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 πθ 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.
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, vxmax , vymax and ωzmax , as TransCurriculum expands the command range. The curriculum steadily expands along forward speed vxmax , while lateral and yaw-rate saturate at lower thresholds, consistent with our reward shaping for forward locomotion.
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.
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).
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±0.05 m/s over a 3-8 m run with 90% task success. Bottom: In simulation at vxcmd=7.0 , Go1 reaches 6.3±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
vx m/s ( vxcmd=7 )
6.3 †
6.1
0.5
ωz 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
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.
Rocky Liu, Tengyu Liu, Baoxiong Jia +4
National Key Laboratory of General Artificial Intelligence, BIGAI · Beijing Normal University · Communication University of China +2
Generalizing learned locomotion policies across quadrupedal robots with different morphologies remains a challenge. Policies trained on a single robot often fail when deployed on embodiments with different mass distributions, kinematics, joint limits, or actuation constraints, forcing per-robot retraining. Prior works have approached this primarily either by scaling via training across real or generated embodiments or using large architectures producing transferable policies which are both storage and compute heavy. We argue that both of these approaches circumvent a key failure mode in actor-critic learning: a shared value function tends to average incompatible value targets across embodiments, yielding miscalibrated advantages and fixing that helps transfer and reduce the compute cost. We present MorFiC, a reinforcement learning approach for zero-shot cross-morphology locomotion which fixes this issue using multiplicative critic conditioning on a morphology latent. Trained with a single source robot with morphology randomization in simulation, MorFiC achieves zero-shot transfer to total seven robots and reaching forward velocity competitive or surpassing scaling-based and morphology-conditioned PPO baselines for examples 1.98 m/s on AlienGo, where as additive PPO baselines remain below 0.65 m/s. MorFiC achieves this using single training robot within 2 hours of training time compared to tens or hundreds of hours required for scaling baselines training on multiple embodiments. We diagnose critic calibration via three metric: Explained variance, advantage sign-flip rate and policy gradient cosine, confirming our critic conditioning as determinant for policy update direction. Finally, we demonstrate zero-shot deployment on Unitree Go1 and Go2 robots without fine-tuning.
Prakhar Mishra, Amir Hossain Raj, Xuesu Xiao +1
University of Maryland, College Park, MD, USA · George Mason University, Fairfax, VA, USA
Rare but consequential failures can persist in learned locomotion policies for legged robots even when average task performance is high, in part because standard curricula primarily adapt task difficulty rather than the distribution of safety-critical experience. We introduce Predictive Safety Curricula (PSC), a framework for allocating locomotion training experience using learned predictions of future safety cost. PSC trains a distributional safety critic from policy rollouts and uses its predictions to prioritize both terrain contexts and previously encountered randomized events. The resulting curriculum modifies the training distribution while leaving the task reward and policy-optimization loss unchanged. We evaluate PSC in controlled rough-terrain locomotion and in production locomotion systems. PSC improves reliability relative to standard terrain progression, advantage-based replay, and learning-progress curricula, with the largest gains on difficult terrain and under degraded observations. The same allocation principle transfers to two production locomotion stacks. On ANYmal-D hardware, PSC reduces shank-collision incidence by 63% relative to the learning-progress curriculum across three matched training seeds, with a reduction in every seed. On a production stair-climbing platform, PSC eliminates observed shank collisions in the evaluated hardware trials. These results show that learned predictions of future safety cost can provide an effective signal for allocating training experience toward rare failure modes and improving locomotion reliability.
Ivan Ovinnikov, Pascal Sutter, Christian Gehring +1