Journal of Bionic Engineering (2025) 22:585–595 https://doi.org/10.1007/s42235-025-00658-z

Adaptive Discrete-Time Sliding Mode Control Applied to the Pitch  Motion of a Micro Air Vehicle with Flapping Wings 

Joshua Hill1  · Farbod Fahimi1  · Chang-kwon Kang1  · Hikaru Aono2

1 Department of Mechanical & Aerospace Engineering,  University of Alabama in Huntsville, Huntsville, AL  35899, USA 

2 Department of Mechanical Engineering and Robotics,  Shinshu University, 3-15-1 Tokida, 3868567 Ueda, Nagano,  Japan

Abstract 

A robust Adaptive Discrete-time Sliding Mode Controller (ADSMC) is formulated, and is applied to control the pitch  motion of a simulated Flapping-Wing Micro Air Vehicle (FWMAV). There is great potential for FWMAVs to be used as  aerial tools to assist with gathering data and surveying environments. Thanks to modern manufacturing and technology,  along with an increased comprehension behind the aerodynamics of wing flaps, these vehicles are now a reality, though not  without limitations. Given their diminutive size, FWMAVs are susceptible to real-world disturbances, such as wind gusts,  and are sensitive to particular variations in their build quality. While external forces such as wind gusts can be reasonably  bounded, the unknown variations in the state may be difficult to characterize or bound without affecting performance. To  address these problems, an ADSMC is developed. First, the FWMAV model is converted from continuous-time to discretetime. Second, an ADSMC for the newly discretized FWMAV model is developed. Using this controller, the trajectory  tracking performance of the FWMAV is assessed against a traditional discrete sliding mode controller, and is found to  have a decreased chattering frequency and decreased control effort for the same task. Therefore, the ADSMC is assessed  as the superior controller, despite being completely unaware of the model parameters or wind gust. 

Keywords Discrete-time sliding-mode control · Adaptive sliding-mode control · Flapping-wing micro air vehicles ·  Wind gust