Point‐to‐Point Motion Control for a Spherical Robot on an Inclined Plane via Sliding Modes

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

Point‐to‐Point Motion Control for a Spherical Robot on an Inclined Plane via Sliding Modes 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 exponential reaching law is presented for point‐to‐point motion control of a spherical mobile robot on an inclined plane. The multibody dynamics of the spherical mobile robot rolling without slipping and spinning on an inclined plane are derived by using the constrained Lagrangian formulation. Based on the complete equations of motion of the robotic system, a sliding mode algorithm is developed for point‐to‐point motion control of the robot by using the theory of VSS. The proposed control approach consists of designing a nonlinear reaching law by using a switching component that dynamically adapts to the variations of the sliding surface. The effectiveness of the proposed controller is validated through numerical simulations and experiments. Keywords Spherical Robot; Inclined Plane; Point‐to‐Point Motion; Sliding Mode Control; Exponential Reaching Law

Introduction Most of the mobile robots that we have today have wheels, this is an obvious choice as there is considerable amount of knowledge about this type of locomotion. However, more and more possible applications occur where wheeled mobile robots have some flaws. Spherical mobile robots, which are a novel type of mobile robots with a spherical exoskeleton and a propulsion mechanism that uses unbalanced masses, might be an effective solution to some of these problems. As a spherical mobile robot is encompassed in a ball, it is possible to seal everything to enable the robot to withstand exposure to dust, dangerous substances and other environmental threats. As we can understand, this could be very handy in such applications as planetary exploration, surveillance and others. The above mentioned situations often involve dealing with difficult terrain as well. While wheeled mobile robots can cope with it pretty good, the risk of falling over still persists. On the other hand, a spherical mobile robot can't fall over at all. Also, it is quite a task to deploy a wheeled mobile robot without direct human intervention ‐ the landing spot has to be carefully chosen, and the robot has to land with wheels down, etc. However, a spherical mobile robot can be simply dropped out above the desired location. Over the last few decades, there has been considerable interests in the development of powerful methods for motion control of spherical mobile robots. The motion control problems addressed in the literature can be roughly classified into two groups: trajectory tracking [1‐4] and path following [5]. Besides the above mentioned two control problems, point‐to‐point motion control is usually viewed as another basic motion control problem of this type of mobile robots, which has not yet been investigated till now. On the other hand, current researches on motion control of spherical mobile robots usually assume that the robot remains strictly on a level plane [1‐5]. Due to some components of the gravitational forces acting on the system, the motion of a spherical mobile robot on an inclined plane differs significantly from those on horizontal planes. As a result, the dynamic models, which are developed on the basis that the spherical mobile robot travels over a level plane, fail to represent the actual motion when the robot rolls along a slope. According to the above review, there have not been any well‐established methodologies to resolve the point‐to‐point motion control problem of spherical mobile robots. Therefore, this paper basically focuses on practical solutions to point‐to‐point motion control of a spherical mobile robot which rolls on an inclined plane. The main contributions of this paper include two parts. Firstly, the kinematics and dynamics of the spherical robot rolling over constant‐slope terrain without slipping and spinning are derived. Secondly, a sliding mode control scheme based on a new exponential reaching law is developed for the point‐to‐point motion of the spherical robot.

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