Stabilization of Underactuated 3D Pendulum Using Partial Angular Velocity Feedback

Models for a 3D pendulum, consisting of a rigid body that is supported at a frictionless pivot, were introduced in a 2004 CDC paper [1]. A subsequent paper, in the 2005 ACC [2], developed stabilizing controllers for a fully actuated 3D pendulum assuming feedback of the reduced attitude and angular velocities. In the present paper, stabilizing controllers are developed for an underactuated, 3D pendulum using partial feedback of the angular velocities. We propose controllers and provide sufficient conditions for stabilization of the hanging equilibrium of an underactuated, 3D pendulum. A controller is proposed to stabilize the inverted equilibrium of the 3D pendulum, using partial angular velocity and reduced attitude feedback.