2025 ASEE Annual Conference & Exposition

A Small, Low-Cost Undergraduate Laboratory for the Study of Graph Theory and the Networked Control of Multi-Agent Systems

Presented at ELOS Technical Session 6: BYOE (Bring Your Own Experiment): Engaging Students with Creative Hands-on Laboratory Experiences

Introduction

Multi-agent systems (MAS) are nowadays used in multiple applications, ranging from autonomous vehicles and smart grids to social networks and financial markets. Future engineers and roboticists will need to understand the complex behaviors of large-scale networked systems and the challenges that distributed and unreliable communication networks can bring. Yet, traditional undergraduate control engineering curricula lack hands-on emphasis on multi-agent systems, partly due to the cost, laboratory space, and time required to conduct experiments.

This paper presents a low-cost experimental undergraduate testbed that provides a practical, portable small platform for studying graph theory concepts and the control of MAS. The testbed consists of five individual rotatory 1-degree-of-freedom links connected via a Controller Area Network (CAN) bus, in which students can explore concepts such as graph connectivity, consensus, stability, and network reliability. Students are assumed to have basic C/C++ programming and linear algebra skills and a laptop computer.

Project Description

The testbed consists of five robotic links placed one next to the other, connected via CAN bus, and mounted on a 60 cm long frame. Each link has a Hitech HS-475HB servo motor, a BOSCH BNO055 Inertia Measurement Unit (IMU) sensor, and a STM32 Nucleo-L432KC microcontroller programable on C/C++, for an approximated cost of $425 per unit. Students can be asked to design a program in C++ that reads the angular orientation from the IMU sensor, implements a coordination algorithm such as the consensus protocol, and regulates the orientation of the link actuated by the servo motor. Students can implement different directed, undirected, and weighted communication graphs, collect position data from each link, and post-analyze the results using other control and data analysis tools like MATLAB. Furthermore, the students can induce larger delays and data losses in the communication network to study their effects on performance and stability.

Assessment of Learning Outcomes

After completing six hours of laboratory activities, a voluntary online questionnaire was given to the students. Ninty four percent or more of the students either agree or strongly agree about the testbed helping them improve their understanding of the course concepts and ABET-related criteria, with the other percentage having no opinion. About 77% agree or strongly agree with linking the use of the testbed as a teaching method for graph theory concepts, with only less than 6% disagreeing.

Authors
  1. Dr. Erick Rodriguez-Seda United States Naval Academy [biography]
Note

The full paper will be available to logged in and registered conference attendees once the conference starts on June 22, 2025, and to all visitors after the conference ends on June 25, 2025