A nonlinear optimal control based on the SDRE technique for the two-wheeled self-balancing robot

ABSTRACT

In this article, for the first time, a nonlinear optimal controller based on the state-dependent Riccati equation (SDRE) technique is proposed for the self-balancing two-wheeled Robot. The proposed optimal control is similar to linear quadratic Gaussian (LQG) control. The LQG controller is based on linearisation, but the proposed nonlinear optimal controller is based on parameterisation. For this purpose, at first, a three-degree-of-freedom (3-DOF) model of the two-wheeled robot including, longitudinal displacement, yaw, and pitch motion of the chassis are obtained using Kane’s method. Then, using the parameterisation method, the state-dependent coefficient (SDC) matrices are derived for the design of the nonlinear quadratic Gaussian (NLQG) controller. Consequently, the 3-DOF model of the two-wheeled robot and the NLQG controller algorithm are simulated in the MATLAB software environment. Also, using the proposed controller and the open-loop simulations the performance of the two-wheeled Robot is discussed. The simulation results demonstrate that the optimal controller based on the SDRE approach performs remarkably well when the system has an extremely nonlinear behaviour.

Abbreviations: KF: Kalman filter; CG: Centre of gravity; DOF: degree of freedom; LQG: linear quadratic Gaussian; NLQG: nonlinear quadratic Gaussian; SDRE: state dependent Riccati equation; LQR: linear quadratic regulator; RBF: radial basis function; SDC: state-dependent coefficient.

KEYWORDS:

• Nonlinear optimal control
• SDRE technique
• self-balancing two-wheeled robot
• parameterisation
• NLQG controller
• extreme nonlinear behaviour

Notations

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Disclosure statement

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes on contributors

Hamze Ahmadi Jeyed

Hamze Ahmadi Jeyed has received his Master of Science degree in Mechanical Engineering from the K. N. Toosi University of Technology in Tehran, Iran. His research interests are in automobile engineering, advanced control theory, optimal estimation, multi-body system dynamics, flexible robots, and intelligent transportation systems.

Ali Ghaffari

Ali Ghaffari is a professor of Mechanical Engineering at K. N. Toosi University of Technology in Tehran, Iran. His major field of study is control and dynamic systems. His researches are now focused on natural and man-made intelligent systems including, biological systems, autonomous and aided driver vehicles, and smart robots.