Geometric Control of a Quadcopter

Abstract

In recent years, with the rise of affordable commercial grade quadcopters, there has been a lot of research done on modeling the motion of quadcopters, however much of it has been focused on creating robust control schemes for quadcopters. This dissertation works to bridge the gap this has left between motion planning and optimal control, with a focus mainly on two areas. First we work towards creating a model of the equations of motion as realistic as possible and connect the work done in geometric control theory in the past on underwater vehicles, to quadcopters. We also study possible simplifications, a specific control scheme and properties of basic motions. Secondly using an affine control model version of the equations of motion we study the time minimization problem with an emphasis on singular extremals. We observe numerically the possibility for optimal control to have an infinite number of switches in a finite time interval.