Geometric path following control in a moving frame∗

The paper describes an approach to the development of the geometric path following control for a dynamical model of the rigid body with unidirectional thrust. The popular example of such system is the dynamical model of the quadcopter. Desired path of movement in the space is represented by an intersection of two implicit surfaces. In this paper we assume that the desired path is attached to a movable frame. This is a natural extension of the classical approaches for stationary frames. Path following control problem is posed as a problem of maintaining the holonomic relationships between the system outputs. Control is synthesized using the differential geometrical method through nonlinear transformation of initial dynamic model. The main results presented are the model of spatial motion and relevant nonlinear control algorithms.