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FCTS: Failure-Guided Curriculum Tree Search Over Generated Terrain for Legged Parkour

Narayanan Palghat Parameswaran, Dong-Ki Kim, Jay Patrikar, Santiago Gutierrez, Harshad Zade, Shayegan Omidshafiei, Harmish Khambhaita

arXiv:2610.22619v1cs.RO

TL;DR

Quadruped parkour curricula often miss irregular, compound terrain, and manually designed families are difficult to extend. FCTS generates training terrain from localized traversal failures and uses MCTS to explore curriculum trajectories. On reconstructed real-world courses, it improves hard-course success over the strongest baseline and transfers to a physical quadruped.

  • Problem

    Hand-designed terrain families remain fixed, while aggregate feedback from LLM-generated curricula does not identify where traversal failed or which local geometry caused it.

    Source: §I · p. 1

  • Method

    FCTS conditions generated terrain on localized failure feedback and uses MCTS to explore alternative curriculum trajectories under a fixed training budget.

    Source: §I · p. 2, 1) Problem setup · p. 3

  • Results

    44.7% success on Hard versus 14.9% for the strongest baseline, and 0.71 Progress IQM on V-Hard versus at most 0.44 for baselines.

    Source: A. Performance on Real-World… · p. 7

  • Takeaways & Limitations

    FCTS improves traversal success and progress on held-out reconstructed real-world routes and transfers to a Boston Dynamics Spot on a compound physical parkour course.

    Source: §V · p. 8

Abstract

from arXiv · show

Quadruped parkour policies handle canonical obstacles well, but their training curricula often miss the irregular, compound geometry of industrial and disaster-response sites, where agile locomotion matters most. Such environments pose a hard generalization problem: even training directly on reconstructed geometry from the target site does not reliably yield policies that traverse it. Hand-designed curricula span only a few terrain families, and recent LLM-generated curricula offer little control over which policy weaknesses they target. We propose FCTS, a failure-conditioned terrain curriculum framework that uses localized traversal failures to automatically generate the terrains a policy should train on next. Each failure's location, termination mode, robot state, and surrounding terrain geometry condition this generation, and Monte Carlo Tree Search explores alternative curriculum trajectories under a fixed training budget. On terrains built from scanned real-world construction sites, FCTS raises success rate from 28.4% to 85.8% on a medium-difficulty course and from 14.9% to 44.7% on a hard course relative to the strongest parkour or LLM-curriculum baselines, and maintains higher progress on extreme terrains where full traversal is rare. Hardware experiments on a quadruped robot confirm that the learned FCTS policies transfer to the real world.

I. INTRODUCTION

Quadruped parkour policies struggle when familiar terrain features cooccur outside their training distributions, while hand-built terrain families remain fixed and LLM curriculum feedback is aggregate. FCTS uses localized failures to generate targeted terrain and Monte Carlo Tree Search to explore curriculum trajectories.

  • Hand-designed curricula use fixed terrain families, making it difficult and time-consuming to extend their coverage for irregular, compound sites.Familiar features can cooccur in arrangements outside the pre-defined training distribution.Source: §I · p. 1
  • Eurekaverse guides terrain generation with aggregate policy performance, which does not identify where traversal failed or which local geometry caused it.FCTS instead uses localized failure feedback to target policy weaknesses.Source: §I · pp. 1–2
  • FCTS casts curriculum discovery as MCTS over policy checkpoints and terrain-conditioned training runs, with ancestor-terrain rehearsal under a fixed wall-clock budget.The search returns a portfolio of checkpoints rather than committing to one curriculum sequence.Source: §I · p. 2
  • FCTS conditions new terrain on failure location, termination condition, robot state, and surrounding geometry rather than an aggregate performance score.The framework treats a failed traversal as a diagnostic of where competence breaks down and what conditions to train on next.Source: §I · p. 2
  • FCTS is evaluated on held-out courses built from scanned industrial and disaster-response geometry, with transfer demonstrated on a physical quadruped.Source: §I · p. 2

II. RELATED WORK

Prior work adapts training environments or uses LLMs to generate terrain, but FCTS combines localized traversal-failure feedback with search over policy-improvement trajectories. Its overview frames this as an outer loop around an otherwise unmodified parkour learner.

II. RELATED WORK

  • Prior quadruped parkour methods train on terrain families and obstacle distributions specified in advance, whereas this work discovers curricula as policy capabilities evolve.Source: §II · p. 2
  • Automatic environment-design methods adapt training to the learner, but typically use parameterized or procedural spaces; TACL uses pre-existing terrain maps, unlike FCTS's failure-derived geometry.Source: §II · p. 2
  • LLM-guided curriculum methods use agent-performance feedback, while FCTS adds localized traversal failures and searches successive policy-improvement trajectories rather than generated programs.Source: §II · p. 2

III. DISCOVERING TERRAIN CURRICULA FROM FAILURES

  • The section introduces FCTS by fixing how policy checkpoints are measured before describing the search loop that uses those measurements.Source: §III · p. 2
  • FCTS wraps an outer-loop terrain and checkpoint selector around an unmodified parkour learner, which turns supplied terrains into a policy.The outer loop needs a common basis for comparing checkpoints, detailed failure descriptions, and a rule for allocating costly training runs.Source: §III · p. 2

1) Problem setup:

FCTS seeks to improve an initial parkour policy through terrain curricula, with each curriculum’s value depending on the checkpoint it trains. Under a limited training-run budget, it uses a fixed validation basis and localized failures to guide curriculum search.

1) Problem setup:

  • FCTS improves the initial policy through a sequence of terrain curricula aimed at traversing complex real-world environments.A training run applies the underlying reinforcement-learning parkour procedure to a checkpoint and a curriculum.Source: 1) Problem setup · p. 3
  • A curriculum’s effectiveness depends on the capabilities of the checkpoint it starts from, so curricula are not interchangeable.The same terrain may advance a weak checkpoint but teach a strong one nothing.Source: 1) Problem setup · p. 3
  • Each training run is costly, so the objective is to find the strongest checkpoint within a limited run budget.The search considers the root policy and checkpoints produced by completed runs.Source: 1) Problem setup · p. 3

2) Validation terrain design:

  • The search uses a fixed validation set generated across parkour challenge types to compare checkpoints trained on different terrain.The same evaluation produces both a common validation signal and localized failure feedback for terrain generation.Source: 2) Validation terrain design · p. 3

B. Failure-Guided Curriculum Tree Search

FCTS treats curriculum discovery as a persistent tree search because training expansions are costly, irreversible, and alter later failures. It selects checkpoints with PUCT, balancing branch value against exploration.

B. Failure-Guided Curriculum Tree Search

  • Expansions are costly and irreversible, and each changes the failures observed later, so FCTS preserves alternatives in a persistent search tree.Each node holds a checkpoint and visit count, and each node admits at most B children.Source: B. Failure-Guided Curriculum Tree Search · p. 3
  • FCTS inserts failure diagnosis between checkpoint selection and curriculum expansion, enabling terrain generation from specific failures rather than scores alone.The loop selects with PUCT, evaluates the checkpoint, gathers failure feedback and branch history, then generates and trains on a curriculum.Source: B. Failure-Guided Curriculum Tree Search · p. 4

1) Selection (line 3):

  • PUCT balances branch value with an exploration term that rewards branches visited rarely relative to their parent.Because LLM-generated children cannot be scored in advance, FCTS uses a uniform prior and absorbs its constant into cpuct.Source: 1) Selection (line 3) · p. 4

2) Failure diagnosis (lines 4–5):

FCTS diagnoses failures using repeated validation trials and records the failure location and surrounding robot–terrain context. This provides the geometric information used to author the next training terrain.

2) Failure diagnosis (lines 4–5):

  • Each checkpoint is evaluated in 512 parallel validation trials, and the failure at modal traversal progress is used to identify where it characteristically stops.This choice avoids relying on a single rollout, whose failure location varies with initialization, or on mean or worst-case progress.Source: 2) Failure diagnosis (lines 4–5) · p. 4
  • The recorded failure context includes traversal distance and location, termination cause, robot base orientation, an 8 m × 8 m heightmap, centerline profile, and simulator views.The context is stored with the checkpoint to describe both the policy weakness and the terrain interaction that exposed it.Source: 2) Failure diagnosis (lines 4–5) · p. 4

3) Expansion (lines 6–9):

FCTS expands a selected checkpoint with failure-conditioned terrain while rehearsing earlier terrain. Its LLM-generated curriculum combines targeted and generalized challenges.

3) Expansion (lines 6–9):

  • Each expansion generates targeted, generalized, and combined terrains: reproducing the observed failure, varying its local geometry, and incorporating both.The LLM also receives failure context and branch curriculum history to avoid reproducing terrain already exhausted on that branch.Source: 3) Expansion (lines 6–9) · p. 4
  • Each training run splits terrain slots equally between the new curriculum and rehearsal terrain, retaining only terrain that did no harm by the search-value criterion.When rehearsal terrain exceeds available slots, recently added terrain is prioritized and the rest retained for later reuse.Source: 3) Expansion (lines 6–9) · p. 4
  • The underlying parkour learner’s difficulty scheduler remains active, while FCTS changes which terrains it trains on.The resulting checkpoint becomes a child of the selected checkpoint.Source: 3) Expansion (lines 6–9) · pp. 4–5

4) Simulation and backpropagation (lines 10–11):

FCTS estimates a child curriculum’s future value through parallel rollouts, evaluating temporary checkpoints on validation terrain. Maximum backup favors the strongest descendant found, while persistent search continues within a wall-clock budget.

4) Simulation and backpropagation (lines 10–11):

  • FCTS estimates a child’s potential using K = 3 parallel search rollouts of depth H = 2, because immediate checkpoint performance may not reflect future curriculum progress.Each transition uses the search’s failure-conditioned expansion.Source: 4) Simulation and backpropagation… · p. 5
  • Temporary rollout checkpoints are discarded, and each is evaluated on every validation terrain with R = 512 trials using modal traversal progress.The mode is used for progress, rather than the mean or worst case.Source: 4) Simulation and backpropagation… · p. 5
  • Rollout returns are averaged to estimate expanded-node value, then propagated with maximum backup so a branch is valued by its best reachable policy rather than its weak children.The backup is applied along each parent–child edge on the selected path.Source: 4) Simulation and backpropagation… · p. 5
  • The rollout depth H = 2 bounds only temporary value estimation; persistent search is anytime and runs under a wall-clock budget of Tmax = 24 hours.Table I describes relief-stratified Debris-site route geometry; relief measures height variation within a 0.4 m robot footprint, and P95 captures the upper tail of terrain difficulty.Source: 4) Simulation and backpropagation… · p. 5, Table I · p. 5

5) Parallel search:

Because each tree expansion requires a full training run, FCTS performs multiple expansions asynchronously. In-flight expansions affect visit counts, not branch values.

5) Parallel search:

  • Multiple tree expansions run asynchronously because each expansion requires a complete training run.The approach follows parallel MCTS principles.Source: 5) Parallel search · p. 5
  • FCTS tracks active expansions with an in-flight count Ninf(s) and incorporates it into visit counts rather than perturbing branch value Q(si, sj).This avoids the virtual-loss alternative described in the passage.Source: 5) Parallel search · p. 5

IV. EXPERIMENTS

The experiments compare FCTS with parkour and LLM-based terrain-curriculum baselines on held-out reconstructed industrial and disaster-site courses. Evaluation uses fixed routes, shared trial conditions, and a portfolio-based checkpoint selection procedure.

IV. EXPERIMENTS

  • The baselines are Extreme Parkour, Eurekaverse, and Eurekaverse + Validation Reference, which adds validation-terrain references while retaining the other Eurekaverse generation procedure.The modified baseline controls for validation-domain information without failure-conditioned feedback or curriculum search.Source: §IV · pp. 5–6
  • Evaluation covers held-out Debris and Exposed Beam sites with complex industrial and disaster-site geometry, using relief-stratified routes for Debris and fixed Mid and Hard routes for Exposed Beam.Debris routes span Easy, Mid, Hard, and V-Hard tiers; Exposed Beam includes gaps, narrow members, and disconnected regions for which local relief is not a reliable difficulty measure.Source: §IV · p. 6
  • All methods share fixed routes, spawn locations, a 0.6 m/s command, a 100 s episode limit, and domain-randomization settings, with 512 trials per route.Trials use two seeds with 256 parallel robots per seed; initial robot state varies across trials.Source: §IV · p. 6
  • Performance is measured by Success Rate, Progress IQM, and Waypoint Progress; for a target reconstructed site, FCTS selects the highest-performing checkpoint from its policy portfolio.Success Rate is the fraction reaching the final waypoint, Progress IQM is the interquartile mean of normalized route completion, and Waypoint Progress is median normalized waypoint completion.Source: §IV · p. 6

A. Performance on Real-World Reconstructed Environments

On reconstructed-site routes, FCTS outperforms the strongest baseline on the reported Hard and V-Hard success and progress measures, though results on directly specified Exposed Beam routes are mixed. The paper relates its successes at difficult regions to a curriculum branch that progressively adds irregular rubble, inclined support, and repeated height-and-gap transitions.

A. Performance on Real-World Reconstructed Environments

  • On Hard routes, FCTS reaches 44.7% success and 0.82 Progress IQM, versus 14.9% success and 0.42 IQM for the strongest baseline; on V-Hard, it reaches 11.4% success and 0.71 IQM while baselines remain below 1% success and at most 0.44 IQM.On Easy, FCTS reaches 84.0% success versus 31.5% for the strongest baseline.Source: A. Performance on Real-World… · pp. 6–7
  • On directly specified routes, FCTS has the highest success rate on all three Debris routes, while Exposed Beam results split between Eurekaverse on Route 1 and FCTS on Route 2.On Exposed Beam Route 1, Eurekaverse reaches 25.0% versus FCTS at 10.2%; on Route 2, FCTS reaches 27.7% versus 23.8% for the next-best method.Source: A. Performance on Real-World… · p. 7

B. Why Does FCTS Succeed Where the Baselines Fail?

  • The highest-valued FCTS branch progresses through Undulating Rubble, Ramped Pillars, Raised Blocks & Voids, Heterogeneous Rubble Field, and Composite Terrain, combining irregular rubble, inclined support, and repeated height-and-gap transitions.The figure pairs the winning branch with three regions where Extreme Parkour and Eurekaverse fail while FCTS completes traversal.Source: B. Why Does FCTS Succeed Where the… · p. 7, Figure 4 · p. 7
  • At a 90° turn over uneven rubble and gaps, FCTS completes the turn while both baselines terminate; its branch begins with strongly varying surface geometry and later adds changes in support height and spacing.Source: B. Why Does FCTS Succeed Where the… · p. 7
  • On an incline with rounded boulders and scattered footholds, both baselines develop large lateral roll and then trip or fall, while FCTS remains upright; the branch introduces sustained slope and nonuniform support through Ramped Pillars.Later branch nodes vary support height and placement further.Source: B. Why Does FCTS Succeed Where the… · p. 7
  • FCTS crosses the broken hurdle sequence while both baselines fail at repeated gap transitions; Raised Blocks & Voids introduces consecutive elevated surfaces separated by gaps, retained with later variation.Source: B. Why Does FCTS Succeed Where the… · p. 7

C. Parallel Search Efficiency

Parallel search completes more curriculum expansions within the same wall-clock budget, and FCTS policies also transfer to a physical Spot course. The conclusion reports improved traversal success and progress on held-out reconstructed routes.

C. Parallel Search Efficiency

  • 5.3× higher search throughput: parallel execution raises completed expansions from 0.21 to 1.13 per hour and increases completed expansions from approximately 5.1 to 25.The comparison uses the same 24-hour search budget.Source: C. Parallel Search Efficiency · p. 8, Table IV · p. 8

D. Real-World Transfer

  • FCTS transfers successfully to a Spot traversing a physical course with a pallet, elevated block, and stair descent.The policy runs at 50 Hz on an onboard Jetson AGX Orin using depth observations and robot proprioception.Source: D. Real-World Transfer · p. 8, Figure 5 · p. 8

V. CONCLUSIONS

  • On held-out routes in reconstructed real-world environments, FCTS improves both traversal success and progress over baselines.The conclusion also reports transfer to a Boston Dynamics Spot on a compound physical parkour course.Source: §V · p. 8

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