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The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control

Authors: Kaheman KFasel UBramburger JJStrom BKutz JNBrunton SL


Affiliations

1 Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, United States of America.
2 Department of Aeronautics, Imperial College London, London, SW7 2AZ, United Kingdom.
3 Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada.
4 XFlow Energy Company, Seattle, WA, 98108, United States of America.
5 Department of Applied Mathematics, University of Washington, Seattle, WA 98195, United States of America.

Description

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.


Keywords: ChaosDouble pendulumDynamical systemNonlinear dynamicsOpen access dataOpen access hardwarePendulum on the cartSimulink real-timeSingle pendulumTriple pendulum


Links

PubMed: https://pubmed.ncbi.nlm.nih.gov/37637793/

DOI: 10.1016/j.ohx.2023.e00465