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Sensors and Materials, Volume 38, Number 9(4) (2026)
Copyright(C) MYU K.K.
pp. 5395-5410
S&M4629 Report
https://doi.org/10.18494/SAM6240
Published: September 30, 2026

Kalman-filter-based Proportional-integral-derivative and Nonlinear Counter-steering for Low-cost Self-balancing Motorcycles [PDF]

Ho-Sheng Chen, Cheng-Fu Yang, and Jian-Chiun Liou

(Received January 29, 2026; Accepted August 31, 2026)

Keywords: two-wheeled vehicles, self-balancing electric motorcycle, proportional-integral-derivative (PID), inertial measurement units (IMUs), Kalman filter

Two-wheeled vehicles present significant stability challenges, particularly at low or zero velocity. In this paper, we present the design, implementation, and validation of a sensor-integrated, self-balancing electric motorcycle prototype that addresses this issue. The system is architected around the inverted pendulum model, employing a proportional-integral-derivative controller for longitudinal (pitch) stability and a novel counter-steering strategy for lateral (roll) stability. A sensor-based attitude sensing module, built around an inertial measurement unit (IMU), continuously detects the motorcycle’s dynamic state. The IMU data are processed through a Kalman filter to provide a robust and accurate estimation of the vehicle’s tilt angle by effectively fusing noisy accelerometer measurements with drifting gyroscope signals. This enhanced state-detection process ensures reliable real-time feedback for control. The entire system is managed by a STMicroelectronics32 microcontroller, demonstrating that advanced sensing, detection, and control algorithms can be efficiently implemented on open-source hardware. Experimental results validate the controller’s effectiveness, showing rapid balance recovery (within 1–2 s) from external disturbances of up to ±5 degrees with less than 15% overshoot (equivalent to ±0.75 degrees). In this work, we not only provide a practical implementation of a self-balancing sensing-driven control system but also offer a valuable and replicable platform for further research in intelligent transportation, sensor-based mobility systems, and robotics education.

Corresponding author: Cheng-Fu Yang and Jian-Chiun Liou


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Cite this article
Ho-Sheng Chen, Cheng-Fu Yang, and Jian-Chiun Liou, Kalman-filter-based Proportional-integral-derivative and Nonlinear Counter-steering for Low-cost Self-balancing Motorcycles, Sens. Mater., Vol. 38, No. 9, 2026, p. 5395-5410.



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