# Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment
When planning a rapid-assessment route for each UAV, it is necessary not only to select the appropriate potential targets based on the priority of the potential target and the endurance of the UAV but also to determine the access order of the UAV to the assigned potential target to maximize the profit of the multi-UAV rapid-assessment routing scheme. The operations research (OR) model, including the team orienteering problem (TOP), can be used to solve this kind of UAV routing problem. However, in the classic TOP model, all vehicles start from the same start depot and return to the same end depot, which is different from the scenario studied in this paper. Since different UAVs are usually launched at different depots in the multi-UAV post-earthquake rapid-assessment scenario, we generalize the classic TOP model to the multi-depot TOP (MD-TOP) model, referenced to the multi-depot traveling salesman problem (MDTSP) model. The MURARP introduced and defined in this paper is a practical problem that is faced in the emergency rescue process in the post-earthquake scenarios. In general, UAV resources available for rapid assessment are limited; therefore, some teams use fixed-wing UAVs and some teams use quad-rotor UAVs. In order to reflect the generality of the model proposed in this paper, we assumed that the UAV swarm performing the rapid assessment task is composed of heterogeneous UAVs which are characterized by different endurance, speed, and turning radius. The heterogeneity of the UAV swarm is reflected in that each UAV has different kinematic constraints. However, the functionality of each UAV is the same, that is, to capture images of damaged buildings in different directions around the epicenter in the shortest possible time. Due to the kinematic constraints of the UAVs, it is necessary to guarantee the flyability of the UAV paths. Specifically, the flyable path refers to a twice differentiable curve [7]; otherwise, the assigned paths might become inefficient and might even be unflyable for UAVs [8]. Dubins [9] proposes a flyable path of minimal length for a UAV, constrained to move at a constant speed along paths of bounded curvature without reversing direction. Since this model satisfies the kinematic constraints of UAVs, it is widely used in UAV path planning [7,10,11]. In this paper, we extend the MD-TOP model to the multi-depot Dubins TOP (MD-DTOP) model. When solving the latter model, the constraints of UAV endurance and minimum turning radius must be considered, so when determining the access sequence of each UAV to the assigned potential target, the UAV heading angle when traversing each target must also be determined. In the process of performing the rapid assessment, there may be some uncertainties, such as the sensors carried by UAVs being out of focus, dithered, or overexposed, resulting in the images or videos acquired by UAVs being unrecognizable. Therefore, the effective information collected by UAVs during a single visit to a potential target is often insufficient, which may reduce the effectiveness of the rapid assessment in turn. For this reason, based on previous research results in the literature [12], the expected profit is introduced to describe the completion quality of the rapid assessment, and the target revisit-allowed strategy is introduced. The expected profit of the multi-UAV rapid assessment can be improved by selecting appropriate targets to access and optimizing the target access sequence, the heading angle of each UAV when traversing each target and the number of times the target was accessed. The MURARP can be described as follows: multiple heterogeneous UAVs are launched at different depots and return to their respective depot after selectively visiting some potential targets in the earthquake affected area.