Breaking speed scaling in quadrupedal robots via Huygens' coupled-pendulum dynamics

Yucheng Tao; Yongbin Jin; Shaowen Cheng; Xianwei Liu; Yanyan Yuan; Yanhong Liang; Chengkai Su; Chaojie Fu; Guorong Lan; Wei Yang; Hongtao Wang

arXiv · 2609.13290

Breaking speed scaling in quadrupedal robots via Huygens' coupled-pendulum dynamics

Yucheng Tao·Yongbin Jin·Shaowen Cheng·Xianwei Liu·Yanyan Yuan·Yanhong Liang·Chengkai Su·Chaojie Fu·Guorong Lan·Wei Yang·Hongtao Wang

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.RO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yucheng Tao, Yongbin Jin, Shaowen Cheng, Xianwei Liu, Yanyan Yuan, Yanhong Liang, Chengkai Su, Chaojie Fu, Guorong Lan, Wei Yang, Hongtao Wang. 2026-09-09. Breaking speed scaling in quadrupedal robots via Huygens' coupled-pendulum dynamics. https://arxiv.org/abs/2609.13290

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

J-PARSE: Jacobian-based Projection Algorithm for Resolving Singularities Effectively in Inverse Kinematic Control of Serial Manipulators

J-PARSE is an algorithm for smooth first-order inverse kinematic control of a serial manipulator near kinematic singularities. The commanded end-effector velocity is interpreted component-wise, according to the available mobility in each dimension of the task space. First, a substitute ''Safety'' Jacobian matrix is created, keeping the aspect ratio of the manipulability ellipsoid above a threshold value. The desired velocity is then projected onto non-singular and singular directions, and the latter projection scaled down by a factor informed by the altered mobility. A right-inverse of the non-singular Safety Jacobian is applied to the modified command. In the absence of joint limits and collisions, this ensures safe transition into and out of low-mobility configurations, guaranteeing locally stable reaching behavior towards target poses within, on the boundary of, and outside the workspace. The behavior is further guaranteed to be locally asymptotically stable if the starting and target configurations are not exactly singular, even if they are nearly singular. Velocity control with J-PARSE is benchmarked against approaches from the literature, illustrating its use of a single tuning parameter to simultaneously achieve high reaching accuracy and stable behavior. Applications in teleoperation, servoing, and learning are demonstrated. Videos and code are available at https://jparse-manip.github.io/.

cs.RO↗

arXiv2026

NeMo-map: Neural Implicit Flow Fields for Spatio-Temporal Motion Mapping

Safe and efficient robot operation in complex human environments can benefit from good models of site-specific motion patterns. Maps of Dynamics (MoDs) provide such models by encoding statistical motion patterns in a map, but existing representations use discrete spatial sampling and typically require costly offline construction. We propose a continuous spatio-temporal MoD representation based on implicit neural functions that directly map coordinates to the parameters of a Semi-Wrapped Gaussian Mixture Model. This removes the need for discretization and imputation for unevenly sampled regions, enabling smooth generalization across both space and time. Evaluated on two public datasets with real-world people tracking data, our method achieves better accuracy of motion representation and smoother velocity distributions in sparse regions while still being computationally efficient, compared to available baselines. The proposed approach demonstrates a powerful and efficient way of modeling complex human motion patterns and high performance in the trajectory prediction downstream task. The code is publicly available at https://github.com/test-bai-cpu/nemo-map.

cs.RO↗

arXiv2026

Spatiotemporal Calibration of Doppler Velocity Logs for Underwater Robots

The calibration of extrinsic parameters and clock offsets between sensors for high-accuracy performance in underwater SLAM systems remains insufficiently explored. Existing methods for Doppler Velocity Log (DVL) calibration are either constrained to specific sensor configurations or rely on oversimplified assumptions, and none jointly estimate translational extrinsics and time offsets. We propose a Unified Iterative Calibration (UIC) framework for general DVL sensor setups, formulated as a Maximum A Posteriori (MAP) estimation with a Gaussian Process (GP) motion prior for high-fidelity motion interpolation. UIC alternates between efficient GP-based motion state updates and gradient-based calibration variable updates, supported by a provably statistically consistent sequential initialization scheme. The proposed UIC can be applied to IMU, cameras and other modalities as co-sensors. We release an open-source DVL-camera calibration toolbox. Beyond underwater applications, several aspects of UIC-such as the integration of GP priors for MAP-based calibration and the design of provably reliable initialization procedures-are broadly applicable to other multi-sensor calibration problems. Finally, simulations and real-world tests validate our approach.

cs.RO↗