TransCurriculum: Multi-Dimensional Curriculum Learning for Fast & Stable Locomotion

Prakhar Mishra; Amir Hossain Raj; Xuesu Xiao; Dinesh Manocha

cs.ROMar 14, 2026

TransCurriculum: Multi-Dimensional Curriculum Learning for Fast & Stable Locomotion

Authors: Prakhar Mishra, Amir Hossain Raj, Xuesu Xiao, Dinesh Manocha

Organizations: University of Maryland, College Park, MD, USA. · George Mason University, Fairfax, VA, USA.

Abstract

High-speed legged locomotion struggles with stability and transfer losses at higher command velocities during deployment. One reason is that most curricula vary difficulty along single axis, for example increase the range of command velocities, terrain difficulty, or domain parameters (e.g. friction or payload mass) using either fixed update rule or instantaneous rewards while ignoring how the history of robot training has evolved. We propose TransCurriculum, a transformer-based multi-dimensional curriculum learning approach for agile quadrupedal locomotion. TransCurriculum adapts to 3 axes, velocity command targets, terrain difficulty, and domain randomization parameters (friction and payload mass). Rather than feeding task reward history directly into the low-level control policy, our formulation exploits it at the curriculum level. A transformer-based teacher retrieves the sequence of rewards and uses it to predict future rewards, success rate, and learning progress to guide expansion of this multidimensional curriculum towards high performing task bins. Finally we validate our approach on the Unitree Go1 robot in simulation (Isaac Gym) and deploy it zero-shot on Go1 hardware. Our TransCurriculum policy achieves a maximum velocity of 6.3 m/s in simulation and outperforms prior curriculum baselines. We tested our TransCurriculum trained policy on terrains (carpets, slopes, tiles, concrete), achieving a forward velocity of 4.1 m/s on carpet surpassing the fastest curriculum methods by 18.8% and achieves maximum zero-shot value among all tested methods. Our multi-dimensional curriculum also reduces the transfer loss to 18% from 27% for command only curriculum, demonstrating the benefits of joint training over velocity, terrain and domain randomization dimension while keeping the task success rate of 80-90% on rigid indoor and outdoor surfaces.

Figures & tables

Fig. 2 : TransCurriculum pipeline. The low-level policy $\pi_{\theta}$ is trained with PPO using rollouts from IsaacGym environment . While the TransCurriculum module maintains bins over multi-dimensional task space of commands, terrain difficulty and domain parameters and use rollouts ( observations and rewards ) to update distribution. The transformer-curriculum retrieves context-outcome history, to predict the rewards, success and progress of these curriculum bins. These sampled task-context $z$ is applied to the simulator for the next PPO rollout.

Input: curriculum weights $w_{i}$ , history buffer $\mathcal{H}\leftarrow\emptyset$ , transformer $f_{\psi}$
for each PPO iteration do
for each parallel environment $k$ do
if episode ended then
Curriculum Update Rule
1. Successful bins: $\mathcal{S}_{t}\leftarrow\{r_{\text{lin},i}>\tau_{\text{lin}}\wedge r_{\text{ang},i}>\tau_{\text{ang}}\}$ [Eq. 10]
2. Build neighbors: $\mathcal{C}_{t}\leftarrow\mathcal{S}_{t}\cup\mathcal{N}(\mathcal{S}_{t})$ [Eq. 11]

TABLE I : TransCurriculum Algorithm

Method	Curriculum target	Curriculum signal	Curriculum History modeling	Zero-shot † robot	Max zero-shot † speed (m/s)
RMA [ 18 ]	None	None	None	A1	—
RLvRL [ 4 ]	Velocity commands	Fixed-rule	EMA	Mini Cheetah	3.9
Risky Terrains [ 11 ]	Terrain difficulty	Task success	None	ANYmal	$2.5$
DreamWaQ [ 21 ]	Terrain difficulty	Curriculum heuristics	None	A1	3.0
CHRL [ 14 ]	Commands + Terrain	Hindsight success	Replay	Custom	3.45
LP-ACRL [ 12 ]	Commands + Terrain	Learning progress	Online estimator	ANYmal	2.5

TABLE II : TransCurriculum vs. representative curriculum baselines. Zero-shot transfer robot and maximum zero-shot real-world speed are reported when available ( † ).

Fig. 3 : Curriculum range expansion over command space: TransCurriculum starts from a narrow command range of $[-1.0,1.0]$ and gradually expands by $[-0.5,0.5]$ as the policy achieves stable velocity tracking performance. We plot the maximum sampled command values during training, $v_{x}^{\text{max}}$ , $v_{y}^{\text{max}}$ and $\omega_{z}^{\text{max}}$ , as TransCurriculum expands the command range. The curriculum steadily expands along forward speed $v_{x}^{\text{max}}$ , while lateral and yaw-rate saturate at lower thresholds, consistent with our reward shaping for forward locomotion.

Panel of Figure 5 — Fig. 4 : Effect of curriculum bin selection criteria: We train TransCurriculum for 250, 1000, 4000 and 6000 bins under identical training conditions and compare the learning curve (1500 PPO updates). Coarse binning (250/1000) do not reach the high-speed within the given training time, plateauing around $1.5$ – $2.0$ m/s. The 4000-bin configuration achieves approximately 6 m/s and reaches 90% of target speed within 8.6M environment steps, providing the best tradeoff between exploration and stable curriculum updates. With increasing resolution to 6000 bins increases velocity to $6-6.3$ m/s and the 90% of target speed within 9.5M steps. We therefore use 4000 bins in our experiment unless noted otherwise.

Panel of Figure 6 — Fig. 5 : Disturbance recovery cases on diverse terrains (zero-shot Go1): The above cases demonstrates that our policy experiences a bump/trip or deviate laterally, and re-stabilizes to its normal gait within few seconds. Above examples demonstrate that TransCurriculum-trained policy remains functional without any additional finetuning under disturbances or terrain irregularities (See accompanying video).

Panel of Figure 7 — Fig. 6 : High-speed locomotion and stable gait with TransCurriculum. Top: zero-shot real-world deployment on Unitree Go1 on carpet, policy reaches $4.1\pm 0.05$ m/s over a 3-8 m run with 90% task success. Bottom: In simulation at $v^{cmd}_{x}=7.0$ , Go1 reaches $6.3\pm 0.2$ m/s and the 12 joint-position time plot shows a consistent periodic pattern, indicating stable running gait at higher command velocity. Together these results substantiate that this is enabled by history-aware and multi-dimensional curriculum task sampling over commands, terrain and dynamics.

Metric	Transformer	RNN	MLP
$v_{x}$ m/s ( $v^{cmd}_{x}=7$ )	6.3 †	6.1	0.5
$\omega_{z}$ rad/s	1.25	1.28	0
History-Aware	Yes	Yes	No
CoT	2.60	5.20	100 x RNN
Stability (S)	2000	1800	1100
Task Success Rate	90%	80%	0%

TABLE III : Non-history vs. History methods (

n=5

runs per method)

Metric	Cmd Only	Cmd + DR	Full (ours)
Max sim velocity (m/s)	6.3	6	5.8
Stability score $(S)$	1850	1900	2000
Task success rate (%)	70%	70%	90 %
Sim-to-real † (m/s)	3.65	3.85	4.1
Transfer loss	27%	23%	18%

TABLE IV : Curriculum dimensionality and transfer loss ablation

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Reinforcement learning for legged locomotion trains walking robots to move across varied terrain, adapt to disturbances, and carry out tasks.

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Aug 17, 2026J/K move · Enter open · S save

Trajectory-Level Automatic Curriculum Learning for Legged Locomotion on Unstructured Terrain

Rocky Liu, Tengyu Liu, Baoxiong Jia, Fangwei Zhong+3

National Key Laboratory of General Artificial Intelligence, BIGAI · Beijing Normal University · Communication University of China+2

Curriculum RL RL for Legged Locomotion Terrain-Aware Robot Locomotion

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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

RL for Legged Locomotion

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