DOI: 10.5061/dryad.bcc2fqzrf
title: Asymmetries-induced nonlinear dynamic behaviors enable a versatile modulation strategy for insect-scale robotics

description: Developing versatile insect-scale robots that can handle various
 unstructured scenarios with a simple design remains a critical challenge.
 Herein, we introduce a single electromagnetic actuator-driven insect-scale
 robot, developed by integrating geometric and mass asymmetries into a
 deformable hexagonal frame. This asymmetric configuration induces
 nonlinear dynamic behaviors in the robot, allowing it to perform a variety
 of complex actions (e.g., forward and backward locomotion, active
 flipping, and lateral movement) and respond to challenging scenarios
 (e.g., granular media and safe landing) through posture transitions. To
 facilitate the behavior modulation and design optimization of the proposed
 insect-scale robot, a nonlinear dynamic model is established to map the
 relationship between motion behaviors and input parameters. Finally, an
 untethered prototype that can work in outdoor environments is constructed
 to further demonstrate the practical applications.
description: # Asymmetries-induced nonlinear dynamic behaviors enable a versatile
 modulation strategy for insect-scale robotics Dataset DOI:
 [10.5061/dryad.bcc2fqzrf](10.5061/dryad.bcc2fqzrf) ## Description of the
 data and file structure The experimental efforts aim to analyze the
 dynamic behavior of a multi-mass mechanical system under periodic forcing
 and frictional interactions. Investigating how **applied force magnitude**
 (`F1_magnitude`), **friction coefficient** (`mu`), and **frequency** (`f`)
 influence the system’s centroid displacement direction (positive
 proportion). 1. Visualizing motion patterns through **displacement
 time-series** and **phase space trajectories** to understand coupling
 dynamics between masses (m1, m2, m3) connected by springs/dampers with
 friction at contact points. 2. Validating theoretical models of nonlinear
 mechanical systems under excitation. 3. Calculating forward and backward
 speed by constructing a specific dynamic model. ### Files and variables
 #### File: source_code.zip **Description:**  The ZIP archive contains 4
 Python files. "forward_movement_ratio_calculation.py" computes
 the proportion of positive centroid displacements under different
 combinations of applied force (F1_magnitude), friction coefficient (mu),
 and frequency (f). "displacement_simulation.py" simulates and
 visualizes the displacement of three masses over time.
 "phase_map.py" generates a phase space plot (displacement vs.
 velocity) and visualizes the dynamic behavior of the system in the phase
 plane. ''Specific_dynamic_model_for_calculating\_
 speed.py'' introduces a specific dynamic model for calculating
 forward and backward speed. ## Code/software To run the provided Python
 scripts and view the generated data, you need the following free,
 open-source software and packages: ### **Required Software** 1. **Python**
 (version 3.7 or higher) * Download from
 [python.org](https://www.python.org/downloads/). * Recommended: Use
 [Anaconda](https://www.anaconda.com/products/distribution) for simplified
 package management. 2. **Required Python Packages** (with versions used in
 development): * `numpy` (numerical computing; tested with v1.21+) *
 `pandas` (data manipulation; tested with v1.3+) * `scipy` (scientific
 computing; tested with v1.7+) * `matplotlib` (plotting; tested with v3.4+)
 * `openpyxl` (Excel file support for pandas; tested with v3.0+)