Formation Control of Quadrotors Based on Interconnected Positive Systems

Abstract

This paper deals with formation control of quadrotors based on interconnected positive linear systems. One of the applications of interconnected positive linear systems is formation control including switching of SISO positive and stable linear subsystems. However, mechanical systems such as quadrotors are neither linear nor positive. This paper proposes an extended feedback linearization technique that is able to convert the dynamics of the reference point of a quadrotor, a virtual rigid body dynamics, into four double integrators with respect to the reference point in the space and yaw angle. In contrast to traditional exact feedback linearization techniques, the extended feedback linearization technique of the quadrotor does not require the jerk to be estimated. The extended feedback linearization and a local linear feedback law are employed to transform each coordinate of the reference point into a SISO positive and stable subsystem. As a result, the reference points as well as the mass centers of the quadrotors achieve formation in the framework of interconnected positive linear systems. The results are illustrated by numerical examples.