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<p>Replicating biological systems’ agile locomotion remains challenging in legged robotics, evidenced by substantial performance gaps between humans and the state-of-the-art bipedal robots in running. Analysis of intrinsic speed limits in bipedal running remains less developed, despite progress in controller design. Inspired by human biomechanics, the present work proposed the power-bounded inverted pendulum (PBIP) model that incorporates the leg power saturation effect. The PBIP model characterizes the maximum running speed of bipedal robots over a complete set of gait parameters, revealing two distinct speed-limiting mechanisms: geometry constraints dominate at low-frequency gaits, and power saturation dictates speed limitation at high-frequency gaits. Simulation of LimX Dynamics Tron, Unitree-G1, and Unitree-H1 robots verified the universality of the dual speed constraint mechanism in physical robot systems. Applying the PBIP model to optimize joint motor parameters, we reduced leg power consumption by 18.0% while increasing the maximum speed of the Tron robot by 0.26 m s<sup>−1</sup>. Furthermore, the maximum speeds of the G1 and H1 robots were raised by 0.09 and 0.51 m s<sup>−1</sup>, respectively. The PBIP model provides a rapid evaluation tool for balancing leg geometry and the actuator power, serving the design of highly agile bipedal robots in engineering practice.</p>

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Power-bounded inverted pendulum model for maximum speed analysis in bipedal robots: a dual constraint mechanism

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Chengkai Su,
  • Chaojie Fu,
  • Yanhong Liang,
  • Kaixin Lan,
  • Yongbin Jin,
  • Hongtao Wang,
  • Wei Yang

摘要

Replicating biological systems’ agile locomotion remains challenging in legged robotics, evidenced by substantial performance gaps between humans and the state-of-the-art bipedal robots in running. Analysis of intrinsic speed limits in bipedal running remains less developed, despite progress in controller design. Inspired by human biomechanics, the present work proposed the power-bounded inverted pendulum (PBIP) model that incorporates the leg power saturation effect. The PBIP model characterizes the maximum running speed of bipedal robots over a complete set of gait parameters, revealing two distinct speed-limiting mechanisms: geometry constraints dominate at low-frequency gaits, and power saturation dictates speed limitation at high-frequency gaits. Simulation of LimX Dynamics Tron, Unitree-G1, and Unitree-H1 robots verified the universality of the dual speed constraint mechanism in physical robot systems. Applying the PBIP model to optimize joint motor parameters, we reduced leg power consumption by 18.0% while increasing the maximum speed of the Tron robot by 0.26 m s−1. Furthermore, the maximum speeds of the G1 and H1 robots were raised by 0.09 and 0.51 m s−1, respectively. The PBIP model provides a rapid evaluation tool for balancing leg geometry and the actuator power, serving the design of highly agile bipedal robots in engineering practice.