ℒ1 Backstepping for Robust Trajectory Tracking*

This paper addresses the problem of making UAVs follow a prescribed trajectory in the presence of modeling uncertainties and external disturbances. The kinematics and dynamics of the trajectory tracking problem are in strict feedback form, appropriate for backstepping deisgn. While there is no uncertainty in the kinematics, rapidly changing uncertainties in the dynamics make this problem an ideal candidate for ℒ1 backstepping control. The trajectory tracking controller serves as the outer-loop in a cascaded design architecture and supplies a reference quaternion and thrust to the inner-loop controller. The inner-loop controller in turn generates a moment demand for the control allocation module. Such an inner-outer loop architecture is modular and does away with the requirement that the commanded trajectory be four times differentiable as would be required if a single monolithic backstepping control law were to be used. Simulations are used to demonstrate the performance of this controller in comparison to a conventional backstepping controller.