The degree of controllability with limited input and an application for hexacopter design

The degree of controllability is in some sense a measure of how easy it is to control a system. The concept of the degree of controllability is the promotion of controllability. It develops from the binary concept controllability into a continuous scalar concept. The degree of controllability at present does not have a unified definition. Some researchers put forward different definitions from different aspects. In this paper, we improved the definition of the degree of controllability proposed by Viswanathan, extending the control input constraint from [−1, 1] to an asymmetric interval [a, b]. And we gave the computation method of the degree of controllability based on system discretization. At last, we compared the degree of controllability of hexacopter's attitude with different structure and analyzed the degree of controllability of the hexacopter's attitude when it has one or two rotors stopped.