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Masked Generative Motion Planning with Geometry-Guided Token Search

Lipeng Zhuang, Yingdong Ru, Shiyu Fan, Edmond S. L. Ho, Gerardo Aragon Camarasa, Paul Henderson

arXiv:2610.10646v1cs.ROcs.AI

TL;DR

Generative motion planners often rely on local continuous refinement at test time, which can struggle when repair requires a substantial route change. MGMP uses masked generation for parallel discrete trajectory candidates and geometry-guided token search for structural repair. It reports high success on basin-escape and route-invalidation benchmarks, with generalization across varied planning settings.

  • Problem

    Continuous refinement of generated trajectories can remain initialization-sensitive and fail when feasibility requires a substantial route change, motivating a way to expose alternative routes for structural repair.

    Source: §1 · p. 1

  • Method

    MGMP uses a shared discrete trajectory-token space for parallel masked generation and geometry-guided search that targets edits and evaluates prior-supported replacements.

    Source: §1 · pp. 1–2

  • Results

    96% success on Ring Maze and 82% repair success on Controlled Route Invalidation exceed the strongest external baselines by 23 and 25 percentage points, respectively.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Across the reported evaluations, learned trajectory priors serve both as generators and as structured proposal spaces for geometry-guided test-time adaptation.

    Source: §5 · pp. 9–10

    The formulation is scoped to finite-horizon trajectories that start and end at specified configurations and remain collision-free with respect to the environment.

    Source: §3 · p. 3

Abstract

from arXiv · show

Generative motion planners typically use learned trajectory priors for initial generation, while leaving test-time repair to local continuous refinement. We introduce Masked Generative Motion Planning (MGMP), which extends the learned prior from efficient parallel generation to structural repair. A masked generative transformer generates discrete trajectory candidates in parallel, and Geometry-Guided Token Search (GGTS) uses scene geometry to target where to edit and which prior-supported alternatives to evaluate. This turns refinement into an efficient search over discrete motion alternatives, enabling route-level restructuring beyond local trajectory deformation. MGMP achieves 96% success on Ring Maze and 82% repair success on Controlled Route Invalidation on Kuka, exceeding the strongest external baselines by 23 and 25 percentage points, respectively. It further generalizes to unseen layouts, additional obstacles, unseen geometries, single- and dual-arm planning, and real-world Baxter tasks.

1 INTRODUCTION

MGMP uses one discrete trajectory-token space for parallel candidate generation and geometry-guided structural repair. Its benchmarks test basin escape and isolate repair quality, with strong reported results across additional planning settings.

1 INTRODUCTION

  • Continuous refinement can correct local feasibility issues but may remain initialization-sensitive or fail to escape unfavorable basins when a substantial route change is needed.The paper frames the central question as how a learned trajectory prior can expose qualitatively different routes for structural repair.Source: §1 · p. 1
  • MGMP formulates planning as masked generation over discrete trajectory tokens, reusing the same token space for test-time structural repair.The MGT predicts token sequences in parallel, while repair searches prior-supported alternatives instead of continuously deforming the current trajectory.Source: §1 · pp. 1–2
  • GGTS uses geometric attribution to select edit positions, then screens MGT-proposed replacements geometrically and verifies them with exact trajectory evaluation.Targeted discrete replacements can produce coordinated route changes beyond the current planning basin; optional continuous polish follows.Source: §1 · p. 2
  • 96% success on Ring Maze and 82% repair success on Controlled Route Invalidation exceed the strongest external baselines by 23 and 25 percentage points, respectively.The evaluations target basin escape and isolate repair from initial-generation quality; the paper also reports generalization across unseen layouts, additional obstacles, unseen geometries, and Baxter tasks.Source: §1 · p. 2

2 RELATED WORK

Prior motion-planning approaches either search configuration space or refine trajectories, while generative planners typically require continuous test-time correction. MGMP instead makes the learned trajectory prior a geometry-guided search space for structural repair.

2 RELATED WORK

  • Sampling-based planners can discover alternative routes but often require extensive sampling and collision checking in cluttered or high-dimensional spaces.Trajectory optimizers efficiently refine collision and smoothness objectives but remain sensitive to initialization and local planning basins.Source: §2 · pp. 2–3
  • Diffusion-based generative planners produce diverse candidates through iterative denoising, then commonly use guidance or optimization for scene constraints.Continuous refinement is effective for local correction but typically cannot move from an infeasible region to a feasible one when substantial route change is required.Source: §2 · p. 3
  • MGMP uses the learned trajectory prior and geometric failure signals to target token proposals for structural repair, unlike generic masked updates or fixed traversal of compressed tokens.Recent masked methods design update decisions for generative quality rather than scene-specific violations; Beyer & Karaman (2026) use fixed coarse-to-fine traversal and candidate evaluation.Source: §2 · p. 3

3 METHODOLOGY

MGMP encodes feasible trajectories as discrete tokens, predicts masked tokens conditioned on the planning scene, and repairs decoded trajectories through geometry-guided search. The search localizes edits, screens prior-supported replacements, verifies them against the exact objective, and optionally polishes the result continuously.

3 METHODOLOGY

  • Given start and goal states and environment constraints, the planner generates a finite-horizon trajectory that begins and ends at those states and remains collision-free.MGMP combines a trajectory tokenizer with a conditional masked generative transformer, then uses GGTS with geometric feedback at test time.Source: §3 · pp. 3–4

3.1 REPRESENTING MOTION CONFIGURATION SPACE VIA CODEBOOKS

  • A VQ-VAE maps trajectories to discrete codebook tokens and decodes quantized embeddings back into continuous trajectories.Tokens summarize approximately T/N trajectory steps; training also uses velocity continuity and, for robot trajectories, a forward-kinematics loss.Source: §3.1 · p. 4

3.2 MASKED GENERATIVE PREDICTOR OVER CODEBOOKS

  • The encoder-only MGT predicts masked trajectory tokens conditioned on start state, goal state, and obstacle information.Training masks or corrupts token indices and uses cross-entropy to recover them from those conditions.Source: §3.2 · p. 4

3.3 GEOMETRY-GUIDED TOKEN SEARCH

  • At test time, GGTS uses the geometric objective to choose which token positions to edit and which prior-supported alternatives to evaluate.The MGT prior preserves learned motion structure while geometry guides the search toward constraint-relevant edits.Source: §3.3 · p. 4

3.3.1 WHERE TO EDIT: GEOMETRY-GUIDED ADAPTIVE REMASKING

  • Geometric gradients identify tokens contributing most to violations, with MGT confidence as a secondary modulation; collision-associated positions are also remasked.The remasking set adapts in size, allowing shallow contacts to prompt few replacements and wrong-side-of-obstacle failures to expose more coordinates for restructuring.Source: §3.3.1 · pp. 4–5

3.3.2 WHAT TO FILL: CANDIDATE PROPOSAL, SCREENING, AND VERIFICATION

  • At selected positions, the MGT proposes top-probability code replacements, and a first-order geometric score screens them before exact evaluation.Shortlisted candidates are decoded and evaluated with the exact objective; the best replacement is committed only if it improves the current solution.Source: §3.3.2 · p. 5

3.3.3 ITERATIVE REFINEMENT

  • Each refinement round recomputes violations and proposals against the latest trajectory, stopping when feasible or at the round limit, then optionally applying a few continuous optimization steps.Discrete replacement supplies structural repair, while continuous polishing performs local correction.Source: §3.3.3 · p. 5

4 EXPERIMENTS

Across controlled and end-to-end settings, eleven classical and learned planners plus two variants are compared using success, valid-sample, timing, and repair metrics. The experiments test basin escape, isolate repair using shared initial trajectories, then assess generalization, ablations, and Baxter tasks.

4.1.1 NATURAL BASIN TRAPS IN RING MAZE.

  • 96% success on Ring Maze is the highest among evaluated refinement-based methods.The benchmark spans 4,000 problems across 100 unseen environments, 70% requiring enclosure escape; MGMP without polishing achieves 91% success and 64% valid-sample fraction.Source: §4.1.1 · p. 6, Table 1 · p. 7

4.1.2 CONTROLLED ROUTE INVALIDATION ON KUKA

  • 82% repair success on Controlled Route Invalidation exceeds MGT+EmbOpt's 60% and STOMP's 57%.The longest changed span covers 71.7% of the trajectory; MGMP without polishing reaches 76% repair success, with polishing resolving residual local infeasibilities.Source: Table 1 · p. 7, §4.1.2 · p. 7

4.2 GENERALIZATION AND ROBUSTNESS

  • On unseen layouts, DualKuka success rate is 0.96 versus BIT* at 0.85, while planning time is 0.39 s versus BIT* at 2.01 s.Obstacle types and counts match training, but placements and start-goal pairs are unseen; MGMP also reduces 7-DoF Kuka planning time from 0.39 s to 0.13 s.Source: §4.2 · p. 7, Table 2 · p. 8
  • With a few GGTS rounds, valid-sample fraction rises from 0.18 to 0.67 on Ring Maze and from 0.28 to 0.70 on DualKuka.Under additional obstacles, MGMP reaches about 0.54 valid-sample fraction, versus roughly 0.21 for MGT+EmbOpt-30 and 0.14 for PBD.Source: Figure 3 · p. 7, §4.2 · p. 8
  • With additional obstacles, DualKuka success rises from BIT*'s 0.63 to MGMP's 0.84, while planning time falls from 3.44 s to 0.90 s.On DualKuka, valid-sample fraction increases over CHOMP from 0.26 to 0.54; on Kuka, success is 0.96 versus BIT* at 0.95.Source: §4.2 · p. 8, Table 3 · p. 9
  • On unseen geometries, DualKuka MGMP has the highest success rate (0.87), compared with BIT* at 0.83 and PBD at 0.75.MGMP reaches a 0.66 valid-sample fraction on Kuka versus PBD's 0.47, and 0.57 on DualKuka versus CHOMP's 0.34.Source: Figure 3 · p. 7, §4.2 · p. 8, Table 3 · p. 9

4.3 ABLATION STUDY

  • Full MGMP reaches 0.96/0.97 success rate on Ring Maze/Kuka, above confidence-only remasking (0.84/0.92) and geometry-only remasking (0.93/0.95).Probability-only screening and independent exact search reach 0.88/0.94 and 0.91/0.95; discrete search performs structural repair while polishing resolves residual local infeasibilities.Source: Table 4 · p. 9, §4.3 · p. 9

4.4 REAL WORLD EXPERIMENTS

  • Real-world Baxter experiments cover shelf placing, button pressing, and pen drawing across five unseen environments.The task-agnostic planner is trained from left-arm demonstrations; each environment has three planning problems, and each method uses five candidate trajectories.Source: §4.4 · p. 9

5 CONCLUSION

MGMP keeps its learned trajectory prior active during repair, using geometry-guided discrete search to restructure trajectories and continuous optimization only for residual correction. The conclusion also points to broader planning evaluations and real-world tasks.

5 CONCLUSION

  • MGMP uses a shared discrete trajectory space for parallel generation and structural repair, with token replacement for restructuring and continuous optimization for residual correction.Controlled basin-escape and route-invalidation experiments identify discrete search as the main repair capability.Source: §5 · p. 9
  • Broader evaluations demonstrate generalization across diverse planning settings, with learned trajectory priors serving as structured proposal spaces for geometry-guided test-time adaptation.Figure 5 identifies button pressing, shelf placing, and drawing as real-world tasks.Source: Figure 5 · p. 9, §5 · p. 10
  • The authors report using generative AI tools only for language editing, with all edits reviewed for technical accuracy and consistency.They state that AI was not used to generate experimental results or determine scientific conclusions.Source: AI USE STATEMENT · p. 10

A ADDITIONAL METHOD DETAILS

MGMP inference generates an initial token trajectory, then iteratively searches selected tokens using geometric attribution, model-proposed alternatives, and exact trajectory evaluation. The appendix also specifies objectives for task settings, hyperparameter selection, and network components.

A.1 MGMP INFERENCE WITH GEOMETRY-GUIDED TOKEN SEARCH

  • Inference generates a trajectory from masked-token predictions, then iteratively selects repair positions, proposes replacement tokens, and verifies edits by exact objective evaluation before optional continuous polishing.The procedure stops when the trajectory is feasible or the search rounds are exhausted; polishing uses momentum-accumulated gradients.Source: §A.1 · p. 15

A.2 PLANNING OBJECTIVES FOR DIFFERENT TASK SETTINGS

  • Single-agent objectives combine start/goal error and scene collision costs; dual-agent planning adds self-collision, while additional obstacles are handled by combining predictions conditioned on obstacle subsets.The obstacle subsets are bounded by the obstacle encoder's training capacity, and their logits are summed for the global condition.Source: §A.2 · p. 16

B.1 HYPERPARAMETERS

  • Hyperparameters are selected on held-out validation data for standard benchmarks, while Ring Maze and Controlled Route Invalidation reuse configurations without further tuning.The test-time settings cap remasked tokens at 40% of trajectory tokens; for Kuka, this is at most four tokens.Source: §B.1 · pp. 16, 18, Table 8 · p. 18

B.2 NETWORK ARCHITECTURE

  • MGMP uses a VQ-VAE tokenizer to encode trajectories as discrete codes and a masked generative transformer conditioned on start, goal, and obstacle information.The transformer uses an obstacle encoder and AdaLN conditioning; the tokenizer's temporal downsampling ratio differs between single- and dual-agent tasks.Source: §B.2 · p. 18

B.3 SIMULATION DATASET AND TRAINING DATA

The simulation data comprise feasible BIT*-generated trajectories across point-robot, manipulator, and dual-arm settings, with test environments and start-goal pairs disjoint from training. The appendix details baseline coverage, timing measures, and controlled Ring Maze comparisons.

B.3 SIMULATION DATASET AND TRAINING DATA

  • Training uses 200K feasible BIT* trajectory samples per task from 500 environments, with evaluation environments and start-goal pairs disjoint from training.Ring Maze uses trap-aware queries, and 70% of its test problems require escaping at least one enclosure.Source: §B.3 · p. 19

B.4 BASELINE DETAILS

  • The evaluation spans eleven classical and learning-based baselines, including sampling-based planners, trajectory optimizers, and generative planners; classical planners receive a 5 s maximum budget.The learning-based set includes MπNets, MPD, PBD, and SafeFlowMatcher.Source: §B.4 · pp. 19–20

B.5 RUNNING TIME

  • Planning time measures time to the first certified feasible trajectory or budget limit, whereas running time covers generation and refinement of all 20 candidates.The reported timings exclude one-time model and dataset loading.Source: §B.5 · p. 20

B.6 EXPERIMENT DETAILS FOR RING MAZE

  • Ring Maze trajectory optimizers receive the same 20 initial trajectories, while learning-based planners use native sampling and refinement; MGMP variants distinguish discrete refinement and continuous polishing.MGT+EmbOpt-30 replaces token refinement with 30 continuous embedding-optimization steps; MGMP w/o Polish omits final polishing.Source: §B.6 · p. 20

B.7 IMPLEMENTATION DETAILS FOR CONTROLLED ROUTE INVALIDATION ON KUKA

The controlled route-invalidation protocol gives every method the same initially feasible trajectory after an obstacle is moved to invalidate it, preserving an alternative feasible route. It also measures how broadly successful repairs change the trajectory.

B.7 IMPLEMENTATION DETAILS FOR CONTROLLED ROUTE INVALIDATION ON KUKA

  • Each case begins with a verified feasible Route A, encoded and decoded through the MGMP tokenizer; an obstacle is then relocated to invalidate it while preserving another feasible route.Only cases where the reconstructed initial route remains feasible before obstacle relocation are retained.Source: §B.7 · p. 21
  • All methods receive the same invalidated trajectory and modified obstacles, and none may generate a new trajectory from scratch, isolating repair from initial-generation quality.Diffusion methods use warm-start refinement variants, while MGMP proposes replacement tokens from the shared initial token sequence.Source: §B.7 · p. 21
  • Repair extent is measured by average and maximum joint-space deviation and by changed span, the longest contiguous run of changed waypoints as a percentage of trajectory length.A waypoint counts as changed when its joint-space deviation exceeds 0.1 rad.Source: §B.7 · p. 21

B.8 IMPLEMENTATION DETAILS FOR UNSEEN OBSTACLE LAYOUTS

The section specifies the models and evaluation setups used to test generalization, including unseen layouts, added obstacles, and unseen mesh geometries. It also describes qualitative simulation results.

B.8 IMPLEMENTATION DETAILS FOR UNSEEN OBSTACLE LAYOUTS

  • DualKuka trajectories use 24 tokens, versus 12 for 7-DoF Kuka, and add a forward-kinematics position loss to improve reconstructed spatial accuracy.The VQ-VAE uses 8,192-entry codebooks; DualKuka uses a temporal downsampling factor of 2, compared with 4 for Kuka.Source: §B.8 · p. 22
  • At inference, Kuka and DualKuka use two token-refinement steps followed by five latent-embedding optimization steps, with SDF-guided weights switched after convergence.For DualKuka, the weights switch from (300, 150) to (600, 450); Maze2D uses a separate objective and convergence schedule.Source: §B.8 · p. 22

B.9 GENERALIZATION TO ADDITIONAL-OBSTACLE ENVIRONMENTS SETUP

  • Additional-obstacle scenes augment held-out base layouts, and BIT* verifies each start-goal problem within 60 seconds to exclude infeasible instances.Added obstacles are placed without overlap with inherited obstacles or invalid workspace regions; these combined configurations are evaluation-only.Source: §B.9 · p. 22

B.10 GENERALIZATION TO UNSEEN OBSTACLE GEOMETRIES ENVIRONMENTS SETUP

  • Ten ShapeNet meshes replace training boxes at test time, including irregular, non-cuboid shapes, to assess geometry generalization without additional training.Meshes are scaled to approximately 0.34 m half-extent, 1.7 times the training box half-extent; the same setting therefore also tests robustness to larger obstacles.Source: §B.10 · p. 22, Figure 6 · p. 23
  • Mesh placement follows the additional-obstacle protocol, with fixed object orientations and variable centers, so the shift centers on geometry and size rather than placement strategy.DeepSDF uses fixed latent codes during planning, and final trajectory validity is checked separately in PyBullet.Source: §B.10 · p. 23

C ADDITIONAL SIMULATION RESULTS

  • The additional simulation figures provide representative trajectory visualizations comparing BIT*, PBD, and MGMP as a complement to the paper’s quantitative results.The section characterizes these figures as visual evidence of planned-trajectory geometric quality.Source: C ADDITIONAL SIMULATION RESULTS · p. 24

C.1 FURTHER ANALYSIS ON RING MAZE

The analyses show that simply extending local refinement does not reliably overcome Ring Maze planning basins, while MGMP’s qualitative examples span unseen layouts, added obstacles, and unseen geometries.

C.1 FURTHER ANALYSIS ON RING MAZE

  • 73.3% CHOMP success remains unchanged from 10 to 50 iterations, while PBD rises only from 63.05% to 67.37% between refinement steps 3 and 5.MPD peaks at 14.40% success after three guidance steps and degrades with further refinement; the table reports success rate and valid-sample fraction.Source: §C.1 · p. 24
  • 93.8%, 84.1%, and 71.4% of trajectories are repaired by MGMP across increasingly severe collision ranges, versus 46.5%, 9.6%, and 5.2% for PBD.The ranges are [−0.05, 0), [−0.15, −0.05), and [−0.30, −0.15), respectively; negative minimum clearance indicates penetration.Source: §C.1 · p. 24

C.2 GENERALIZATION TO UNSEEN OBSTACLE LAYOUTS

  • Across Maze2D-6 and Concave Maze2D, MGMP’s qualitative paths reach goals without collisions under unseen obstacle layouts; Kuka and DualKuka examples show feasible plans in cluttered scenes.The examples include different obstacle placements and start-goal configurations.Source: §C.2 · p. 24, Figure 7 · p. 25

C.3 GENERALIZATION TO ADDITIONAL-OBSTACLE ENVIRONMENTS

  • In additional-obstacle DualKuka scenes, MGMP generates feasible trajectories despite more test-time obstacles than in training, using obstacle-conditioned predictions and collision-aware refinement.Source: §C.3 · p. 25

C.4 GENERALIZATION TO UNSEEN OBSTACLE GEOMETRIES

  • With training boxes replaced by unseen mesh objects, MGMP’s qualitative examples show adaptation to irregular, non-convex geometries through SDF-guided code refinement.Source: §C.4 · p. 25

C.5 ABLATION STUDY AND HYPERPARAMETER EXPERIMENTS

The ablations examine how GGTS candidate screening, refinement scheduling, and polishing budgets affect Kuka results. The real-world setup uses task-agnostic Baxter demonstrations and evaluates three downstream tasks.

C.5 ABLATION STUDY AND HYPERPARAMETER EXPERIMENTS

  • Exhaustive Verification evaluates all M = 16 proposals with the exact objective, achieving 0.98/0.89 SR/VSF versus Full GGTS at 0.97/0.87, but requires 8× more exact evaluations and raises runtime from 0.44 s to 1.28 s.First-order Only directly commits the top-ranked candidate without exact verification and yields 0.93/0.78 SR/VSF.Source: §C.5 · p. 26
  • 0.97 SR and 0.87 VSF at k = 2 improve on 0.95 SR / 0.84 VSF at k = 1, while k = 4 or 16 brings only marginal gains at higher runtime.The proposal pool is M = 16, and the selected shortlist retains two candidates for exact verification.Source: §C.5 · p. 26
  • The 2 × 2 schedule reaches 0.97 SR and 0.87 VSF, compared with 0.95/0.83 for 1×4 and 0.96/0.85 for 4 × 1.Five polishing steps raise feasibility from 0.94/0.83 to 0.97/0.87; ten steps yield VSF 0.88 without further SR gain.Source: §C.5 · pp. 26–27

D.1 ENVIRONMENT SETUP

  • The real-world 3D dataset contains 200 trajectories across 20 obstacle configurations, and the 2D tabletop drawing dataset contains 200 trajectories across 10 configurations.The 3D setting supports shelf placing and button pressing; drawing uses near-surface pen trajectories, with a hand-coded primitive action after the planned trajectory for the first two tasks.Source: §D.1 · p. 27

D.2 QUALITATIVE RESULTS

Qualitative results cover real-world Baxter drawing, button pressing, and shelf placing, alongside simulated unseen-layout, added-obstacle, and unseen-geometry examples. The figures show both successful executions and task-specific failure cases.

D.2 QUALITATIVE RESULTS

  • Successful pen-drawing trials follow the planned tabletop path toward the target while avoiding obstacles; failures include obstacle contact or stopping short of the desired final location.Source: §D.2 · p. 27, Figure 17 · p. 34
  • In button pressing, successful plans bring the end-effector above the button before a downward primitive, while the failure case misses a suitable pre-press pose.Source: §D.2 · p. 27, Figure 18 · p. 35
  • Shelf-placement examples reach valid release poses around obstacles, while failures involve collisions or an approach blocked by the upper shelf; different plans in one scene illustrate multimodal actions.Source: §D.2 · p. 27, Figure 19 · p. 35
  • In unseen-layout 7-DoF Kuka and 14-DoF DualKuka scenes, MGMP produces feasible, collision-free trajectories across obstacle placements and start-goal pairs.Source: Figure 8 · p. 28, Figure 9 · p. 29, Figure 10 · p. 29
  • In additional-obstacle DualKuka scenes, MGMP generates collision-free trajectories in more constrained workspaces, including scenes with more test-time obstacles than training scenes.Source: Figure 12 · p. 31, Figure 13 · p. 32
  • When box obstacles are replaced by unseen object-level meshes, MGMP generates collision-free paths around irregular objects and maintains feasible planning under realistic mesh obstacles.Source: Figure 14 · p. 32, Figure 15 · p. 33
  • The real-world setups include 3D obstacle-avoidance trajectories for shelf placing and button pressing, plus a near-surface 2D pen-drawing trajectory.Source: Figure 16 · p. 34
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