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JRM Vol.38 No.1 pp. 350-363
(2026)

Paper:

Pendulum Model-Less Inversion

Hideki Toda*, Masahiro Sekimoto* ORCID Icon, Junji Ohyama** ORCID Icon, and Hiroaki Kawamoto***

*Faculty of Engineering, University of Toyama
3190 Gofuku, Toyama, Toyama 930-8555, Japan

**Human Augmentation Research Center, National Institute of Advanced Industrial Science and Technology (AIST)
1-1-1 Higashi, Tsukuba, Ibaraki 305-8560, Japan

***Institute of Systems and Information Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

Received:
March 17, 2025
Accepted:
October 11, 2025
Published:
February 20, 2026
Keywords:
inverted pendulum, unstable equilibrium angle estimator, integral only controller, anti-friction, non predictable disturbances
Abstract

This paper presents a novel approach to inverted pendulum control and unstable equilibrium angle (UEA) estimation through a proposed velocity suppression mechanism implemented in a single code. The key innovation lies in achieving control using solely an integral controller whose parameters satisfy a specific velocity suppression condition. Traditional inverted pendulum systems face a fundamental challenge: the arduous task of finding optimal proportional–differential–integral parameters, complicated by the system’s inherent sensitivity to minor physical variations (such as pendulum weight, length, distortion, and cart-rail friction). Our solution introduces a streamlined integral controller that includes the pendulum’s position, velocity parameters (θ, dotθ), achieving stabilization through the proposed mechanism. This same mechanism is effectively utilized for UEA estimation. The effectiveness was demonstrated on an unknown layout, weight, and moment pendulum inversion with unknown friction or deteriorated effect of 12-years-old device. This work signals a paradigm shift away from complex, model-dependent approaches to more practical, adaptive solutions.

Cite this article as:
H. Toda, M. Sekimoto, J. Ohyama, and H. Kawamoto, “Pendulum Model-Less Inversion,” J. Robot. Mechatron., Vol.38 No.1, pp. 350-363, 2026.
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Last updated on Feb. 19, 2026