Tracking of a moving ground target by a quadrotor using a backstepping approach based on a full state cascaded dynamics

In this paper, a tracking controller is formulated for a quadrotor to track a moving ground target. The quadrotor exhibits distinct hierarchical dynamics that allows its position to be controlled by its attitude. This motivates the use of backstepping control on the underactuated quadrotor. Most backstepping architecture controls the quadrotor position and attitude independently, and couples them with inverse kinematics. Inverse kinematics computes the attitude angles required to achieve a desired acceleration. However unmodelled effects are shown to cause inexact inversion resulting in tracking error. The approach proposed in this paper uses a re-formulated full state cascaded dynamics to eliminate the need for inverse kinematics in a full state backstepping control architecture. It is shown that zero steady state error is achieved in the presence of unmodelled aerodynamics effect and wind disturbance despite no integral action. In addition, a backstepping formulation is derived using contraction theory that guarantees the boundedness of state response under bounded disturbances such as wind. This improves the system performance. Numerical simulations are performed using the proposed controller to track a target moving along predefined paths and the results are compared with a benchmark controller derived using inverse kinematics. The results show that the proposed controller is able to achieve better tracking performance under unmodelled aerodynamic effects and wind disturbance as compared with the benchmark controller.