hamilton-jacobi reachability: A brief overview and recent advances. In 2017 IEEE 56th Annual Conf. on Decision and Control (CDC), 2242--2253. IEEE

work page 2017