3D Guidance Law for Flexible Target Enclosing with Inherent Safety

In this paper, we address the problem of enclosing an arbitrarily moving target in three dimensions by a single pursuer while 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 and excluding 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. 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. Further, we demonstrate the effectiveness of the proposed guidance law in managing arbitrarily maneuvering targets and other uncertainties (such as vehicle/autopilot dynamics and external disturbances) by enabling the pursuer to consistently achieve stable global enclosing behaviors by switching between stable enclosing trajectories within the safe region whenever necessary, even in response to aggressive target maneuvers. To attest to the merits of our work, we conduct experimental tests with various plant models, including a high-fidelity quadrotor model within Software-in-the-loop (SITL) simulations, encompassing various challenging target maneuver scenarios and requiring only relative information for successful execution.