Control of a 2-DOF omnidirectional mobile inverted pendulum

• Published in: Journal of mechanical science and technology Vol. 26; no. 9; pp. 2921 - 2928
• Main Authors: Viet, Tuan Dinh, Doan, Phuc Thinh, Giang, Hoang, Kim, Hak Kyeong, Kim, Sang Bong
• Format: Journal Article
• Language: English
• Published: Heidelberg Korean Society of Mechanical Engineers 01.09.2012; Springer Nature B.V; 대한기계학회
• Subjects: Adaptative systems; Adaptive control systems; Applied sciences; Computer science; control theory; systems; Control; Control theory. Systems; Differential equations; Disks; Dynamical Systems; Dynamics; Engineering; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Industrial and Production Engineering; Mathematical models; Mechanical Engineering; Pendulums; Physics; Robotics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Stabilization; Universal joints; Vibration; 기계공학; Omnidirectional mobile platform (OMP); 2-DOF inverted pendulum (2-DOF IP); Adaptive backstepping controller (ABC); Omnidirectional mobile inverted pendulum (OM-IP); Inversed pendulum; Wheel; Differential equation; Stabilization; Solid dynamic; Substructure; Experimental study; Recursive algorithm; Adaptive control; Modeling; Adaptive method; Backstepping control; Center of mass; Dynamic model; omnidirectional vehicle; Universal joint; Lyapunov function
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-012-0710-2

In this paper, stabilization of a 2-degrees-of-freedom (2-DOF) omnidirectional mobile inverted pendulum (OM-IP) is studied. The OM-IP consists of the rod that rotates around a rotary point of a universal joint which is connected at the center of the omnidirectional mobile platform (OMP). For ease of analysis, the OM-IP is decoupled into two subsystems: a 2-DOF inverted pendulum (IP) and an OMP. The IP is a rod that rotates around a universal joint with 2-DOF. The OMP is a body consisting of disk and three omnidirectional wheels that moves on plane and keeps the rod in balance. Dynamic modeling of the 2-DOF OM-IP is presented. From the dynamic equation, an adaptive backstepping control method is proposed to keep the rod in balance. Update law is presented as differential equation of an unknown parameter when the distance from the center of gravity of the rod to the rotary point on the OMP is unknown. Stability of the adaptive controller is proven by using Lyapunov function. Simulation and experimental results show the effectiveness of the proposed controller.