Here I’ll provide a brief summary of each of my professional publications. As you can find a more in-depth technical abstract in the corresponding pdf linked in each description, I’ll aim to keep the discussion very high-level and casual, with an emphasis on my particular contribution to each work.
In addition to the papers here, I have a few works in draft form: a follow-on AmoeBot journal paper that will contain the material that served as my PhD capstone and a conference paper focusing on underwater origami thrusters. Until these papers are submitted and accepted for publication, I will not include them here.
Table of Contents
- Journal Papers
- 2024 – Optimal Gaits for Inertia-Dominated Swimmers with Passive Elastic Joints
- 2023 – Geometric Analysis of Gaits and Optimal Control for Three-Link Kinematic Swimmers
- 2023 – Web Vibrations in Intraspecific Contests of Female Black Widow Spiders, Latrodectus hesperus
- 2022 – The Geometry of Optimal Gaits for Inertia-Dominated Kinematic Systems
- 2022 – Validation of a Novel Stereo Vibrometry Technique for Spiderweb Signal Analysis
- Conference Papers
- Other
Journal Papers
Optimal Gaits for Inertia-Dominated Swimmers with Passive Elastic Joints
Nathan Justus, Ross L Hatton
March 2024
American Physical Society: Physical Review E
One of my major theoretical contributions to the field! Similar to a work discussed below, this paper focuses on inertial locomotors. However, whereas systems in the former work were fully controlled, this work adds complexity by including passive-elastic degrees of freedom. In both of the systems we examined here, there are two geometric shapes: one active shape controlled by an idealized actuator that we can send torque signals to, and one passive shape driven by local stiffness and damping and by whole-body inertial effects.
Major contributions of this paper include developing motion optimization strategies for passive dynamic locomotors, discussion of potential optimization functions to use when considering ideal locomotor behavior, and comparison of continuous vs discrete swimmer geometry. Spoiler alert: continuously flexible systems are generally better!
Geometric Analysis of Gaits and Optimal Control for Three-Link Kinematic Swimmers
Oren Wiezel, Suresh Ramasamy, Nathan Justus, Yizhar Or, Ross L Hatton
December 2023
Automatica
This paper was a collaboration with some colleagues at the Israel Institute of Technology and compares two techniques for the analysis of maximum-displacement gaits in locomoting swimmers. In a maximum displacement gait, the swimmer moves the maximum possible distance each gait cycle.
Our collaborators used a shooting method to find a profile in shape-space that executes this gait. My contribution to this work was to discuss a geometric alternative wherein a height function is produced as a function of shape-space that indicates the value of including this region inside an enclosed gait. Maximum displacement gaits are then the zero-contours on the height map.
Web Vibrations in Intraspecific Contests of Female Black Widow Spiders,
Latrodectus hesperus
Rodrigo Krugner, Crystal Espindola, Nathan Justus, Ross L Hatton
April 2023
Environmental Entomology
This paper was a collaboration with some entomologists working at the USDA in California. In this work, we dropped female black widows into the nests of other female widows and recorded the vibration signals that resulted. When the host widow sensed an intruder widow, they would communicate signals through the web using a variety of modes, including large and small web plucks and abdominal “thumping.”
My contribution was to enable some of the measurement of the spiderweb signals using a stereo-vision methodology presented in one of my previous papers. It was fun to analyze videos of spiders talking to each other!
The Geometry of Optimal Gaits for Inertia-Dominated Kinematic Systems
Ross L Hatton, Zachary Brock, Shuoqi Chen, Howie Choset, Hossein Faraji, Ruijie Fu, Nathan Justus, Suresh Ramasami
May 2022
IEEE Transactions on Robotics
This was one of the first journal papers that I served as coauthor for. My main contribution was to generate many of the figures, including the one presented here which discusses path length (top right) and inertial cost (bottom right) for traversing circles of increasing radii on positively curved manifolds (top left) and negatively curved manifolds (bottom left) compared to the flat manifold (grey line in right subfigures). I’m quite proud of them!
Generally, the paper discusses how to construct and exploit mathematical structures to examine and optimize locomotion for mobile systems that are driven by dynamic effects. The physics of these systems resolves as the geometric structure and curvature of the underlying manifold, and observations about this geometry can lead to useful methodologies to improve locomotor behavior
Validation of a Novel Stereo Vibrometry Technique for Spiderweb Signal Analysis
Nathan Justus, Rodrigo Krugker, Ross L Hatton
March 2022
Insects
My first primary author academic paper! I implemented some prior optical flow computer vision techniques out of MIT-CSAIL and combined them with stereo vision techniques to build a way to track 3D vibration signals. We then validated these techniques on black widow spiderweb signals that were measured using laser vibrometry.
Using this stereo vision technique for spiderweb signal analysis has a few advantages over laser vibrometry, including the ability to examine vibrations in the whole field of view with a single measurement, the ability to take measurements directly on the spiders as they move around, and the ability to take measurements without having to suspend foreign objects in the web. We used this technique in later works to examine spiderweb signals in more depth.
Conference Papers
Amoeba-Inspired Swimming Through Isoperimetric Modulation of Body Shape
Curtis Sparks, Nathan Justus, Ross L Hatton, Nick Gravish
October 2022
International Conference on Intelligent Robots and Systems (IROS) 2022
This work was a collaboration with some fellow researchers down at UCSD. They built a cool robot that floats on the surface of water and locomotes using two buckling tape-spring mechanisms. By changing the angle and base length setting for the tape fins, the robot can maneuver and locomote across the water surface.
My contribution here was to perform a rudimentary locomotion analysis for the robot and compare to experimental results. I later spun this work into a more holistic project where I used experimental data to algorithmically generate a control planner for the AmoeBot so that it could be driven using a handheld joystick. I’m currently in the process of trying to develop and publish that journal paper!
Other
PhD Dissertation: The Geometry of Passive and Constrained Locomotion
Nathan Justus
June 2024
Oregon State University
My PhD Dissertation! What more can be said? This document contains an in-depth summary of the vast majority of the research content I generated over the course of my PhD.
Generally, I focused on three major contributions:
- Geometric analysis for low Reynolds number locomoting systems with passive elements
- Geometric analysis for high Reynolds number locomoting systems with passive elements
- Combination of these techniques for real-time control implementation of intermediate Reynolds number systems.
