Orientation control via a non-minimal state representation: the pendulum case study

Three degrees of freedom are required to completely describe the orientation (attitude) of a rigid body. Nevertheless, it is possible to use a non—minimal set of state variables, plus some holonomic constraints, for representing orientation (e.g. Euler parameters). This paper deals with orientation control problem using this latter approach, when the motion is constrained to a plane. The simplest testbed for such a motion is the pendulum. First, an alternative dynamic model of the pendulum is presented, which uses a non—minimal state representation. Once the orientation control objective for the plane is established, two controllers that solve this problem are introduced, and LaSalle’s invariance principle is used to show the achievement of the control aim.