Bounded Control for Double Integrator in Quadrotor Dynamics

In this paper we construct a trajectory tracking controller for a quadrotor system by finding a coordinate change which transforms the quadrotor’s vector field into that of a thust propelled system. In a thrust propelled system, the goal is to stabilize its position around the origin, while the system is actuated by a one dimensional acceleration/thrust along a direction vector, by a time-varying gravity, and by the angular acceleration of the direction vector. For this system, a solution has been proposed in [1] based on the implicit knowledge of a bounded controller for a double integrator system, and on the implicit knowledge of a Lyapunov function that guarantees the origin is asymptotically stable for the double integrator controlled by the bounded controller. In this paper, we present two alternative bounded controllers for a double integrator system, and corresponding Lyapunov functions.