Adaptive Super-Twisting Control for Mobile Wheeled Inverted Pendulum Systems

Abstract

Recently, the mobile wheeled inverted pendulum (MWIP) has gained an increasing interest in the field of robotics due to traffic and environmental protection problems. However, the MWIP system is characterized by its nonlinearity, underactuation, time-varying parameters, and natural instability, which make its modeling and control challenging. Traditionally, sliding mode control is a typical method for such systems, but it has the main shortcoming of a "chattering" phenomenon. To solve this problem, a super-twisting algorithm (STA)-based controller is proposed for the self-balancing and velocity tracking control of the MWIP system. Since the STA is essentially a second-order sliding mode control, it not only contains the merits of sliding mode control (SMC) in dealing with the uncertainties and disturbances but can also be effective in chattering elimination. Based on the STA, we develop an adaptive gain that helps to learn the upper bound of the disturbance by applying an adaptive law, called an adaptive super-twisting control algorithm (ASTA). The stability of the closed-loop system is ensured according to the Lyapunov theorem. Both nominal experiments and experiments with uncertainties are conducted to verify the superior performance of the proposed method.

Control of the two-wheeled inverted pendulum (TWIP) robot in presence of model uncertainty and motion restriction

“…To apply the designed controller into a real robotic systems, it is unavoidable to confront the mismatch issue between real system and its mathematical model (Xu et al , 2014; Zhang et al , 2019; Huang et al , 2020). The mismatch, referred to lumped model uncertainties in this paper, includes dynamics parameter uncertainty, unmodeled dynamics, wheel actuator friction, ground friction, sensor error, external disturbance and so on.…”

“…ε 0 is a positive constant. Note that ε must contain the bounds of lumped model uncertainty terms to guarantee that the state can asymptotically approach the sliding surface (Xu et al , 2014; Zhang et al , 2019).…”

“…In Esmaeili et al (2017), the backstepping SMC is used to balance and track trajectory of TWIP, but only considering model uncertainties and exogenous disturbance in simulation. Zhang et al (2019) adopt an adaptive second-order sliding mode to control TWIP to avoid the shortcoming of "chattering" phenomenon. However, the unknown disturbance boundary is not directly given but estimated via the adaptive control law.…”

“…As for control of TWIP robots in 3D, there are many works done by scholars verified not only in simulation (Pathak et al , 2005; Yue et al , 2013; Cui et al , 2015; Brisilla and Sankaranarayanan, 2015; Yue et al , 2016; Rigatos et al , 2020) but also in practical system (Ha and Yuta, 1996; Grasser et al , 2002; Jeong and Takahashi, 2008; Takei et al , 2009; Do and Seet, 2010; Huang et al , 2011a, 2011b; Lin et al , 2011; Muralidharan and Mahindrakar, 2014; Huang et al , 2015; Dai et al , 2015; Hirose et al , 2016; Kim and Jung, 2016; Esmaeili et al , 2017; Zhang et al , 2019; Jleilaty et al , 2019; Huang et al , 2020). Part of these contributions are involved to little model uncertainty or external disturbance.…”