研究双足机器人尺寸缩放规律，发现其质量与腿长平方相关。
Allometric Scaling Laws for Bipedal Robots
- 基于仿真和文献数据，分析腿长对机器人设计的影响。
- 速度随腿长平方根增长，扭矩需求与质量×腿长成正比。
- 适合机器人设计者参考尺寸缩放策略，尤其关注扭矩与结构匹配。
机器人的尺寸缩放仍是核心挑战。尽管生物系统遵循质量、步频、速度和扭矩之间的等比例与异速生长规律，但这些规律在机器人中是否适用尚不明确。本文通过分析文献中三数量级跨度的双足机器人数据，发现机器人质量更接近于腿长的平方（L^2），而非等比例缩放预测的立方（L^3）。随后，在Drake中对三种真实准被动髋驱动步行者进行控制仿真，测试不同足部几何与控制策略下的缩放表现。结果表明：所有机器人步行速度均符合动态相似性预期的L^(1/2)趋势；最小所需扭矩更接近于质量×腿长（m×L），而非等比例模型的m×L^2；足部几何与腿长呈线性比例（L^1）缩放。这些发现揭示了机器人设计在不同尺寸下的异速生长规律，且不同于等比例或生物系统规律。
原文摘要 · Abstract (English)
Scaling the design of robots up or down remains a fundamental challenge. While biological systems follow well-established isometric and allometric scaling laws relating mass, stride frequency, velocity, and torque, it is unclear how these relationships translate to robotic systems. In this paper, we generate similar allometric scaling laws for bipedal robots across three orders of magnitude in leg length. First, we conduct a review of legged robots from the literature and extract empirical relationships between leg length (L), body length, mass, and speed. These data show that robot mass scales more closely to L^2, in contrast to the L^3 scaling predicted by isometric scaling. We then perform controlled simulation studies in Drake using three variants of real quasi-passive, hip-actuated walkers with different foot geometries and control strategies. We evaluate the performance of each design scaled with leg length, L. Across all robots, walking velocity follows the expected L^(1/2) trend from dynamic similarity. Minimum required torque scales more closely with m*L than the isometric model of m*L^2. Foot geometry scaled proportionally with L^1. These results provide new insight into how robot designs allometrically scale to different sizes, and how that scaling is different from isometric or biological scaling laws.
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