The experimental multi-arm pendulum on a cart: a benchmark system for chaos, learning, and control
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Published version
Author(s)
Type
Journal Article
Abstract
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors, from simple harmonic motion in the single pendulum to chaotic dynamics in multi-arm pendulums. Under forcing, even the single pendulum may exhibit chaos, providing a simple example of a damped-driven system. All multi-armed pendulums are characterized by the existence of index-one saddle points, which mediate the transport of trajectories in the system, providing a simple mechanical analog of various complex transport phenomena, from biolocomotion to transport within the solar system. Further, pendulum systems have long been used to design and test both linear and nonlinear control strategies, with the addition of more arms making the problem more challenging. In this work, we provide extensive designs for the construction and operation of a high-performance, multi-link pendulum on a cart system. Although many experimental setups have been built to study the behavior of pendulum systems, such an extensive documentation on the design, construction, and operation is missing from the literature. The resulting experimental system is highly flexible, enabling a wide range of benchmark problems in dynamical systems modeling, system identification and learning, and control. To promote reproducible research, we have made our entire system open-source, including 3D CAD drawings, basic tutorial code, and data. Moreover, we discuss the possibility of extending our system capability to be operated remotely, enabling researchers all around the world to use it, thus increasing access.
Date Issued
2023-09
Date Acceptance
2023-07-15
Citation
HardwareX, 2023, 15, pp.1-21
ISSN
2468-0672
Publisher
Elsevier
Start Page
1
End Page
21
Journal / Book Title
HardwareX
Volume
15
Copyright Statement
© 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/37637793
PII: S2468-0672(23)00072-X
Subjects
Chaos
Double pendulum
Dynamical system
Nonlinear dynamics
Open access data
Open access hardware
Pendulum on the cart
Simulink real-time
Single pendulum
Triple pendulum
Publication Status
Published
Coverage Spatial
England
Article Number
e00465
Date Publish Online
2023-08-07