Singular Zone in Quadrotor Yaw–Position Feedback Linearization

Abstract

Feedback linearization-based controllers are widely exploited in stabilizing a tilt rotor (eight or twelve inputs); each degree of freedom (six degrees of freedom in total) is manipulated individually to track the desired trajectory, since no singular decoupling matrix is introduced while applying this method. The conventional quadrotor (four inputs), on the other hand, is an under-actuated MIMO system that can directly track four independent degrees of freedom at most. Common selections of these outputs can be yaw–position and attitude–altitude. It is reported that no singularity is found in the decoupling matrix while applying feedback linearization in the yaw–position-tracking problem. However, in this research, we argue the existence of the ignored singular zone within the range of interest, which can cause the failure in the controller design. This paper visualizes this noninvertible area and details the process of deduction for the first time. An attempt (switch controller) to avert the singular problem is later discussed with the verification by simulation in Simulink and MATLAB. All the results are sketched in the roll–pitch diagram.

Keywords

• feedback linearization
• quadrotor
• singularity
• underactuated system
• MIMO