Dynamics and Control of a Spherical Rolling Robot Equipped with a Gyro

In this paper, we propose a new driving mechanism for a spherical rolling robot and investigate the dynamic characteristics of the robot by theoretical analysis and numerical simulations. The spherical robot has a momentum wheel(gyro) that rotates at a large velocity inside the robot, and its mechanism may be expected to provide the driving force efficiently. However, the dynamics of the robot is very complex because of the angular momentum of the gyro. We derive the equations of motion for the spherical robot that include the effects of frictional forces, and perform numerical simulations in order to examine the behavior of the robot. INTRODUCTION Many studies on autonomous mobile robots such as a wheeled mobile robot and a biped walking robot have been carried out so far. In recent years, development of another kind of mobile robot, a spherical rolling robot, has attracted the interest of many researchers. A spherical robot rolls and moves on the floor by using some actuators located in its inside, and would be practically useful because it can achieve omnidirectional motion. The driving mechanisms of the robot that have already been proposed are grouped into several types according to the actuators; reaction wheel type(Bhattacharya and Agrawal, 2000), moving mass type(Javadi and Mojabi, 2004, Alves and Dias, 2003), and so on. We are now developing a spherical robot that has a new type of driving mechanism equipped with a gyro(Figs. 1 and 2). The gyro is rotating with a large velocity in the inside of the robot, and the mechanism is designed so that the center of mass of the robot lies at the geometric center of the sphere. By using three motors located inside the robot, some of the angular momentum of the gyro is transferred to an outer spherical shell of the robot, and the spherical robot moves on the flat floor. Although the mechanism may be expected to provide the driving force efficiently, the dynamics of the robot is very complicated because of the angular momentum that the gyro has. In this paper, we investigate the dynamic characteristics of the robot by theoretical analysis and numerical simulations. The equations of motion for the spherical robot are derived by modeling it as a multi body system. These equations include the effects of friction at the contact point between the outer shell and the floor and friction at the internal mechanism. Under some assumptions, the motion equations show that the angular momentum of the robot about the contact point is conserved and that nutation of an inner subsystem may be caused like a dual-spin satellite. We design some simple controllers to control the translational motion of the outer shell, and examine the behavior of the controlled system by numerical simulations. If there is a friction at the internal mechanism, nutation of the inner subsystem may be quickly damped. If the mass center of the robot is a short distance away from the center of the sphere, precession of the system may be caused by the gravitational force. MODEL OF THE SPHERICAL ROBOT Prototype of the Robot Figure 1 shows a photograph of the spherical mobile robot under development. The radius of sphere is 15[cm], the weight of the robot is about 4.9[kg], and power supply, sensor and etc. are located in the robot so that it can move autonomously. The spherical robot is composed of four bodies, gyro, gimbal, gyro Figure 1. Prototype of a spherical robot roller ω10 outer shell gyro case gimbal