Organizations: Center for X-Mechanics and Institute of Applied Mechanics, Zhejiang University, Hangzhou 310012, China · ZJU-Hangzhou Global Scientific and Technological Innovation Center, Hangzhou 311200, China · MirrorMe Robotics Co., Ltd., Hangzhou 311215, China
Achieving high-speed locomotion in quadrupedal robots remains highly challenging, as actuators operate near their physical limits and exhibit pronounced nonlinearities. However, many existing methods neglect actuator nonlinearities and physical constraints during training, leading to a significant sim-to-real gap under highly dynamic motions and limiting achievable performance. To address this issue, we propose a high-speed locomotion framework that reduces sim-to-real discrepancies and stabilizes learning over a wide command distribution. A refined actuator model explicitly captures high-speed voltage coupling and magnetic saturation, enabling a more accurate representation of the torque-speed envelope. In addition, a reinforcement learning framework incorporating a two-stage curriculum and adaptive command scheduling (ACS) ensures stable training. Experiments on the 36.5 kg quadruped BlackPanther2 (BP2) demonstrate speeds of up to 13.2 m/s on a treadmill and 11.65 m/s outdoors, establishing a new state-of-the-art and, to the best of our knowledge, a world record for quadrupedal robot locomotion. The results further highlight the importance of accurate actuator modeling in preventing non-physical policy exploitation, and show that ACS improves robustness without sacrificing performance.
Figures & tables
Fig. 1: First-quadrant operating envelopes of a representative joint actuator under different actuator modeling paradigms.
Fig. 2: Training pipeline for high-speed locomotion. In simulation, policy actions are mapped to joint torques and constrained by actuator limits, including torque–speed envelope constraints and magnetic saturation. During hardware deployment, the commanded torques are directly tracked by low-level motor controllers.
Reward Term
Equation ( ri )
Weight
Part A: Constant Weights
Lin. vel. track.
exp{−(vxycmd−vxy)2}
1.0
Ang. vel. track.
exp{−(ωzcmd−ωz)2}
0.5
Lin. vel. ( z )
vz2
−2.0
Joint power
∣τ⋅θ˙∣
−1.0×10−6
Action rate
(at−at−1)2
−0.01
TABLE I: Reward Function Elements and Multi-Stage Weight Schedules
Fig. 3: Comparison between the baseline without torque–speed envelope constraints and the proposed method in their respective training environments, where both policies operate at the limits of actuator performance.
Fig. 4: Visualization of locomotion patterns under diverse command scheduling modes enabled by the proposed ACS. The method generalizes across different command update paradigms while preserving acceleration profiles consistent with the robot dynamics.
Method
Max Velocity (m/s)
Relative Stability ( Jnorm )
Baseline
9.4
0.876
w/o torque–speed envelope
11.0
1.212
Simplified DC
11.7
1.070
Fixed acceleration scheduling
—
—
Uniform command sampling
11.0
1.452
Ours
12.4
1.000
TABLE II: Comparison of Velocity and Stability Metrics
Fig. 5: Experimental setup and representative snapshots from indoor locomotion experiments. (a)–(d) depict one complete gait cycle. (e) Snapshot at the instant when the robot reaches its maximum velocity.
Method
Max Sim Speed (m/s)
Max Outdoor Speed (m/s)
WildCat [ 12 ]
—
8.89
RLvRL [ 1 ]
5.7
3.9
HACL [ 30 ]
6.7
4.1
Hound [ 2 ]
6.5
5.9
Spot [ 22 ]
—
5.2
Ours
12.4
11.65
TABLE III: Comparison of Reported Maximum Speeds in Simulation and Outdoor Hardware
Fig. 6: Outdoor locomotion experiment results. (a) Time series of body velocity measured by the RTK system. (b) Corresponding torque–speed profiles of representative actuators, illustrating operation near actuator limits and close agreement with simulated behaviors.
Achieving biological-level running speeds has largely been pursued through advances in control algorithms, which improve the utilization of existing hardware. However, the ultimate speed limits remain governed by the underlying force and torque requirements of rapid locomotion, which are typically addressed through increased actuator capacity. Inspired by Huygens' coupled pendulums, we demonstrate that superior locomotion can emerge from principled exploitation of intrinsic dynamics rather than brute-force hardware scaling. Inter-limb inertial coupling redistributes energy across the gait cycle and reduces peak joint torque required for rapid periodic motion, thereby expanding the achievable speed without proportional increases in actuator capability. Incorporating hardware parameters as additional design variables further extends this analysis into a co-optimization framework, enabling the systematic utilization of inertial coupling in robot design. Guided by this framework, a quadruped robot achieves a running speed of 10.74 m/s (Froude number 21.4) and completes a 100-meter sprint in 12.2 seconds, representing the first legged robot to surpass 10 m/s. These results establish inertial coupling as an underlying mechanism governing high-speed legged locomotion and highlight its role in reducing force requirements, offering new insights into the design of agile robotic systems.
Yucheng Tao, Yongbin Jin, Shaowen Cheng +8
Center for X-Mechanics, Zhejiang University, Hangzhou, China. · ZJU-Hangzhou Global Scientific and Technological Innovation Center, Hangzhou, China. · Mirrorme Technology Co., Ltd., Shanghai, China.
Reinforcement learning (RL) for legged robots is advancing locomotion, demonstrating its ability to adapt to new and challenging terrain. Traditionally, these RL locomotion frameworks are position-based, making the policy less adaptable to terrain types and requiring state estimation techniques in the observation space, i.e., linear velocity. Moreover, these RL frameworks often use small, lightweight quadrupeds that are limited in their viability for high-complexity tasks due to hardware constraints. This work explores an RL torque control framework for heavyweight high-torque quadrupeds. The RL framework in this paper can traverse rough terrain and effectively track a desired linear velocity without requiring knowledge of the agent's current velocity. Using Nvidia's Isaac Sim and Isaac Lab, simulation results of the RL torque control policy are shown on the Unitree B1 quadruped, achieving speeds of 3.5 m/s and 1.5 rad/s. In addition, the quadruped can walk up and down stairs without the aid of an exteroceptive sensor.
Jordan Dowdy, Jean Chagas Vaz
Department of Electrical and Computer Engineering at the University of Louisville. · Faculty of Electrical and Computer Engineering, University of Louisville, Louisville, KY, 40208, USA.
Learning-based approaches to locomotion have risen in popularity in recent years, showing the capability for complex legged locomotion and whole-body control. Reinforcement learning (RL), the primary learning-based approach for locomotion, often utilizes a high-performance simulation tool, providing a controlled and efficient training and development environment. However, policies that perform well in simulation frequently encounter unexpected challenges when deployed on a physical system, known as the sim-to-real gap. This work presents a robust RL locomotion framework capable of whole-body control. The proposed RL framework utilizes Nvidia's new set of simulation tools, Isaac Sim, and its companion RL framework, Isaac Lab, for training, achieving a zero-shot sim-to-real policy. The performance of our policy is validated on physical hardware using the Unitree Go1, with experimental results showing similar velocity tracking performance to the quadruped's integrated controller, with a greater ability to recover from large disturbances, and achieve linear velocities of 2.0 m/s and angular velocities of 1.8 rad/s.
Jordan Dowdy, Jean Chagas Vaz
Department of Electrical and Computer Engineering, University of Louisville · Faculty of Electrical and Computer Engineering, University of Louisville, Louisville, KY, 40208, USA