Kinematics Modelling for Omnidirectional Rolling Robot
A ball-shaped mobile robot, called a ballbot, has a single point of contact with the ground. Thus, it has low energy consumption for motion because of the reduced friction. This paper presents the systematic kinematics modelling for a type of ballbot with
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Abstract A ball-shaped mobile robot, called a ballbot, has a single point of contact with the ground. Thus, it has low energy consumption for motion because of the reduced friction. This paper presents the systematic kinematics modelling for a type of ballbot with omnidirectional motion capability. This kinematics modelling describes the velocity relationship between the driving motors and the robot body for the motion control of the robot.
1 Introduction A ball-shaped robot has a single point of contact with the ground, which reduces its friction with the ground. A ball-shaped robot is generally called a ballbot. In comparison with a conventional wheeled mobile robot, a ballbot consumes less energy for motion because of the reduced friction [1]. There are two types of ballbots, as illustrated in Fig. 1. The ballbot shown in Fig. 1a has a cylindrical body on the top of a ball [2, 3]. This cylindrical body has driving motor and wheel assemblies in contact with the exterior of the ball to exert a driving force. In contrast, the ballbot shown in Fig. 1b has a pure spherical shape and contains a driving mechanism inside the ball [4]. The driving mechanisms can be classified into two types: (i) the wheeled platform type (Fig. 1b) [4] and (ii) the pendulum type (Fig. 2) [1]. The ballbot shown in Fig. 1a has many motion control difficulties because its posture is essentially unstable. In contrast, the pure ball-shaped robots shown in Fig. 1b and Fig. 2 are inherently stable, so the motion control is relatively stable.
S.-Y. Yi (&) Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul, Republic of Korea e-mail: [email protected]
J. J. (Jong Hyuk) Park et al. (eds.), Multimedia and Ubiquitous Engineering, Lecture Notes in Electrical Engineering 240, DOI: 10.1007/978-94-007-6738-6_93, Ó Springer Science+Business Media Dordrecht(Outside the USA) 2013
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Fig. 1 Types of the ballbot. a Cylindrical robot body. b Spherical robot body Fig. 2 Pendulum type driving mechanism
However, these ballbots still have a motion control problem because the driving mechanism cannot provide omnidirectional motion capability. In this paper, the systematic kinematics modelling for a ballbot with a wheeltype driving mechanism inside a ball is addressed for the motion control of the ballbot. More specifically, the driving mechanism is a platform with three Swedish wheels, so the ballbot has omnidirectional motion capability without nonholonomic constraints. Thus, the motion control of the ballbot becomes comparatively simple.
2 Differential Motion Between Coordinate Frames The kinematics modelling can be described by the velocity relationship between the active driving motor and the robot body. When the transformation between two coordinate frames, B and C, is given as TBC , the relationship of the differential motions between the coordinate frames shown in Fig. 3 is described as DC ¼ TBC1 DB TBC ;
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Kinematics Modelling for Omnidirectional Ro
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