Incorporating Stochastic Models of Controller Behavior into Kinodynamic Efficiently Adaptive State Lattices for Mobile Robot Motion Planning in Off-Road Environments

Eli S. Lancaster; Eric R. Damm; Felix A. Sanchez; Jason M. Gregory; Kiana Bronder; Thomas M. Howard

REVIEW 3 major objections 5 minor 15 references

Incorporating Stochastic Models of Controller Behavior into Kinodynamic Efficiently Adaptive State Lattices for Mobile Robot Motion Planning in Off-Road Environments

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

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Pith's one-line read Incorporating stochastic pure-pursuit controller rollouts into KEASL search produces more conservative off-road trajectories with lower predicted collision likelihood than controller-agnostic planning.

desk verdict A useful, honest engineering paper on folding stochastic controller rollouts into a state-lattice planner, with one real caveat: the headline collision-reduction claim is made on the easy subset of problems where both planners succeed. read the letter →

arxiv 2508.04384 v1 pith:ERTJO6OM submitted 2025-08-06 cs.RO

Eric R. Damm , Eli S. Lancaster , Felix A. Sanchez , Kiana Bronder , Jason M. Gregory , Thomas M. Howard This is my paper · ORCID

classification cs.RO

keywords kinodynamicmotionplanningoff-roadroboticsstatelatticesstochasticuncertaintycontrollerrolloutspurepursuitunstructuredenvironmentsrobotnavigation

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

This paper addresses the gap between planned and executed motion in off-road robots: planners assume the low-level controller will follow the trajectory, but real controllers deviate. The authors augment the KEASL state-lattice planner with three ways of simulating noisy controller behavior during search, and show that the best one—deferring rollouts to the goal edge and revising the search graph after collisions—reduces predicted collision likelihood while staying within a one-second planning budget. The value is that planners can account for execution uncertainty without resorting to obstacle inflation, which can close off navigable corridors. The paper argues that predicting potential controller behavior during planning is a practical route to safer autonomous off-road navigation.

What carries the argument

The load-bearing tool is the stochastic controller rollout: a pure-pursuit controller tracks the candidate trajectory while zero-mean Gaussian noise is added to its velocity commands, and the resulting states are integrated at 0.1 s intervals to produce a distribution of possible executions. GEGR uses these rollouts lazily—only at the goal-edge—and after any collision performs graph revision, deleting all descendants of the collision node from the open and closed lists so search re-expands in valid regions. This combination keeps the per-search cost low enough for real-time use while still biasing the search away from trajectories that are risky under controller noise.

What would settle it

Record the actual trajectories the Warthog executes when following NR and GEGR plans under the same lookahead settings, and compare the realized collision rate against the predicted collision rate from the 100-rollout evaluation. If the model's predicted collision likelihood neither matches nor bounds the realized frequency of collisions across the test sets, then the reported safety gains are an artifact of the rollout model, not a property of real execution.

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Extended reading notes

Core claim

The central claim is that embedding stochastic controller rollouts into KEASL's recombinant search space yields plans that are more conservative—longer in duration but with lower predicted collision likelihood—than plans generated without rollouts. Of the three proposed methods, only Goal-Edge Graph Revision (GEGR) achieves this within the one-second planning constraint: it runs rollouts only when a candidate edge reaches the goal, and when a rollout collides it prunes all descendants of the collision node from the graph and continues search. Experiments on a Warthog UGV with two perception maps and a Perlin-noise ablation suite show that GEGR's predicted collision counts stay below NR's acr

Load-bearing premise

The stochastic model—zero-mean Gaussian velocity noise integrated at 0.1 s—is assumed to approximate the actual distribution of Warthog tracking errors, but the paper does not validate this against measured execution data.

Editorial extensions

If this is right

GEGR reduces predicted collision likelihood compared to no-rollout KEASL at every tested pure-pursuit lookahead from 0.5 m to 3.0 m, across both mapping algorithms and the simulated ablation maps.
At increasing obstacle-expansion radii, NR and GEGR achieve comparable predicted collision counts, but GEGR maintains a much higher planning success rate, since inflated footprints close off corridors and can make planning impossible.
The graph-revision step is decisive: PER and GER consistently fail to find solutions within the one-second time budget, while GEGR succeeds, showing that removing descendants of the collision node prevents search from being trapped near the goal.
GEGR planning times and path durations remain within the one-second budget and are only marginally higher than NR, supporting viability for field use.
GEGR's planning failures increase with lookahead distance, which the paper reads as an indicator that the underlying controller's path-following ability may be inadequate for the environment.

Reading between the lines

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

The same lazy-rollout-plus-graph-revision pattern could be applied to other lattice or graph-based planners that evaluate edges with computationally expensive models, not just controller rollouts.
The stochastic controller model could be calibrated online from logged tracking error, letting the planner adapt its risk estimate to the actual robot-controller pair rather than relying on a fixed Gaussian noise level.
A natural testable extension is to vary the noise distribution and integration step and measure how predicted collision likelihood changes, which would show whether the safety benefit is robust to model misspecification or dependent on the exact noise parameters.
Because predicted collision likelihood, not realized collision rate, is the reported metric, the practical safety claim needs a real-world collision study; if realized rates match predictions, GEGR becomes a drop-in alternative to conservative obstacle inflation in cluttered off-road maps.

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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

The new thing here is GEGR: instead of just checking rollouts on the goal edge, it finds the node where a rollout collides and prunes all descendants from the search graph. That is a sensible, concrete mechanism, and the progression from PER (too expensive) to GER (too brittle) to GEGR is clearly explained. The experimental scope is a plus: two real perception maps and 45 Perlin-noise ablations, with consistent trends across all of them. The paper also reports its failure counts honestly, in tables, rather than hiding them.

The main soft spot is exactly what the stress test flags. Figures 5 and 6 are built only over planning cycles where both GEGR and NR found a solution, and the failure tables show that subset is heavily biased. At LD=3.0 with Mapping Algorithm 1, GEGR fails 125 of 273 cycles while NR fails none. The GEGR box plots at high lookahead are therefore summarizing the easiest half of the problems. The paper even acknowledges this in Section 5.1 ("the only successful solutions were likely with the most simple set of maps"), but the abstract and conclusion still state the unqualified claim that rollouts decrease predicted collision likelihood. That is a real gap between evidence and headline.

A second, independent concern: the evaluation metric is generated by the same zero-mean Gaussian pure-pursuit model the planner uses during search. There is no validation of that noise model against measured tracking error on the Warthog, so the "predicted collision likelihood" reductions are internal to the model. It is fine as an ablation of planner behavior, but the paper sometimes reads as if it proves safer real-world plans. The reader's CIRCULARITY score of 2.0 is about right; it is a self-contained comparison, not circular, but the metric is self-referential.

Minor issues: no error bars or statistical tests, and the path duration / planning time comparisons are descriptive only. The PER/GER numbers are dire, but they are positioned as design iterations, not as competing methods, so omitting them from the main plots is acceptable.

Who is this for? Anyone building lattice planners for off-road UGVs and wondering whether to fold controller uncertainty into search. It is not a theoretical breakthrough and it does not close a long-open question, but it is a credible, well-scoped contribution with a clean ablation. I would send it to peer review with a request for all-problem comparisons or an explicit restriction of the claim, plus some real-robot tracking data or at least a model-validation experiment. It deserves referee time.

Referee Report

3 major / 5 minor

Summary. The paper addresses the problem of controller execution uncertainty in kinodynamic lattice planning by augmenting the KEASL planner with stochastic pure-pursuit rollouts. Three variants are proposed: Per-Expansion Rollout (PER), Goal-Edge Rollout (GER), and Goal-Edge Graph Revision (GEGR). The authors find PER and GER impractical under a one-second planning budget, and focus on GEGR, which performs lazy rollouts on the goal edge and revises the search graph when a rollout collides. Experiments compare GEGR with the no-rollout baseline (NR) across three map conditions: two field-derived mapping algorithms (273 and 402 planning problems) and 360 simulated Perlin-noise maps. The independent variables are pure-pursuit lookahead distance (0.5\(\text{--}\)3.0 m) and obstacle inflation radius (0.4\(\text{--}\)1.2 m). The headline claim is that GEGR yields more conservative trajectories with lower predicted collision counts than NR, while NR with inflated obstacles suffers many planning failures. The paper does not claim real-vehicle collision results; all collision numbers are produced by the same stochastic rollout model used during planning.

Significance. If the claims hold, GEGR is a useful and computationally practical way to inject controller-tracking uncertainty into state-lattice search; the graph-revision mechanism is a sensible fix for the inefficiency of naively rolling out every edge. The experimental scope is a strength: multiple mapping algorithms, a large number of planning problems, and an ablation over map complexity are more than is typical in this area. The authors also report failure counts openly, which is valuable. However, the central empirical comparison is weakened by the fact that the collision plots are restricted to the both-succeed subset, and the stochastic controller model is never validated against actual Warthog tracking data. As a result, the paper currently supports a model-relative and subset-restricted statement, not the unqualified conclusion that GEGR decreases collision likelihood during real operation. With re-analysis and a calibrated model, the contribution would be solid.

major comments (3)

[Section 5, Figures 5 and 6] The collision-rate comparison is computed only over planning problems where both GEGR and NR succeeded, while the failure tables show that this subset is strongly selected. For Mapping Algorithm 1, NR fails 0/273 at every lookahead, whereas GEGR fails 6/273 at LD=0.5 and 125/273 at LD=3.0. Thus the LD=3.0 GEGR box plot summarizes only the easiest ~54% of problems. Section 5.1 itself attributes the drop in GEGR planning times to the fact that 'the only successful solutions were likely with the most simple set of maps.' A lower GEGR median collision count on this selected subset does not establish safer planning on the full problem distribution. Please report an all-problem comparison (e.g., assign a collision penalty to failed cycles) or explicitly restrict the claim to the both-succeed subset and justify that the subset is representative.
[Section 3 and Section 4] The stochastic controller model is uncalibrated. The rollout adds zero-mean Gaussian noise to pure-pursuit velocity commands and integrates at 0.1 s, but no noise covariance is reported and no comparison is made to measured Warthog tracking error from the field trials. All 'collision likelihood' values are therefore predictions generated by the same model used for planning, not validated predictions about real execution. Please either calibrate the noise model to the vehicle/controller (for example, from recorded path-following data) or clearly state that the empirical claims are model-relative. The abstract and conclusion currently use language such as 'decrease predicted collision likelihood' and 'less likelihood for collisions' that can be misread as real safety guarantees.
[Sections 5.1 and 5.2] No statistical treatment supports the headline trend. The box plots show medians and ranges, but there are no error bars on the key comparisons, no confidence intervals, and no paired tests across planning cycles. Because the experiment has many paired planning problems (273, 402, and 360), a paired bootstrap or a paired significance test is feasible. Without this, 'decrease predicted collision likelihood' is supported only by directional visual inspection. Please add quantitative uncertainty estimates to the central collision comparisons.

minor comments (5)

[Section 5] The text says GEGR 'succeeded in all cases using 30 rollouts per goal edge revision,' which directly contradicts the failure counts in Figure 5 (e.g., 6 failures at LD=0.5). Please reconcile this wording with the table. If the intended meaning is that GEGR succeeded in a preliminary test set, say so explicitly.
[Section 4] Please define 'planning problem' and 'planning cycle' precisely, and give the total number of planning problems used in each failure-table column. The figures embed tables without explicit denominators, making it hard to interpret the failure percentages.
[Section 3] The rollout configuration for the main experiments is underspecified: the number of rollouts per goal-edge revision, the Gaussian noise standard deviation, and the pure-pursuit gains are not stated. Section 5 mentions 30 and 5 rollouts for PER/GER but not the final GEGR configuration. Please provide these parameters for reproducibility.
[Conclusion] Typo: 'sytems' should be 'systems.'
[Figure captions] The caption notes that plots correspond to problems where both GEGR and NR found solutions, but the main text does not repeat this caveat before drawing conclusions. Please state the subset restriction in Sections 5.1 and 5.2 where the trends are interpreted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper evaluates an internal metric with fresh rollouts and consistently labels it 'predicted,' so the central comparison is self-contained but not circular.

full rationale

The paper's claimed chain is empirical rather than formal. It augments KEASL with stochastic controller rollouts (Section 3) and measures 'predicted collision likelihood' by performing 100 additional rollouts after planning (Section 4). Although the evaluation metric is generated by the same stochastic controller model that GEGR uses internally, this is not circular: the 100 evaluation rollouts are independent fresh samples drawn after planning, and the paper consistently says 'predicted' rather than claiming validated real-world execution safety. The internal filter ('if every rollout(start node, n) is valid', Algorithm 4) and the evaluation tally are related by design, but this is the intended mechanism of the method, not a hidden reuse of the same samples or a fitted parameter renamed as a prediction. The comparison with NR on the same nominal map is a valid ablation, and the paper explicitly notes cases where GEGR fails to plan, so the failure tables are reported rather than concealed. The self-citations ([4] KEASL, [11] homotopy-aware lattices/Perlin maps) are ordinary prior-work citations and are not used to forbid alternatives or to smuggle in an ansatz. The substantive weaknesses—the unvalidated zero-mean Gaussian controller model and the fact that Figures 5/6 are restricted to problems where both planners succeed—are correctness/validity concerns, not circularity. Therefore no circular step is exhibited.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical entities. Its main unstated premise is that the stochastic rollout model is a faithful predictor of execution risk, and that reducing rollout collisions is the right safety objective. The free parameters listed are engineering choices that affect the comparison.

free parameters (4)

number of rollouts per edge = 30 for PER and GER initially, reduced to 5; GEGR uses 30
The number of controller rollouts per edge was chosen by experiment: 30 made PER and GER too slow, 5 improved success but not enough. This is a hand-tuned parameter affecting the collision detection and cost estimates.
rollout integration timestep = 0.1 s
The controller simulation integrates at 0.1 second intervals; this discretization affects collision detection and duration estimates.
pure-pursuit lookahead distance in GEGR = 1.0 m in obstacle expansion experiments
The lookahead distance determines the simulated controller's tracking behavior; chosen as a baseline value for the obstacle expansion experiments.
planning time limit = 1 second
The one-second ARA* budget constrains all experiments; it is a design choice that influences which methods succeed.

assumptions (3)

domain assumption Pure-pursuit with zero-mean Gaussian velocity noise is a reasonable model of the real Warthog controller's execution distribution.
The whole evaluation, including the 'predicted collision likelihood' metric, depends on this model. The paper does not validate it against measured tracking errors.
domain assumption The predicted collision likelihood from simulated rollouts is a valid proxy for real-world collision risk.
All safety conclusions are framed in terms of rollout collisions, not actual robot collisions; no real-world collision data is reported.
domain assumption ARA* with a one-second runtime provides a fair comparison between NR and GEGR.
The success rate metric is heavily influenced by this budget; the paper does not show how results change with more time, and GEGR's extra computation time is reported but not controlled for.

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Cite this review

Pith. "Pith review of Incorporating Stochastic Models of Controller Behavior into Kinodynamic Efficiently Adaptive State Lattices for Mobile Robot Motion Planning in Off-Road Environments." pith.science (2026). https://pith.science/paper/ERTJO6OM

@misc{pith2026250804384,
  author       = {Pith},
  title        = {Pith review of: Incorporating Stochastic Models of Controller Behavior into Kinodynamic Efficiently Adaptive State Lattices for Mobile Robot Motion Planning in Off-Road Environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ERTJO6OM}},
  note         = {Machine review of arXiv:2508.04384}
}

read the original abstract

Mobile robot motion planners rely on theoretical models to predict how the robot will move through the world. However, when deployed on a physical robot, these models are subject to errors due to real-world physics and uncertainty in how the lower-level controller follows the planned trajectory. In this work, we address this problem by presenting three methods of incorporating stochastic controller behavior into the recombinant search space of the Kinodynamic Efficiently Adaptive State Lattice (KEASL) planner. To demonstrate this work, we analyze the results of experiments performed on a Clearpath Robotics Warthog Unmanned Ground Vehicle (UGV) in an off-road, unstructured environment using two different perception algorithms, and performed an ablation study using a full spectrum of simulated environment map complexities. Analysis of the data found that incorporating stochastic controller sampling into KEASL leads to more conservative trajectories that decrease predicted collision likelihood when compared to KEASL without sampling. When compared to baseline planning with expanded obstacle footprints, the predicted likelihood of collisions becomes more comparable, but reduces the planning success rate for baseline search.

Figures

Figures reproduced from arXiv: 2508.04384 by the authors.

**Figure 1.** Search spaces for (a) the baseline with no rollouts (NR), (b) PER, (c) GER, (d) GEGR. The start and goal states are depicted as a yellow robot on the left and right of each image respectively. Valid and invalid expansions of KEASL are marked in black and red respectively. NR and GEGR were the only methods able to find a solution (green path) within the one-second planning time constraint [PITH_FULL_IMAGE:figures/fu… view at source ↗

**Figure 2.** UGV in an unstructured, off-road environment during experiments. 4.1 Mapping Conditions Field experiments were performed on a UGV in an unstructured, offroad environment, shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Top row: Map samples from Mapping Algorithm 1, each with a width and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: A sample of 5 of the 45 simulated maps used for the ablation experiments [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Planning Metrics of NR and GEGR using different lookahead values. LD: Lookahead distance in meters, Gray boxes: 25th to 75th percentile, Red lines: Median value (50th percentile), Whiskers: The range of data (excluding outliers), Circles: Outliers beyond 1.5 times the …

**Figure 6.** Figure 6: Planning metrics of NR and GEGR using different levels of obstacle expansion. OE: Obstacle expansion radius in meters, Gray boxes: 25th to 75th percentile, Red lines: Median value (50th percentile), Whiskers: The range of data (excluding outliers), Circles: Outliers b…

**Figure 7.** Figure 7: Left: Planned NR (red) and GEGR (cyan) trajectories with robot depictions. Right: 10 simulated controller rollouts on the solutions generated by NR (dark red) and GEGR (dark cyan) with collisions shown as robots surrounded by a red square. The map was generated by Mapp…

**Figure 8.** Figure 8: A map with obstacle expansion radii from left to right: 0.0m, 0.4m, 0.8m, 1.2m. In the field experiments, NR was unable to consistently find solutions because of the obstacle distributions. The ablation experiment supports this finding, but also shows the benefit of ob…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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

[1] [1]

IEEE transactions on automatic control 16, 529–552 (1971)

Athans, M.: The role and use of the stochastic linear-quadratic-gaussian problem in control system design. IEEE transactions on automatic control 16, 529–552 (1971)

work page 1971

[2] [2]

In: 2011 IEEE international conference on robotics and automation

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work page 2011

[3] [3]

Coulter, R.C.: Implementation of the pure pursuit path tracking algorithm. Tech. Rep. CMU-RI-TR-92-01, Robotics Institute, Pittsburgh, PA (January 1992)

work page 1992

[4] [4]

In: 2023 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS)

Damm, E.R., Gregory, J.M., Lancaster, E.S., Sanchez, F.A., Sahu, D.M., Howard, T.M.: Terrain-aware kinodynamic planning with efficiently adaptive state lattices for mobile robot navigation in off-road environments. In: 2023 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS). IEEE (2023)

work page 2023

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In: ROBOT2013: First Iberian Robotics Conference: Advances in Robotics, Vol

Gonz´ alez-Sieira, A., Mucientes, M., Bugar ´ ın, A.: A state lattice approach for mo- tion planning under control and sensor uncertainty. In: ROBOT2013: First Iberian Robotics Conference: Advances in Robotics, Vol. 2. pp. 247–260. Springer (2014)

work page 2014

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In: Robotics Research: Volume 2, pp

Janson, L., Schmerling, E., Pavone, M.: Monte carlo motion planning for robot trajectory optimization under uncertainty. In: Robotics Research: Volume 2, pp. 343–361. Springer (2017)

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[7] [7]

In: Thrun, S., Saul, L.K., Sch¨ olkopf, B

Likhachev, M., Gordon, G.J., Thrun, S.: ARA* : Anytime A* with provable bounds on sub-optimality. In: Thrun, S., Saul, L.K., Sch¨ olkopf, B. (eds.) Advances in Neural Information Processing Sys- tems 16, pp. 767–774. MIT Press (2004), http://papers.nips.cc/paper/ 2382-ara-anytime-a-with-provable-bounds-on-sub-optimality.pdf

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In: Proceedings of the International Conference on Automated Planning and Scheduling

Mandalika, A., Choudhury, S., Salzman, O., Srinivasa, S.: Generalized lazy search for robot motion planning: Interleaving search and edge evaluation via event-based toggles. In: Proceedings of the International Conference on Automated Planning and Scheduling. vol. 29, pp. 745–753 (2019)

work page 2019