  In this paper, we address the problem of enclosing an arbitrarily moving
target in three dimensions by a single pursuer, which is an unmanned aerial
vehicle (UAV), for maximum coverage while also ensuring the pursuer's safety by
preventing collisions with the target. The proposed guidance strategy steers
the pursuer to a safe region of space surrounding the target, allowing it to
maintain a certain distance from the latter while offering greater flexibility
in positioning and converging to any orbit within this safe zone. Our approach
is distinguished by the use of nonholonomic constraints to model vehicles with
accelerations serving as control inputs and coupled engagement kinematics to
craft the pursuer's guidance law meticulously. Furthermore, we leverage the
concept of the Lyapunov Barrier Function as a powerful tool to constrain the
distance between the pursuer and the target within asymmetric bounds, thereby
ensuring the pursuer's safety within the predefined region. To validate the
efficacy and robustness of our algorithm, we conduct experimental tests by
implementing a high-fidelity quadrotor model within Software-in-the-loop (SITL)
simulations, encompassing various challenging target maneuver scenarios. The
results obtained showcase the resilience of the proposed guidance law,
effectively handling arbitrarily maneuvering targets, vehicle/autopilot
dynamics, and external disturbances. Our method consistently delivers stable
global enclosing behaviors, even in response to aggressive target maneuvers,
and requires only relative information for successful execution.
