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Unformatted text preview: 564 IEEE TRANSACTIONS ON ROBOTICS, VOL. 23, NO. 3, JUNE 2007 Controllability and Posture Control of a Wheeled Pendulum Moving on an Inclined Plane Danielle Sami Nasrallah, Hannah Michalska, and Jorge Angeles , Fellow, IEEE Abstract— The paper considers a specific class of wheeled mo- bile robots, namely, mobile wheeled pendulums (MWPs). Robots pertaining to this class are composed of two wheels rotating about a central body. The main feature of MWP pertains to the central body, which can rotate about the wheel axis. As such motion is un- desirable, the problem of the stabilization of the central body in an MWP is crucial. The novelty of the work reported here resides in the construction of: 1) the system controllability Lie algebra for the purpose of a rigorous controllability analysis and the computa- tion of the largest feedback-linearizable subsystem; 2) a controller by input–output linearization of the system for achieving the de- sired steering rate of the robot while stabilizing the central body; 3) a controller based on the internal properties of the system to achieve the desired heading velocity of the robot; and 4) a con- troller based on the sliding-mode approach for controlling both the position and the orientation of the robot. The entire control struc- ture that permits full control of the robot posture comprises three imbricated loops. Simulations showing good performance of the controlled system are provided. Preliminary tests performed on an experimental platform confirm the validity of the controller. Index Terms— Inclined plane, Lyapunov functions, non- holonomy, nonlinear controllability, posture control, sliding mode, stability analysis, wheeled robots, zero-dynamics. I. INTRODUCTION T HIS paper studies the controllability of an antitilting out- door mobile robot (ATOM) moving on an inclined plane and proposes a multiloop control scheme for its implementa- tion. ATOM is composed of three rigid bodies: the central body, modeled as a cylinder whose center of mass is offset from its geometric center , and two spherical wheels rotating about the central body, as shown in Fig. 1. Notice that, although lies below in this figure, the control results reported here re- main valid when lies above . The system inputs are the two torques applied to the wheels. According to its structure, ATOM pertains to the class of mobile wheeled pendulums (MWPs). Many developments in the field of MWPs have been reported recently: the U.S. patent behind the Ginger and then the Segway Manuscript received April 8, 2006; revised November 10, 2006. This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP4532. This paper was recommended by Associate Editor L. Whitcomb and Editor K. Lynch upon evaluation of the reviewers’ comments....
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This note was uploaded on 02/07/2011 for the course MECH 646 taught by Professor Danielnassrallah during the Fall '10 term at American University of Beirut.
- Fall '10