Hovering Stability of Helicopters With Elastic Constraints

Aerial vehicles are difficult to stabilize, especially when acted upon by external forces. A hovering vehicle in contact with objects and surfaces must maintain flight stability while subject to forces imparted to the airframe through the point of contact. These forces couple with the motion of the aircraft to produce distinctly different dynamics from free flight. While external contact is generally avoided, extending aerial robot functionality to include contact with the environment during flight opens up new and useful areas such as perching, object grasping and manipulation. In this paper, we present a general elastic contact constraint model and analyze helicopter stability in the presence of those contacts. As an example, we evaluate the stability of a proof-of-concept helicopter system for manipulating objects using a compliant gripper that can be modeled as an elastic linkage with angular reaction forces. An off-the-shelf PID flight controller is used to stabilize the helicopter in free flight, as well as during the aerial manipulation task. We show that the planar dynamics of the object-helicopter system in vertical, horizontal and pitch motion around equilibrium are shown to remain stable, within a range of contact stiffnesses, under unmodified PID control.