Feedback tracking control schemes for a class of underactuated vehicles in SE(3)

A trajectory tracking control scheme for a class of underactuated vehicles is presented here. The underactuated vehicle is modeled as a rigid body to which control thrust is applied along a single body-fixed axis and control torque can be applied along all three body-fixed coordinate axes. The combined rotational and translational motion of the rigid body is underactuated with the degree of underactuation two. Such an actuation scheme is reflective of a wide range of vehicles such as vertical take-off and landing (VTOL) aircraft, fixed-wing aircraft, and quadcopter uncrewed aerial vehicles (UAVs). For this class of underactuated vehicles, the proposed controller gives exponential stabilization of the position tracking error. Additionally, the component of the angular velocity parallel to the thrust direction, is regulated to be zero under the proposed control scheme. The other two components of the angular velocity track desired profiles that lead to exponential stabilization of the desired position trajectory; this angular velocity tracking control scheme is finite time stable. The combination of these schemes leads to guaranteed exponential stability of the overall feedback control scheme. A set of numerical simulation results that illustrate the performance of the overall feedback tracking control scheme is provided.