Organizations: Hanwen Wang, Zhenlong Fang, and Josiah Hanna are with the University of Wisconsin - Madison. · Xiaobin Xiong was with the University of Wisconsin - Madison, and now with the Shanghai Innovation Institute (SII).
In this paper, we present a hardware-control co-design approach that enables efficient and versatile roller skating on quadrupedal robots equipped with passive wheels. Passive-wheel skating reduces leg inertia and improves energy efficiency, particularly at high speeds. However, the absence of direct wheel actuation tightly couples mechanical design and control. To unlock the full potential of this modality, we formulate a bilevel optimization framework: an upper-level Bayesian Optimization searches the mechanical design space, while a lower-level Reinforcement Learning trains a motor control policy for each candidate design. The resulting design-policy pairs not only outperform human-engineered baselines, but also exhibit versatile behaviors such as hockey stop (rapid braking by turning sideways to maximize friction) and self-aligning motion (automatic reorientation to improve energy efficiency in the direction of travel), offering the first system-level study of dynamic skating motion on quadrupedal robots.
Figures & tables
Fig. 1 : Quadrupedal skating setup with passive wheels. Each foot is equipped with a 3D-printed roller support that holds a passive wheel. In the default standing configuration, the wheel yaw installation angle ψ is defined as the deviation of the wheel’s x-axis, xwheel , from the x-axis of the robot’s sagittal plane. This angle is our key design parameter.
Fig. 2 : Bilevel co-design framework for quadrupedal skating. The outer loop uses BO to propose the next candidate design dnext . For each candidate design, the inner loop uses RL to optimize the policy πθ . The resulting performance J(πθ∗,d,T) is fed back to BO, enabling efficient search over design-policy pairs that maximize skating performance.
Fig. 3 : Naive P configuration ( ψ=0∘ ) on Unitree Go1 [ 33 ] yields uncontrollable forward velocity vx due to leg kinematic constraints. Similar limitations arise on many state-of-the-art quadrupedal robots.
Name
Expression
Base Velocity
Bv , Bω
Commanded Base Velocity
Bvxyd,Bωzd
Projected Gravity
Bug
Joint Position and Velocity
qj,q˙j
Last Actions
aprev
TABLE I : Observation space.
Name
Expression
Base Linear Velocity xy
rvxy using ( 6a ) or ( 7a )
Base Angular Velocity z
rωz using ( 6b ) or ( 7 )
Base Height
(z−zd)2
Base Orientation
Bug,xy22
Base Linear Velocity z
Bvz2
Base Angular Velocity xy
Bωxy22
TABLE II : Reward terms.
Fig. 4 : Illustration of World Frame Command angular velocity tracking reward scaling to prioritize linear velocity tracking.
Fig. 5 : Illustration of the human-engineered roller wheel angles and the resultant gait pattern.
Fig. 6 : A rapid stopping strategy known as the “hockey stop” emerged when using World Frame Command with the human-engineered design in Fig. 5 . When the robot is moving forward quickly and is suddenly commanded to stop, it rotates its body so that its lateral direction (which corresponds to the direction of maximal wheel friction) aligns with the velocity direction, thereby generating a large lateral friction force for deceleration.
Fig. 7 : An energy-efficient self-aligning behavior emerged when combining World Frame Command with the 2D design parameterization. For the optimal design in Fig. 9 , the backward direction is the most energy-efficient. As a result, the robot learns to consistently align its backward direction with the commanded velocity direction.
Fig. 8 : Directional CoT comparison. The left figure compares the CoT of walking and skating using human-engineered and 1D co-designed roller wheels. The right figure compares skating with 1D and 2D co-designed roller wheels.
Passive-wheel quadrupedal robots offer energy-efficient locomotion through leg-driven propulsion and momentum-driven gliding. However, navigation requires coordinating steering with intermittent propulsion and adapting push-glide timing to task demands. Velocity-tracking objectives may suppress the speed variations inherent in skating, discouraging efficient gliding. To address these challenges, we propose SkateNav, a unified skating-navigation framework based on reinforcement learning. A time-budgeted goal-reaching objective allows the policy to jointly learn steering, propulsion, and their temporal allocation. An adaptive skating cycle structures gliding, pushing, and recovery, while frequency modulation at every control step adjusts phase durations to navigation demands. Simulation experiments demonstrate higher average success rates and lower cost of transport than the evaluated planner-controller baselines, with ablations confirming the contributions of cycle structure and frequency adaptation. Real-world experiments demonstrate zero-shot transfer from simulation to a passive-wheel Mini Cheetah across cluttered indoor spaces, slopes, and paved outdoor surfaces. Supplementary videos are available on the project page: https://ktw1404.github.io/SkateNav/
Jeil Jeong, Taeyun Kim, Sangjin Kim +2
NAVER LABS, Republic of Korea. · School of Computing, KAIST, Republic of Korea.
As humanoid robots become increasingly dynamic, coupling them with reinforcement learning offers a promising approach to solving the complex, underactuated mechanics of passive inline skating. Equipping a humanoid robot with passive inline skating wheels presents an opportunity to combine the versatile agility of humanoids with the high-speed, energy-efficient locomotion strategies utilized by human skaters. In this paper, we train and deploy a reinforcement learning control policy that enables novel locomotion strategies for a humanoid robot modified to equip consumer inline skates instead of conventional feet. Unlike previous work limited to quadrupedal robots or actively driven wheels, our system allows for precise 6-DoF control of the skates to execute dynamic, edge-driven propulsion strategies. Our skating strategies emerge entirely from our reward structure, without reliance on human motion data, imitation learning, or kinematic priors. We overcome the inherent instability of passive wheels and simulation contact artifacts by utilizing different geometric wheel models (spherical and ellipsoidal) during training and validation, along with a custom success-based command curriculum and a specialized rolling reward. Consequently, our policy demonstrates up to a 50% reduction in Cost of Transport (CoT) compared to standard walking gaits. The resulting policy successfully transfers zero-shot to the physical Booster T1 hardware. Real-world deployments demonstrate dynamic balance, the ability to reject active physical perturbations, and agile locomotion strategies capable of turning at speed. A video of our results can be found at https://www.youtube.com/watch?v=-_APcOS7uFo.
Ethan Marot, Thomas Bi, Clemens Schwarke +3
Institute for Dynamic Systems and Control, ETH Zurich, Switzerland. · Robotic Systems Lab, ETH Zurich, Switzerland
Although recent years have seen significant progress of humanoid robots in walking and running, the frequent foot strikes with ground during these locomotion gaits inevitably generate high instantaneous impact forces, which leads to exacerbated joint wear and poor energy utilization. Roller skating, as a sport with substantial biomechanical value, can achieve fast and continuous sliding through rational utilization of body inertia, featuring minimal kinetic energy loss. Therefore, this study proposes a novel humanoid robot with each foot equipped with a row of four passive wheels for roller skating. A deep reinforcement learning control framework is also developed for the swizzle gait with the reward function design based on the intrinsic characteristics of roller skating. The learned policy is first analyzed in simulation and then deployed on the physical robot to demonstrate the smoothness and efficiency of the swizzle gait over traditional bipedal walking gait in terms of Impact Intensity and Cost of Transport during locomotion. A reduction of 75.86% and 63.34% of these two metrics indicate roller skating as a superior locomotion mode for enhanced energy efficiency and joint longevity.
Junchi Gu, Feiyang Yuan, Weize Shi +6
Institute of Humanoid Robots, Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei, Anhui 230026, China.