oa Vision-based control of a flying spherical inverted pendulum on a Quadrotor

A spherical inverted pendulum represents an example of a nonlinear and unstable dynamical system. It has the property of the impossibility of measurement at the ball joint. The control of under-actuated systems is currently a field of research that is very active due to their vast applications in robotics, aerospace and marine vehicles. Furthermore, the interest of the scientific community to the theme of controlling the spherical inverted pendulum has continued to increase where most of researchers have developed strategies to control the spherical inverted pendulum by applying two planar forces fx and fy along the x-axis and y-axis, respectively. However, they were all discussed in terms of decoupled techniques which means that they have considered the spherical inverted pendulum as two simple inverted pendulums which has made the region of stability limited [1]. From an application point of view, such limitations can be removed by enlarging the region of stability via adding a vertical force fz along the z-axis. In this way, the base will become capable of moving in the space in order to control the pendulum. In order to achieve this goal, this paper proposes an inverted pendulum that is attached by a ball joint to a Quadrotor such that the last enables the control of the spherical inverted pendulum in its unstable equilibrium upright position [2-3]. However, most of this research was discussed either in terms of decoupling or was considered a simple inverted pendulum with different initial conditions of the angle and angular velocity of the pendulum. In other terms, in order to control an inverted pendulum in real life, the angular positions and angular speeds must be measured using an encoder at the bearing. The thing that is impossible for the case of the spherical inverted pendulum. In this paper, the visual servoing of a spherical inverted pendulum on a Quadrotor (Fig.1) is treated. This technique will control the spherical pendulum in the vertical position based on visual information from a camera placed over the Quadrotor. The camera records images from the environment and on the basis of certain characteristic points of the observed image, the current position of the pendulum will, therefore, be derived from the desired position as shown in (Fig.2). This difference in image characteristics between the current location and the desired location is then used to generate a back stepping-based control which will cause the Quadrotor to move in order to adjust the position of the spherical pendulum in its equilibrium position (Fig.3).