Pith. sign in

REVIEW 4 major objections 7 minor 19 references

Cluster rollouts by collision direction, cut MPPI hesitation by 48%

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · glm-5.2

2026-07-08 03:32 UTC pith:IR53NLZI

load-bearing objection CE-MPPI: clustering with geometric direction features for MPPI the 4 major comments →

arxiv 2607.06499 v1 pith:IR53NLZI submitted 2026-07-07 cs.RO

Clustering-Embedded Model Predictive Path Integral Control: Avoiding Averaging-Induced Failure and Enabling Efficient Cluster Selection for Dynamic Obstacles

Zidong Liu , Kaixin Chang , Xu Chen This is my paper
classification cs.RO
keywords MPPImotion planningDBSCAN clusteringaveraging-induced failureobstacle avoidanceroboticstrajectory optimizationmanipulator control
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Model Predictive Path Integral (MPPI) control is a sampling-based robot motion planner: it stochastically perturbs a nominal control sequence, forward-simulates hundreds of parallel rollouts, and updates the control via an importance-weighted average of those rollouts. The paper identifies a structural failure mode in this averaging step: when an obstacle blocks the path, some feasible rollouts go left and some go right, but averaging their perturbations produces a control update that points toward the obstacle, causing hesitation or collision. The authors propose Clustering-Embedded MPPI (CE-MPPI), which inserts a pruning and clustering stage between rollout generation and the weighted update. First, all colliding rollouts are pruned. Second, the mean terminal position of those colliding rollouts is computed as a reference point. Third, each surviving rollout is assigned a geometric feature: the normalized direction vector from that collision-derived reference point to the rollout's own terminal position. DBSCAN clusters these direction vectors into groups that correspond to distinct avoidance modes (e.g., left-passing vs. right-passing). Fourth, a single cluster is selected—by minimum average cost for static obstacles, or by maximum directional opposition to obstacle motion for dynamic obstacles—and the MPPI weighted update is computed using only rollouts within that selected cluster. This ensures the averaged perturbations are always from a single, coherent avoidance mode, eliminating the cross-mode cancellation that causes averaging-induced failure. On a UR5e 6-DoF manipulator, CE-MPPI achieves a 48% reduction in time-to-goal and a 12% shorter end-effector path compared to standard MPPI, primarily by eliminating near-obstacle hesitation.

Core claim

The central mechanism is the collision-derived reference point: the mean terminal position of all colliding rollouts. By measuring the direction from this reference to each feasible rollout's terminal state, CE-MPPI obtains a geometric feature that naturally separates rollouts into clusters by which side of the obstacle they pass on. This is a sharper clustering signal than the velocity-based statistics used in prior work (CSC-MPPI), because two rollouts passing on opposite sides of an obstacle can have similar average velocities but necessarily have different direction vectors relative to the collision centroid. The within-cluster update then guarantees that the importance-weighted average只

What carries the argument

The collision-derived reference point (mean terminal position of colliding rollouts), the normalized direction feature from this point to each feasible rollout's terminal position, DBSCAN clustering of these features, and the dual selection logic (minimum-cost for static, dot-product opposition for dynamic).

Load-bearing premise

The dot-product heuristic for dynamic obstacles—picking the cluster whose average motion is most opposite to the obstacle's motion direction—is validated on a single scenario with one obstacle moving along the x-axis. Whether this criterion generalizes to multiple moving obstacles or obstacles whose motion is not aligned with the robot's nominal direction is untested.

What would settle it

Construct a dynamic environment with two obstacles moving in opposite directions along the robot's path. If the dot-product opposition criterion selects a cluster that avoids one obstacle but drives the robot into the other, the heuristic fails and the selection logic would need to be replaced with a multi-obstacle-aware criterion.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The pruning-and-clustering approach could generalize to any sampling-based planner that uses a weighted average over diverse rollouts, including trajectory optimization methods that blend sampled candidates.
  • The collision-derived reference point concept could extend to higher-dimensional configuration spaces where 'left vs. right' generalizes to distinct homotopy classes of paths around obstacles.
  • For dynamic obstacles, replacing the hand-designed dot-product heuristic with a learned or model-predictive selection criterion could handle multi-obstacle scenarios where a single opposition direction is insufficient.
  • The method's reliance on GPU-parallel rollout generation and pruning suggests that as parallel compute scales, the clustering stage's overhead becomes negligible relative to the simulation cost, making the approach increasingly practical.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The dot-product opposition criterion for dynamic obstacles is validated only on a single obstacle moving along one axis. In environments with multiple moving obstacles, selecting the cluster most opposite to one obstacle's motion could steer the robot toward another obstacle. A multi-obstacle extension would need a vector sum or priority-weighted combination of opposition scores.
  • The method reverts to standard MPPI when no colliding rollouts are observed (|C_col| = 0), which means the clustering benefit is only activated once the robot has already sampled trajectories that hit obstacles. In sparse-obstacle environments where the robot approaches at high speed, the first time collisions are detected may be too late for clustering to prevent a crash, suggesting a proactive c
  • The geometric direction feature is defined in task space (planar or end-effector position). For high-DoF manipulators where joint-space configuration matters for self-collision or joint-limit avoidance, clustering purely on end-effector direction may miss infeasible modes that share a terminal direction but differ in joint configuration.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. This paper proposes Clustering-Embedded MPPI (CE-MPPI), which augments standard MPPI with three stages: (1) pruning colliding rollouts, (2) DBSCAN clustering of feasible rollouts using a geometric direction feature derived from collision-derived reference points, and (3) obstacle-aware cluster selection (minimum cost for static obstacles, opposite-to-obstacle-motion for dynamic obstacles). The within-cluster MPPI update then uses only rollouts from the selected cluster. The method is evaluated in two 2-D simulation scenarios (static and dynamic obstacles) against standard MPPI and CSC-MPPI, and on a 6-DoF UR5e manipulator against standard MPPI. The authors report improvements in time-to-goal and path length in all experiments.

Significance. The paper addresses a well-known practical limitation of MPPI—averaging-induced failure in multi-modal environments—and proposes a constructive, modular solution. The geometric direction feature (Eqs. 12–13) anchored to collision-derived reference points is a sensible improvement over velocity-based clustering features used in prior work (CSC-MPPI), and the obstacle-aware selection criterion for dynamic scenes (Eq. 18) addresses a gap in the existing literature. The real-world deployment on a UR5e with GPU-accelerated rollouts demonstrates practical feasibility. However, the experimental evaluation has significant limitations (small sample sizes, confounded parameters, limited scenario diversity) that constrain the strength of the claims that can be drawn from the evidence.

major comments (4)
  1. Tables II and IV: All quantitative results are averaged over only 3 runs with no variance or standard deviation reported. With n=3, confidence intervals on the means are extremely wide. For example, the 17.4% improvement over CSC-MPPI in Scenario 2 (9.66s vs. 7.98s) could easily fall within noise. The authors should report standard deviations and, ideally, increase the number of runs to support the comparative claims.
  2. Table I and Table III: The temperature parameter λ differs dramatically across settings (0.7 for Scenario 1, 0.01 for Scenario 2, 0.05 for real-world). Since λ directly controls the sharpness of importance weighting—and thus whether averaging-induced failure occurs at all—the choice of λ is confounded with the method comparison. A fairer test would tune λ for the baseline or report results across a λ sweep. Without this, it is unclear whether CE-MPPI's advantage comes from the clustering architecture or from the baseline operating at a particularly unfavorable λ.
  3. Table IV: The headline 48% time-to-goal reduction comes from a real-world experiment where standard MPPI took 179.20s to traverse 0.83m—an average end-effector speed of approximately 0.005 m/s, indicating near-complete stagnation. This represents an extreme failure mode rather than a representative operating point. Any method that breaks the deadlock would show dramatic relative improvement, inflating the headline number. The authors should either provide a more representative baseline or explicitly contextualize this as a worst-case comparison.
  4. Eq. 18 and Section III-B.2: The dot-product heuristic for dynamic obstacle selection—choosing the cluster whose average motion is most opposite to the obstacle's motion direction—is validated on a single dynamic scenario with one obstacle moving along the x-axis. In environments with multiple moving obstacles or obstacles whose motion is not aligned with the robot's nominal direction, this criterion could select a cluster that is safe from one obstacle but collides with another, or that is suboptimal overall. The paper should discuss this limitation and, at minimum, test with a second dynamic-obstacle configuration (e.g., obstacle moving along y-axis, or two obstacles).
minor comments (7)
  1. Section III-C.1: The statement that CSC-MPPI 'exceeds the 10 Hz control budget' on the UR5e is stated without quantitative timing data. Reporting the per-iteration computation time for each method would strengthen this claim.
  2. Algorithm 1, line 7: The fallback to standard MPPI when |C_col_t| = 0 is mentioned, but the frequency of this fallback in practice is not reported. This information would help readers understand how often the clustering pipeline is actually invoked.
  3. Eq. 13: The small constant ε is introduced for numerical stability but its value is not specified in the simulation or real-world parameter tables.
  4. Section III-A.2: The robot model is described as a differential-drive platform, but the heading angle θ_t has no cost weight in Q (Q = diag(10, 10, 0)). This should be clarified—whether the heading is irrelevant to the task or whether this is a deliberate design choice.
  5. Fig. 5: The figure caption references sub-panels (a)–(k) but the distinction between time-steps within each method's row is not clearly explained in the caption. A brief note on what each sub-panel represents (e.g., different time-steps) would improve readability.
  6. Section III-D.2: The collision penalty w_c = 1000 is described as 'sufficiently large' but no analysis of its sensitivity or interaction with the clustering pipeline is provided. A brief discussion would be helpful.
  7. Table I: The DBSCAN ε parameter is listed only for the real-world experiment (Table III, 0.3 m) but not for the 2-D simulation. The simulation DBSCAN parameters should be reported.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a careful and constructive review. The referee correctly identifies that our experimental evaluation has limitations in sample size, parameter confounding, baseline representativeness, and scenario diversity for the dynamic-obstacle heuristic. We agree with all four major comments and will revise the manuscript accordingly. Specifically, we will (1) increase the number of runs and report standard deviations, (2) conduct a λ-sweep for the baseline and report results, (3) contextualize the real-world headline number as a worst-case comparison and add a more representative baseline, and (4) add a second dynamic-obstacle configuration and discuss the limitations of the dot-product heuristic for multi-obstacle settings. One practical constraint—re-running the real-world UR5e experiments with additional configurations—requires hardware access, but we are committed to completing this before resubmission.

read point-by-point responses

  1. Referee: Tables II and IV: All quantitative results are averaged over only 3 runs with no variance or standard deviation reported. With n=3, confidence intervals on the means are extremely wide. The 17.4% improvement over CSC-MPPI in Scenario 2 could easily fall within noise. The authors should report standard deviations and, ideally, increase the number of runs.

    Authors: The referee is correct. With n=3 and no reported variance, the comparative claims are not adequately supported. We will increase the number of runs for both simulation scenarios (to at least 10) and for the real-world experiment (to at least 5), and report means and standard deviations in all results tables. If any comparison loses statistical significance after this, we will adjust the corresponding claims accordingly. revision: yes

  2. Referee: Table I and Table III: The temperature parameter λ differs dramatically across settings (0.7 for Scenario 1, 0.01 for Scenario 2, 0.05 for real-world). Since λ directly controls the sharpness of importance weighting—and thus whether averaging-induced failure occurs at all—the choice of λ is confounded with the method comparison. A fairer test would tune λ for the baseline or report results across a λ sweep.

    Authors: This is a valid and important concern. The different λ values across scenarios were chosen based on per-scenario tuning, but we did not control for whether the baseline was operating at a favorable or unfavorable λ. We will conduct a λ-sweep for both standard MPPI and CSC-MPPI in each scenario and report performance across multiple λ values. This will allow readers to assess whether CE-MPPI's advantage is robust to the baseline's λ setting or whether part of the gain is attributable to parameter confounding. We will present these results either as a table or a figure in the revised manuscript. revision: yes

  3. Referee: Table IV: The headline 48% time-to-goal reduction comes from a real-world experiment where standard MPPI took 179.20s to traverse 0.83m—an average end-effector speed of approximately 0.005 m/s, indicating near-complete stagnation. This represents an extreme failure mode rather than a representative operating point. Any method that breaks the deadlock would show dramatic relative improvement, inflating the headline number. The authors should either provide a more representative baseline or explicitly contextualize this as a worst-case comparison.

    Authors: We agree with this assessment. The standard MPPI baseline in the real-world experiment was in a near-stagnation regime, and the 48% figure is inflated by this extreme failure mode. We will take two corrective steps: (1) We will explicitly contextualize the real-world result as a comparison against a worst-case MPPI failure mode, rather than a representative operating point, and adjust the abstract and conclusions to avoid implying that 48% is a representative improvement. (2) We will add an additional real-world baseline condition where MPPI operates at a more favorable λ or with a higher collision penalty that reduces stagnation, providing a more representative comparison point. We acknowledge that this requires additional hardware experiments, which we will conduct before resubmission. revision: yes

  4. Referee: Eq. 18 and Section III-B.2: The dot-product heuristic for dynamic obstacle selection is validated on a single dynamic scenario with one obstacle moving along the x-axis. In environments with multiple moving obstacles or obstacles whose motion is not aligned with the robot's nominal direction, this criterion could select a cluster that is safe from one obstacle but collides with another, or that is suboptimal overall. The paper should discuss this limitation and, at minimum, test with a second dynamic-obstacle configuration.

    Authors: The referee's concern is well-founded. The dot-product criterion in Eq. 18 was designed for and tested in a single-obstacle scenario, and its behavior in multi-obstacle or non-axis-aligned settings is not validated. We will address this in two ways: (1) We will add a second dynamic-obstacle simulation in which the obstacle moves along the y-axis (perpendicular to the robot's nominal direction), and report comparative results. If feasible within the revision timeline, we will also test a two-obstacle configuration. (2) We will add an explicit discussion of the limitation of the current heuristic for multi-obstacle environments, noting that the single-dot-product criterion does not account for interactions between multiple obstacle motion directions and may require extension (e.g., a weighted combination over obstacles or a different selection criterion) in such settings. We will frame this as a scope limitation and a direction for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity: CE-MPPI is a constructive algorithm whose components are defined independently of their outputs.

full rationale

The paper proposes CE-MPPI as a constructive algorithmic framework, not a derivation from theoretical first principles. Walking the derivation chain: (1) The clustering feature (Eq. 12-13) is defined as the normalized direction vector from a collision-derived reference point (Eq. 11) to each rollout's terminal position. This feature is computed from rollout geometry and is not defined in terms of the clustering output or the final control update. (2) The static cluster selection (Eq. 14) selects the minimum-average-cost cluster — the cost S(k) (Eq. 5) is computed from the rollout trajectory and is independent of the selection criterion. (3) The dynamic selection (Eq. 18) uses a dot-product between cluster-average motion direction (Eq. 16) and estimated obstacle motion (Eq. 17); neither quantity is defined in terms of the selection result. (4) The within-cluster MPPI update (Eq. 19-20) is a renormalization of standard MPPI weights (Eq. 6) over the selected cluster — a straightforward modification that does not feed back into the clustering or selection stages. No fitted constants are presented as predictions. The temperature parameter λ is set externally (Table I, Table III) and is not claimed as a derived quantity. The only self-referential element is that the collision-derived reference point (Eq. 11) depends on which rollouts collide, but this is a runtime computation from forward simulation, not a circular definition. The experimental results (Tables II, IV) are empirical comparisons, not predictions derived from the method's own definitions. The concerns raised by the skeptic (small sample size, λ confounding, extreme baseline failure) are correctness and experimental-design risks, not circularity. The derivation is self-contained.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities, forces, or mathematical objects. The 'geometric direction feature' and 'collision-derived reference point' are constructed from standard operations on existing state variables. All free parameters are standard algorithmic hyperparameters (temperature, cost weights, DBSCAN radius) rather than constants of nature or fitted model parameters. The axioms are domain-specific modeling choices, not mathematical postulates.

free parameters (5)
  • λ (temperature) = 0.7 (Scenario 1), 0.01 (Scenario 2), 0.05 (real-world)
    Standard MPPI parameter controlling weight sharpness; tuned per scenario.
  • DBSCAN ε (real-world) = 0.3 m
    Neighborhood radius for clustering; set for the UR5e task space.
  • Q, H (cost matrices) = Q=diag(10,10,0), H=diag(50,50,50)
    Quadratic cost weights for simulation; chosen by hand similar to CSC-MPPI.
  • w_p, w_R, w_c (real-world cost weights) = (10, 3, 1000)
    Goal-reaching and collision penalty weights for UR5e experiments.
  • H (obstacle history window) = Not specified
    Number of recent position measurements for obstacle velocity estimation; value not stated in the paper.
axioms (4)
  • domain assumption DBSCAN with the proposed geometric direction feature yields well-separated clusters corresponding to distinct avoidance modes.
    Section II-B.2; assumed but not formally proven; empirically supported by Fig. 5.
  • domain assumption Selecting the cluster whose average motion is most opposite to the obstacle motion reduces persistent coupling in dynamic environments.
    Section II-B.3, Eq. 18; a heuristic assumption validated on one dynamic scenario.
  • domain assumption Collision-derived reference point (mean terminal position of colliding rollouts) is a meaningful anchor for clustering direction features.
    Section II-B.2, Eq. 11; assumed without analysis of cases where colliding rollouts are dispersed.
  • domain assumption Pruning all colliding rollouts before clustering does not discard useful gradient information that could improve the control update.
    Section II-B.1; hard pruning is chosen over soft penalization without comparison.

pith-pipeline@v1.1.0-glm · 14333 in / 2700 out tokens · 355253 ms · 2026-07-08T03:32:49.684452+00:00 · methodology

0 comments
read the original abstract

With the widespread availability of parallel computing hardware, sampling-based motion planning methods such as Model Predictive Path Integral (MPPI) control have become increasingly powerful for complex nonlinear systems in non-smooth task spaces. However, the sampling and forward-simulation pipeline in MPPI suffers from averaging-induced failure in cluttered environments, where the importance-weighted update averages incompatible rollouts and leads to hesitation or even collision when an obstacle lies directly ahead. This paper proposes Clustering-Embedded MPPI (CE-MPPI), a framework that architecturally resolves the averaging-induced failures inherent in standard MPPI within non-convex environments. Rather than simply mitigating interference, CE-MPPI redefines the control law by integrating a high-fidelity pruning and clustering stage. By leveraging density-based spatial clustering of applications with noise (DBSCAN) alongside a novel geometric direction feature that is extracted from collision-derived reference points, the system isolates feasible trajectory modes from the noise of infeasible rollouts. This is paired with an intelligent selection logic that optimizes for minimum cost in static scenes while actively steering opposite to obstacle flux in dynamic environments. Experiments in 2-D JAX-accelerated simulations show that CE-MPPI alleviates obstacle-front hesitation and avoids persistent coupling with moving obstacles in dynamic scenes. In particular, real-world tests on a 6-DoF UR5e manipulator with CUDA-parallel rollouts in Isaac Gym achieve a 48\% reduction in time-to-goal and a 12\% shorter end-effector path.

Figures

Figures reproduced from arXiv: 2607.06499 by Kaixin Chang, Xu Chen, Zidong Liu.

Figure 1
Figure 1. Figure 1: Averaging-induced failure in MPPI: the weighted control update [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed CE-MPPI. CE-MPPI samples perturbed control sequences and performs parallel forward simulation to obtain trajectory [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Static obstacle case in CE-MPPI. Colliding rollouts are pruned [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dynamic obstacle case in CE-MPPI. Colliding rollouts are [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simulation results in two scenarios. Scenario 1 (static obstacle) is shown in (a), (b), and (c) for MPPI, CSC-MPPI, and CE-MPPI, respectively. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Experimental setup. where dR(·, ·) measures orientation mismatch (e.g., quater￾nion angle error), and Icol(qt) ∈ {0, 1} indicates collision or contact with the table, shelf and obstacle. For the UR5e robot and our task space, we set (wp, wR, wc) = (10, 3, 1000). D. Real-World Experimental Results We conduct real-world experiments on the UR5e platform shown in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Real-world UR5e tabletop experiment. A black box serves as the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Recent advances in path integral control for trajectory optimization: An overview in theoretical and algorithmic perspectives,

    M. Kazim, J. Hong, M.-G. Kim, and K.-K. K. Kim, “Recent advances in path integral control for trajectory optimization: An overview in theoretical and algorithmic perspectives,”Annual Reviews in Control, vol. 57, p. 100931, 2024

    work page 2024

  2. [2]

    Sampling-based motion planning: A comparative review,

    A. Orthey, C. Chamzas, and L. E. Kavraki, “Sampling-based motion planning: A comparative review,”Annual Review of Control, Robotics, and Autonomous Systems, vol. 7, 2023

    work page 2023

  3. [3]

    Information-theoretic model predictive control: Theory and applica- tions to autonomous driving,

    G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou, “Information-theoretic model predictive control: Theory and applica- tions to autonomous driving,”IEEE Transactions on Robotics, vol. 34, no. 6, pp. 1603–1622, 2018

    work page 2018

  4. [4]

    Review on model predictive control: An engineering perspective,

    M. Schwenzer, M. Ay, T. Bergs, and D. Abel, “Review on model predictive control: An engineering perspective,”The international journal of advanced manufacturing technology, vol. 117, no. 5, pp. 1327–1349, 2021

    work page 2021

  5. [5]

    Storm: An integrated framework for fast joint-space model-predictive control for reactive manipulation,

    M. Bhardwaj, B. Sundaralingam, A. Mousavian, N. D. Ratliff, D. Fox, F. Ramos, and B. Boots, “Storm: An integrated framework for fast joint-space model-predictive control for reactive manipulation,” in Conference on Robot Learning. PMLR, 2022, pp. 750–759

    work page 2022

  6. [6]

    Deep reinforcement learning for robotics: A survey of real-world successes,

    C. Tang, B. Abbatematteo, J. Hu, R. Chandra, R. Mart ´ın-Mart´ın, and P. Stone, “Deep reinforcement learning for robotics: A survey of real-world successes,”Annual Review of Control, Robotics, and Autonomous Systems, vol. 8, no. 1, pp. 153–188, 2025

    work page 2025

  7. [7]

    Gpu-enabled parallel trajectory optimization framework for safe motion planning of autonomous vehicles,

    Y . Lee, K. H. Choi, and K.-S. Kim, “Gpu-enabled parallel trajectory optimization framework for safe motion planning of autonomous vehicles,”IEEE Robotics and Automation Letters, vol. 9, no. 11, pp. 10 407–10 414, 2024

    work page 2024

  8. [8]

    Sampling-based con- strained motion planning with products of experts,

    A. Razmjoo, T. Xue, S. Shetty, and S. Calinon, “Sampling-based con- strained motion planning with products of experts,”The International Journal of Robotics Research, p. 02783649251404955, 2024

    work page 2024

  9. [9]

    Csc-mppi: A novel constrained mppi framework with dbscan for reliable obstacle avoidance,

    L. Park, K. Jang, and S. Kim, “Csc-mppi: A novel constrained mppi framework with dbscan for reliable obstacle avoidance,” in2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2025, pp. 19 645–19 652

    work page 2025

  10. [10]

    Dbscan clustering algorithm based on density,

    D. Deng, “Dbscan clustering algorithm based on density,” in2020 7th international forum on electrical engineering and automation (IFEEA). IEEE, 2020, pp. 949–953

    work page 2020

  11. [11]

    Jax: composable transformations of python+ numpy programs,

    J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman- Milne,et al., “Jax: composable transformations of python+ numpy programs,” 2018

    work page 2018

  12. [12]

    Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning

    V . Makoviychuk, L. Wawrzyniak, Y . Guo, M. Lu, K. Storey, M. Mack- lin, D. Hoeller, N. Rudin, A. Allshire, A. Handa,et al., “Isaac gym: High performance gpu-based physics simulation for robot learning,” arXiv preprint arXiv:2108.10470, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  13. [13]

    Ramp: Hierarchical reactive motion planning for manipulation tasks using implicit signed distance functions,

    V . Vasilopoulos, S. Garg, P. Piacenza, J. Huh, and V . Isler, “Ramp: Hierarchical reactive motion planning for manipulation tasks using implicit signed distance functions,” in2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2023, pp. 10 551–10 558

    work page 2023

  14. [14]

    Parallel mppi with gradient-velocity modulated sdf cost for high-performance real-time dynamic obstacle avoidance by robot manipulators,

    L. Zhou, Z. Li, Y . Li, and S. Bai, “Parallel mppi with gradient-velocity modulated sdf cost for high-performance real-time dynamic obstacle avoidance by robot manipulators,”IEEE Transactions on Robotics, 2025

    work page 2025

  15. [15]

    Pa-mppi: Perception-aware model predictive path integral control for quadrotor navigation in unknown environments,

    Y . Zhai, R. Reiter, and D. Scaramuzza, “Pa-mppi: Perception-aware model predictive path integral control for quadrotor navigation in unknown environments,”IEEE Robotics and Automation Letters, 2026

    work page 2026

  16. [16]

    Real-time whole-body control of legged robots with model- predictive path integral control,

    J. Alvarez-Padilla, J. Z. Zhang, S. Kwok, J. M. Dolan, and Z. Manch- ester, “Real-time whole-body control of legged robots with model- predictive path integral control,” in2025 IEEE International Confer- ence on Robotics and Automation (ICRA). IEEE, 2025, pp. 14 721– 14 727

    work page 2025

  17. [17]

    Single-instance sampling for computationally efficient and accurate real-time task space mppi control,

    D. Kim, E. Im, Y . Kim, M. Lim, and Y . Lee, “Single-instance sampling for computationally efficient and accurate real-time task space mppi control,”IEEE Transactions on Robotics, vol. 41, pp. 6327–6344, 2025

    work page 2025

  18. [18]

    Output-sampled model predictive path integral control (o-mppi) for increased efficiency,

    L. L. Yan and S. Devasia, “Output-sampled model predictive path integral control (o-mppi) for increased efficiency,” in2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024, pp. 14 279–14 285

    work page 2024

  19. [19]

    Switching sampling space of model predictive path-integral controller to balance efficiency and safety in 4wids vehicle navigation,

    M. Aoki, K. Honda, H. Okuda, and T. Suzuki, “Switching sampling space of model predictive path-integral controller to balance efficiency and safety in 4wids vehicle navigation,” in2024 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS). IEEE, 2024, pp. 3196–3203

    work page 2024