Dual quaternion based trajectory tracking of underactuated multirotors

In this work we use dual quaternions to model and control the underactuated quadrotor vehicle. Exploiting the similarity between the dual quaternion formulation of the equations of motion with that of the quaternion formulation of attitude kinematics and dynamics, we derive a backstepping controller based on a quaternion-based attitude controller from literature. The control law solves the state feedback trajectory tracking problem while negating the need of generating a desired attitude trajectory to handle the underactuation. Employing the hand-position approach, the translational error is mapped directly onto the rotational actuators through a virtual frame, thus augmenting the system. More precisely, we show uniform asymptotic stability of the equilibrium points for the closed-loop augmented system without the presence of disturbances. The control law is applied to a simplified model of a quadrotor and simulation results illustrate the theoretical results.