Energy-based Attitude Control Of Spherical Pendulum

In this paper, we study the attitude control problems based on model of spherical pendulum. Three degrees of freedom pendulum (3D pendulum) is a rigid body supported by a frictionless pivot. According to relative position of the center of mass and the fixed pivot without friction, the 3D rigid pendulum can be divided into two balanced attitudes, Hanging equilibrium and inverted equilibrium. For the axisymmetric 3D rigid pendulum, the axis of symmetry is equivalent to axis of inertia of rigid body, and angular velocity around the axis of symmetry is equal to zero, as a result, the 3D rigid pendulum can be equal to the spherical pendulum. According to the motion attitude of spherical pendulum, one control method based on passive theory is proposed in this paper, Firstly, we use the passive theory to research the equilibrium stability of spherical pendulum. Secondly, passive theory and the Lyapunov function are utilized to deduce the control law. Finally, the spherical pendulum reach asymptotically stable in equilibrium position.