Scaling Laws in Robotics

Abstract

Scaling laws are pervasive in biological systems, found in a large number of life processes, and across 27 orders of magnitude. Recent findings show both biological and engineered motors adhering to two fundamental regimes for the mass scaling of maximum force output. This scaling law is of particular interest for the robotics field as it can affect the design stage of a robot. In this study we present data of motors commonly used in robotic applications and find an adherence to a similar power law of mass scaling of maximum torque output in two groups, group a, (Ga ∝ m1.00) and group b (Gb ∝ m1.27). Findings imply that there could exist an upper motor limit of maximum specific torque/force that should be taken under consideration in robot design. Additionally, we show how a robot's minimum mass can be calculated with motor mass being the only necessary parameter.