International Journal of Control, Automation, and Systems Vol. 1, No. 3, September 2003 376 Geometric Kinematics and Applications of a Mobile Robot Dong-Sung Kim, Wook Hyun Kwon, and Hong Sung Park Abstract: In this paper, the simple geometric kinematics of a three-wheeled holonomic mobile robot is proposed. Wheel architecture is developed for the holonomic mobile platform in order to provide omni-directional motions by three individually driven and steered wheels. Three types of basic motions are proposed for the path generation of the developed mobile robot. All paths of the mobile robot can be achieved through a combination of the proposed basic motion trajecto- ries. The proposed method is verified through computer simulations and the developed mobile robot. Keywords: Geometric kinematics, three-wheeled mobile robot, basic motion trajectory. 1. INTRODUCTION Numerous types of kinematics modeling and platform designs have been studied for wheeled mo- bile robots [1-3]. For large and heavy outdoor mobile robots, car-like driving mechanisms or skid-steer platforms have been used. However, these mobile robots are quite restricted in their motion by non- holonomic constraints on their wheel mechanism in tight indoor environments. One way to reduce these restrictions on four- wheeled mobile robots is to replace the coupled steer- ing wheels with one wheel, as in the case of three- wheeled mobile robots. The three-wheeled mobile robot has the advantage that wheel-to-ground contact can be maintained on all wheels without any suspen- sion system. In [4], the single wheel is the drive wheel as well as the steering wheel, enabling all other wheels to be idle. Some mobile robots have three wheels controlled by a synchronous drive system. In those systems, all the wheels are utilized for both driving and steering [5]. However, in the case of these mobile robots, wheels are coupled with a belt drive or gears, allowing them to be steered by a sin- gle motor. This three-wheeled mobile robot allows rotation of the mobile robot around any point, but does not allow sideways and full mobility by non- holonomic constraints [4,5]. In general, there are two types of three-wheeled mobile robots: non-holonomic and holonomic [6]. A non-holonomic mobile robot has the ability to reach an arbitrary position and orientation, but it is unable to rotate while simultaneously moving in an arbitrary direction. In contrast, a holonomic mobile robot is able to rotate while simultaneously translat- ing in a free direction. To achieve full mobility in the design of the omni-directional mobile robot, the holonomic property was adopted as a design goal. For the support of the holonomic property, certain types of mechanisms for an omni-directional holonomic mobile robot have been considered [6,7]. In these papers, the wheels are designed to operate as driving and steering wheels, using motors on concen- tric shafts. Three wheels are mounted 120 apart on a circular platform. As they are all driven, they must rotate at different speeds when turning in order to provide omni-directional motion. However, the kinematics of this model are known to be complex and furthermore that the controllers are unable to control each wheel efficiently. This design used three complex assemblies, each having an independent degree of freedom. There was some difficulty in con- trolling six degrees of freedom in the wheel for prac- tical implementation in [8,9]. This was due to the complex kinematics modeling that caused problems during operation. In this paper, a kinematics modeling based on a simple geometric approach for an omni-directional three-wheeled mobile robot is proposed. It is applied to reduce the kinematics complexity and to simplify the modeling method, in that all three wheels operate as both driving and steering wheels simultaneously. Independent flexible wheel architecture is applied to achieve omni-directional motions of the holonomic __________ Manuscript received May 22, 2002; revised December 10, 2002; accepted March 10, 2003. This work was sup- ported by the Korea Science and Engineering Foundation. Dong-Sung Kim is with Wireless Network Lab. in the School of Electrical and Computer Engineering, Cornell University, Ithaca, NY14853, U.S.A (e-mail: dsk27@ corn ell.edu). Wook Hyun Kwon is with the School of Electrical and Computer Engineering, Seoul National University, Seoul, Korea (e-mail: whkwon@cisl.snu.ac.kr). Hong Sung Park is with the Department of Electrilcal and Computer Engineering, Kangwon National University, Korea (e-mail: hspark@cc.kangwon.ac.kr).