Dynamic Modelling, Tracking Control and Simulation Results of a Novel Underactuated Wheeled Manipulator (WAcrobot)

Abstract

Being an inherently open loop unstable mechanical system with highly nonlinear dynamics and with the number of actuators less than the number of degrees of freedom, the inverted pendulum system is a perfect benchmark for the design of a wide range of classical and contemporary control techniques. There are a number of different versions of the inverted pendulum systems offering a variety of control challenges. The most common types are the single inverted pendulum on a cart (Ohsumi & Izumikawa, 1995; Astrom & Furuta, 2000; Yoshida, 1999), the double inverted pendulum on a cart (Zhong & Rock, 2001), the double inverted pendulum with an actuator at the first joint only (Pendubot) (Spong, 1996; Graichen & Zeitz, 2005; Fantoni et al., 2000), the double inverted pendulum with an actuator at the second joint only (Acrobot) (Spong, 1994; 1995; Hauser & Murray, 1990), the rotational single-arm pendulum (Furuta et al., 1991; 1992) and the rotational two-arm pendulum (Yamakita & Furuta, 1999). Beyond non-mobile inverted pendulum robots, wheeled inverted pendulum robots or commonly known as balancing robots (e.g., Segway (Browning et al., 2005), Quasimoro (Salerno & Angeles, 2003), and Joe (Grasser et al., 2002)) have induced much interests by researchers. The control techniques involved in various types of inverted pendulum systems are also numerous, ranging from simple conventional controllers to advanced control techniques based on modern nonlinear control theory. A vast range of contributions exists for the stabilization of different types of inverted pendulums (Mori et al., 1976; Chaturvedi et al., 2008; Angeli, 2001). Besides the stabilization aspect, the swing-up of various types of single and double inverted pendulum(s) is also addressed in the literature. Examples include classic single pendulum on a cart (Astrom et al., 2008; Astrom & Furuta, 2000), Acrobot and Pendubot (Fantoni et al., 2000; Spong, 1994; 1995; Graichen et al., 2007; Brown & Passino, 1997) and the rotary double inverted pendulum (Yamakita et al., 1993; 1995). In addition to the stabilization and swing-up of different kinds of inverted pendulum robots, trajectory tracking of these underactuated systems has gained attention by researches (Cho & Jung, 2003; Chanchareon et al., 2006; Hung et al., 1997; Magana & Holzapfel, 1998). There are two major approaches to construct the trajectory tracking controller for such nonlinear systems. The first one is based on system inversion (Devasia et al., 1996; Wang & Chen, 2006) and the