## 1 Introduction  
This article introduces a ship defense strategy using a clustered formation of multiple drones. We handle a scenario where a high-speed target with variable velocity heads towards the ship. The role of the drone team is to protect the ship from the incoming target. We propose a ship defense approach with multiple drones, such that each drone is not equipped with powerful sensors or an on-board computer. Thus, a drone cannot measure the target, and the target moves based on the commands sent by the ship. In this way, we can decrease the cost of a drone, which can be destroyed once it intersects the target. This enables us to develop rather cheap drones. Instead, the ship measures the position of the target in real time. Position measurements can be provided by various sensors, such as radar, IR, or laser sensors of the ship. Each drone's guidance law is calculated by the ship's on-board computer and is transmitted to each drone in real time. (This approach relies on the communication between the ship and a drone. Since the signal speed is sufficiently fast (\(3\times 10^{8}\) m/s) in the air, we argue that signal delay is negligible in our ship defense scenario.) Consider a high-speed target whose goal is to hit a ship. The target heads towards its goal (ship) at least in the terminal phase. Otherwise, it is impossible to make a target hit the ship. Therefore, this paper lets multiple drones form a planar grid formation, whose center lies on the line segment connecting the target and the ship. Moreover, the planar grid formation is generated to be perpendicular to the line segment connecting the target and the formation center. The grid formation can be considered as a \"net\" structure for capturing the incoming target. The target may perform elusive maneuvers, and there may be measurement noise in measuring the target position. By maximizing the grid formation size, we can increase the capture rate, even when there exists error in the prediction of the target's position. Since the target is guided to hit its goal (ship), the drones can effectively block the target using this grid formation. As an interceptor, we consider a highly maneuverable drone, such as a quadrotor drone [1; 2; 3], which is much slower than the incoming target. This article addresses a high-level path planner, which generates reference position signals for a low-level controller [1; 2; 3]. To the best of our knowledge, our paper is novel in developing a ship defense approach using clustered multiple drones. Our paper is novel in addressing a 3D formation of multiple drones for intercepting a high-speed target with variable speeds. We show that in the case where the drones block the LOS line between the target and the ship, the target cannot reach the ship without being captured by the drones. Since the target is guided to hit its goal (ship), the drones can effectively block the target using this strategy. We further let slow drones stay close to the ship in order to protect the ship from the fast target. As far as we know, our paper is novel in showing that slow drones can capture a fast target by staying close to the ship while blocking the LOS at all times. Our paper is unique in capturing a maneuvering target with variable speeds, which can be faster than the interceptors. In order to estimate the pose of a maneuvering high-speed target, we applied target-tracking filters in [4]. We control the drone formation, based on the prediction of the target's position after one sample-index in the future. This prediction may be erroneous due to the target's elusive maneuvers or measurement noise. This is the motivation for utilizing a grid formation of drones instead of a single drone. Since we use a grid formation, we can increase the capture rate even when the target prediction is erroneous. By maximizing the grid formation size, we can increase the capture rate even when there exists error in the prediction of the target's position. To the best of our knowledge, our paper is novel in the following aspects:  
1.