Is It the Curriculum or Just the Easy Start? Benchmarking Unsupervised Environment Design on Quadrupeds

Jakub Gilewicz; Dominik Galus; Piotr Wojdas

cs.LGOct 29, 2026

Is It the Curriculum or Just the Easy Start? Benchmarking Unsupervised Environment Design on Quadrupeds

Authors: Jakub Gilewicz, Dominik Galus, Piotr Wojdas

Organizations: Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland · Machinekind, Wrocław, Poland · Koło Naukowe Solvro, Wrocław University of Science and Technology, Wrocław, Poland

Abstract

Unsupervised environment design (UED) methods such as PLR, ACCEL, SFL and PAIRED are compared mostly on 2D mazes, grid worlds and BipedalWalker, while terrain curricula for legged robots are hand-designed and evaluated against a few baselines. We present a benchmark that runs fourteen UED, domain-randomisation and robotics curricula under one protocol on five 3D quadrupeds in MuJoCo MJX: the closed-chain W01-TEK and the open-chain Unitree Go1 and Go2, Google Barkour vB and Boston Dynamics Spot. Levels are vectors of eight interpretable terrain parameters, and all curricula drive the same PPO student at matched environment-step budgets. The evaluation reports success on random and held-out structured terrains, interquartile means with stratified bootstrap intervals, capability envelopes and a level-by-level domination comparison. We compare methods within each robot and report, per level set, the top group of methods not significantly below the best. No method is in the top group on every robot and level set. Methods with easy or low-difficulty training levels, curated or not, fill the top groups on in-distribution random levels of Go1 and Barkour, and of W01-TEK apart from PAIRED+BiBC. The success-driven terrain curriculum from legged-robot practice is in a top group most often, domain randomisation on uniform levels in none, and PAIRED in none outside Spot, where the fourteen methods lie within 3.8 points on random levels of difficulty 0.25. On three robots the leader on in-distribution random levels is not the leader on held-out terrain. We collect the results into a per-robot guide to choosing a curriculum.

Figures & tables

Robot	Legs	Episode	Physics
W01-TEK	closed chain (four-bar)	300 steps	MJX
Go1	open chain	300 steps	MJX
Go2	open chain	300 steps	MJX
Barkour vB	open chain	300 steps	MJX
Spot	open chain	780 steps	MJX

Table 1: Robots. Success = no fall and travel of at least

s

metres within the episode.

Method	New levels	Replay	Edit	Score
DR ( Tobin et al., 2017 )	uniform	-	-	-
DR-easy	easy	-	-	-
DR-mixed	mixed	-	-	-
Terrain-CL ( Rudin et al., 2021 )	rows	-	-	-
PLR ⟂ ( Jiang et al., 2021a )	uniform	buffer	-	PVL
SFL † ( Rutherford et al., 2024 )	uniform	buffer	-	learnability

Table 2: Curricula. Easy: uniform level shrunk to

d=0.1

. Mixed: per-level

d\sim\mathcal{U}(0,1)

. Rows: a fixed uniform level per lane at

d=r/10

r

promoted or demoted each iteration. Edit: perturb 2 parameters by

\mathcal{U}(-0.1,0.1)

. Grow: also scale the distance from flat by

\mathcal{U}(1,1.3)

. PVL: positive value loss.

Figure 2: Success of the deterministic policy on 512 random levels at

d=0.25

(top) and

d=0.5

(bottom) during training. Mean over 5 seeds, shaded min-max. PAIRED and its variants dashed.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

	W01-TEK	Go1	Go2	Barkour vB	Spot
Model	Machinekind	Playground	Menagerie	Menagerie	Playground
Episode (steps)	300	300	300	300	780
Physics DR	own	Playground	Go1’s	none	none

Appendix

Table 5: Per-robot settings.

Parameter	Range
Noise amplitude	0-0.10 m
Noise wavelength	0.2-1.0 m
Radial slope	$-20^{\circ}$ to $+18^{\circ}$
Stair height	$-0.08$ to $+0.05$ m
Stair width	0.15-0.60 m
Gap width	0-0.06 m

Appendix

Table 6: Level space, reference units. Every length is multiplied by the robot’s size

s

. A level is

\theta\in[0,1]^{8}

plus a noise seed.

Figure 3: W01-TEK on example levels. The first panel is flat. Each of the next seven sets one feature to the end of its range with every other feature flat. The last two are uniform samples at $d=0.5$ and $d=1$ . Features start at the edge of the flat spawn disc.

Figure 4: One level genome ( $d=0.6$ ) rendered for each robot in its own arena. Terrain lengths and camera distance scale with the robot’s size $s$ , so robots of different proportions fill their panels differently.

Lanes $\times$ environments per lane	$256\times 32$
Steps per level (episode)	300 (Spot 780)
Environment steps	300M (W01-TEK), 1B (others)
PPO	brax, 20-step unroll, 4 epochs $\times$ 32 minibatches
$\gamma$ , $\lambda$ , learning rate, entropy, clip, grad norm	0.97, 0.95, $3\times 10^{-4}$ , 0.01, 0.2, 1.0
Networks	MLP 512-256-128, ELU, observation normalisation
Buffer	4000 levels, replay probability 0.8

Appendix

Table 7: Hyperparameters shared by all methods.

Figure 5: ACCEL vs. DR, level by level, on the 2048 uniform levels. Read as Figure 6 .

Figure 6: ACCEL vs. DR, level by level, on the 2048 $d=0.25$ levels. Each level’s solve rate is pooled over 5 seeds $\times$ 8 episodes. The colour is the fraction of levels (log scale) per cell. Mass below the diagonal: levels ACCEL solves more often. Panel titles give the fractions of levels ACCEL wins, loses and ties, the mean difference with its 95% bootstrap interval, and the mean absolute difference against the binomial noise reference.

Figure 7: Fraction of $d=0.25$ levels on which the row method’s solve rate exceeds the column method’s, per robot. Darker cells: the row method wins on more levels. The diagonal is blank, and $1-M_{ab}-M_{ba}$ is the fraction of ties.

Figure 8: Aggregate scores over five robots

\times

five seeds: success min-max normalised per robot over the method means, interquartile mean and mean with 95% stratified bootstrap intervals.

Figure 9: Probability of improvement

P(X>Y)

for the named method pairs, with 95% stratified bootstrap intervals, on

d=0.25

and the held-out suite.

Figure 10: Mean physical value of each magnitude parameter among the levels the student trains on, and the mean genome distance from flat, vs. environment steps (reference units, running mean over 9 points). Mean over 5 seeds, shaded min-max.

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Training locomotion policies for complex unstructured terrain requires a curriculum to avoid early exploration failures. However, since unstructured terrain lacks explicit difficulty ordering for curriculum design, existing methods resort to heuristic curricula over parameterized terrains. This abstraction limits generalization, as policies can overadapt to near-fixed perceptual patterns. To address this, we propose \ourname{}, an Trajectory-level Automatic Curriculum Learning framework that generates training tasks directly from unstructured terrain maps. At each curriculum update, the evaluator learns a difficulty function for the current policy that maps a given trajectory task to a difficulty score. The sampler then proposes new trajectories guided by the learned evaluator as the curriculum for the next policy update. This forms a closed loop in which the curriculum is iteratively matched to the evolving policy. Quantitative and qualitative experiments show that \ourname{} continuously provides effective curricula on unstructured terrain, improving trajectory success rate by

56.3\%

over direct training without curriculum. Compared with handcrafted curriculum learning, our method improves success rate by

18.5\%

on the hardest terrain tasks and by up to

39.74\%

when evaluating traversal from diverse approach directions on the same obstacle type.

Abstract

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