Allometric Scaling Laws for Bipedal Robots
This provides insights for robotics engineers designing robots of varying sizes, though it is incremental as it adapts known biological principles to robotics.
The paper tackled the challenge of scaling bipedal robot designs by generating allometric scaling laws across leg lengths, finding that robot mass scales with L^2 and torque with m*L, differing from biological isometric predictions.
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.