Scaling in Robot Design for Locomotion and Manipulation

December 2025

Scaling in Robot Design for Locomotion and Manipulation

Authors:

Steven Man

Abstract:

The principles of scaling predict significant performance advantages for robots miniaturized to the millimeter and micrometer scales, including faster movements and higher precision. However, realizing these benefits is often hindered by manufacturing limitations and complex system-level interactions. This thesis investigates the effects of scaling on robot design for both manipulation and locomotion through the development, fabrication, and characterization of two novel robotic systems.

First, we present the microDelta robots, the smallest (1.6 mm base diameter for the 0.5X version) and fastest (resonant frequencies exceeding 1 kHz) Delta manipulators developed to date. Fabricated using two photon polymerization (TPP) with integrated 3D electrostatic comb-drive actuators, two versions of the microDelta (1X and 0.5X scale) were characterized. Results demonstrate high-precision trajectory following and significant power delivery capabilities, exemplified by launching a micro-projectile. The comparative analysis of these two scales empirically validates theoretical scaling law predictions, such as increased operational frequency, while also highlighting practical manufacturing constraints that impact achievable torque and workspace.

Second, we introduce Zippy, a 3.6 cm-tall, self-contained bipedal walking robot that leverages quasi-passive dynamic walking principles with only a single hip actuator. By modifying established design rules for passive walkers, notably through the implementation of ellipsoidal feet and open-loop motor control with a physical hard stop, Zippy achieves robust and high-speed locomotion. It is the smallest dynamic bipedal robot and the fastest relative to its leg length (10 LL/s), capable of self-starting, achieving a flight phase via a ”skipping gait,” controlled turning, and traversing steps and uneven terrain.

Collectively, this work demonstrates the impact of geometric scaling on robotic capabilities, offering new benchmarks for miniature manipulators and agile locomotors. It provides critical insights into the practical challenges and emergent system-level behaviors encountered when downscaling robotic systems, thereby informing future design and fabrication strategies for advanced meso-scale and micro-scale robots.

Notes:

@mastersthesis{Man-2025-149646,
author = {Steven Man},
title = {Scaling in Robot Design for Locomotion and Manipulation},
year = {2025},
month = {December},
school = {Carnegie Mellon University},
address = {Pittsburgh, PA},
number = {CMU-RI-TR-25-48},
keywords = {microrobotics, passive dynamic walkers, robot design, 3d printing},
}
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