Circumnavigation of an unknown target using UAVs with range and range rate measurements

This paper presents two control algorithms enabling a UAV to circumnavigate an unknown target using range and range rate (i.e., the derivative of range) measurements. Given a prescribed orbit radius, both control algorithms (i) tend to drive the UAV toward the tangent of prescribed orbit when the UAV is outside or on the orbit, and (ii) apply zero control input if the UAV is inside the desired orbit. The algorithms differ in that, the first algorithm is smooth and unsaturated while the second algorithm is non-smooth and saturated. By analyzing properties associated with the bearing angle of the UAV relative to the target and through proper design of Lyapunov functions, it is shown that both algorithms produce the desired orbit for an arbitrary initial state. Two examples are provided as a proof of concept.