A Sliding Mode Approach for Trajectory Tracking Control of a Spherical Robot

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www.as‐se.org/sss Studies in System Science (SSS) Volume 2, 2014

A Sliding Mode Approach for Trajectory Tracking Control of a Spherical Robot Tao Yu*1, Hanxu Sun2 1

Faculty of Mechanical Engineering and Automation, Liaoning University of Technology, Jinzhou, Liaoning, China

2

School of Automation, Beijing University of Posts and Telecommunications, Haidian District, Beijing, China

*1

yutaolanjie@163.com; 2hxsun@bupt.edu.cn

Abstract In this study, a variable structure approach based on sliding mode is presented for trajectory tracking control of a spherical mobile robot. The spatial dynamics of the spherical robot rolling without slipping and spinning on a level plane is derived by using the constrained Lagrangian formulation. Based on the complete equations of motion of the robotic system, a sliding mode control algorithm combined with an adaptive scheme, which is used to estimate the unknown parameter bounds, is developed for trajectory control of the robot. Simulation results show the validity of accurate tracking capability and robust performance of the proposed controller. Keywords Spherical Robot; Trajectory Tracking; Sliding Mode Control; Adaptive Estimation

Introduction A spherical robot is a robotic device without wheels or legs which has a single spherical form that, literally, scrolls by itself to conduct the missions and being inherently stable. The spherical shape of this type of mobile robots offers several advantages over other forms of surface‐based locomotion such as wheels, tracks or legs. The sphere is a strong shape providing a high level of robustness with no major weakness points on its surface, whereas wheels, tracks or legs can be damaged, potentially disabling the mobility of the robot. The shell can also be resilient and serve as a protective barrier between the outside environment and the inside equipments. A spherical robot is by nature non‐ invertible further limiting the risk of becoming disabled, while most other mobile robot designs are vulnerable to tipping over or becoming stuck on the terrain where their means of locomotion lose contact with the ground. These advantages indicate that a spherical robot is appropriate for many different applications such as surveillance, reconnaissance, hazardous environment assessment, search and rescue, as well as planetary exploration. Over the last few decades, there has been considerable interests in the development of powerful methods for motion control of mobile robots. The control problems addressed in the literature can be roughly classified into three groups: trajectory tracking, path following and point stabilization [1]. With respect to trajectory tracking control of spherical robots, many studies had been carried out in the past few years. Alves and Dias [2] presented a line tracking method for a spherical robot based on the robot kinematics. Zhan and Liu et al. [3] designed a trajectory tracking controller for a spherical robot via backstepping method. Zheng and Zhan et al. [4] proposed a trajectory tracking control algorithm for a spherical robot based on a RBF‐PD controller. Cai and Zhan et al. [5] synthesized a hierarchical sliding mode controller integrated with a fuzzy guidance scheme for trajectory tracking of a spherical robot through a backstepping strategy. According to the above review, there have not been any well‐established methodologies for effectively resolving the trajectory tracking problem of spherical robots, although it plays an important role in many practical applications of this type of mobile robots. This paper is intended to provide practical solutions for trajectory tracking control of a spherical robot rolling on a level plane. The main contributions of this paper include two parts. Firstly, the kinematics and dynamics of the spherical robot subject to non‐slipping and non‐spinning constraints are derived. Secondly, an adaptive sliding mode scheme is developed for trajectory control of the spherical robot. Mathematical Model System Description Our robot, named BYQ‐VIII [6], is a pendulum‐driven spherical mobile robot with dual inputs. The mechanical structure of the robot BYQ‐VIII is illustrated in Fig. 1. BYQ‐VIII is mainly made of three rigid bodies: the spherical

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