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This paper presents a solution for the problem of minimum time coverage of ground areas using a group of unmanned air vehicles (UAVs) equipped with image sensors. The solution is divided into two parts: (i) the task modeling as a graph whose vertices are geographic coordinates determined in such a way that a single UAV would cover the area in minimum time; and (ii) the solution of a mixed integer linear programming problem, formulated according to the graph variables defined in the first part, to route the team of UAVs over the area. The main contribution of the proposed methodology, when compared with the traditional vehicle routing problem’s (VRP) solutions, is the fact that our method solves some practical problems only encountered during the execution of the task with actual UAVs. In this line, one of the main contributions of the paper is that the number of UAVs used to cover the area is automatically selected by solving the optimization problem. The number of UAVs is influenced by the vehicles’ maximum flight time and by the setup time, which is the time needed to prepare and launch a UAV. To illustrate the methodology, the paper presents experimental results obtained with two hand-launched, fixed-wing UAVs.

The world is on the verge of a major breakthrough, as we reach a moment in history when UAV flights become regulated in many countries around the world. Companies from different fields are currently using UAV and sensor technologies to acquire information of ground regions and to reduce the time and costs of operation. Applications, such as environment monitoring, search and rescue, precision agriculture and surveillance, may benefit from this usage of UAVs with onboard sensors for spatial coverage [

This work, which was motivated and mainly financed by FINEP (Funding Agency for Studies and Projects), a funding agency of the Brazilian government, deals with one of the most common uses of aerial robot technologies, which is the one for obtaining a series of overlapping aerial images from the ground. These images are usually post-processed for the extraction of desired information, such as digital terrain maps and vegetation indexes. In this context, efficient UAV path planning algorithms are of great importance, since the operation time, costs and the quality of the information extracted from the images are directly related to the quality of such a planning. We propose an area coverage path planning strategy to obtain images of the ground considering a multi-UAV scenario.

Several area coverage strategies have been proposed in the literature. A comprehensive recent survey of methods can be found in [

The only optimization involved in the previously mentioned methods is in the choice of the order of cells to be followed. A simple form of path optimization is to choose the direction of the back and forth movements in each cell. This may reduce the number of turns in the path, thus reducing the effects of vehicle deceleration and acceleration due to each turn [

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Some researchers have focused on solutions that take into account multiple robots, such as the work in [

In general, a VRP is the problem of finding a set of routes to be executed by a set of vehicles that must visit a set of customers at different geographical locations, given a transportation road network. These routes must fulfill all of the customers’ demands of goods, satisfy the operational constraints and minimize an objective function that reflects the global transportation cost [

In [

This paper presents a methodology for optimal time coverage of ground areas using multiple fixed-wing UAVs. Similar to other works, we solve the coverage problem by creating a graph and transforming the original problem into a vehicle routing problem. The main contribution of this work is the incorporation of specific features that are relevant in a real-world deployment. We assume the common scenario in which the number of human operators responsible for launching and retrieving the UAVs is smaller than the number of vehicles. This is incorporated in the method by defining a so-called setup time. In some situations, the setup time prevents two UAVs from being launched within small intervals of time. This means that, since one operator cannot prepare more than one UAV at the same time, the setup time of each UAV is cumulative. For example, consider a mission with one operator, two UAVs and a setup time of

This paper is organized as follows.

In this paper, it is assumed that a group of

Given this, the specific problems we are dealing with in this paper are: (i) to discover the number

Our strategy for solving the problem presented in the previous section is divided into two parts. In the first part, we decompose the area to be covered as a set of sweeping rows, using a methodology similar to the one proposed in [

In this work, we assume that the UAVs will fly over the area to be covered executing a back and forth motion in rows perpendicular to a given sweep direction, as shown in

Coverage strategy used in this work. A rectangular area is covered using a back and forth motion along lines perpendicular to the sweep direction. Notice that the sweep direction highly influences the number of turns outside the area to be covered, thus affecting the coverage time. The optimal sweep direction is parallel to the smallest linear dimension of the area [

To find the optimal direction of coverage of a given polygon, a simple search procedure may be used. As shown in

Procedure to search the optimal direction of coverage. The area is rotated until the smallest height is found.

Once the optimal sweep direction is found, it is then possible to distribute the rows over the area. In our approach, the distance between two rows is chosen as a function of the footprint of the on-board cameras on the ground. As shown in

Relation between the size of the camera sensor, the height of flight and the camera footprint on the ground.

The number of coverage rows is then computed as:

Assuming that the polygon that represents the region is rotated in a way that the optimal direction of coverage is parallel to the

The extreme points of the coverage rows, along with the coordinates of the UAV launch position, called the base or depot, are considered to be the set of nodes

Graph representing the coverage problem. On the left, a rectangular region to be covered, the launch position and the covered rows. The nodes of the graph on the right are composed of the launch position and the intersection points between the coverage rows and the borders of the region. All nodes are connected by edges, forming a complete graph.

Mathematically, graph

Once a graph associated with the region to be covered is created, the coverage problem can be posed as a vehicle routing problem (VRP) [

Before presenting the mathematical formulation of the routing problem, we will define the constants and variables necessary for this formulation. As defined in the previous section, constant

Based on the variables previously defined, the time spent by UAV

Our main objective is to minimize the mission time. This can be accomplished by minimizing the time of the longest route among the routes of all UAVs. Therefore, our problem is in fact a min-max problem in which we want to minimize the maximum

As previously shown, constraint in Equation (

In Equation (

Since the setup time is one of the main contributions of this work, before proceeding with the additional constraints necessary to guarantee a coverage solution, we will explore the effect of constraint in Equation (

Notice that the cumulative setup time for UAV 3,

The second example explores the case when the number of operators is larger than one, but is smaller than the number of UAVs available. Suppose a team of

As can be seen, UAVs 1 and 2 have the same setup time, because the two operators will prepare them simultaneously. After the takeoff of these UAVs, UAVs 3 and 4 will be prepared. Their setup time is

In a third example, consider the case where the number of operators is equal to the number of UAVs. In this case, since

To complete the optimization problem and to guarantee its solution, a solution to the problem posed in

To guarantee that each node of the graph is visited only once by a single UAV, two other constraints are necessary:

Notice that constraint in Equation (

To enforce that each UAV path starts and finishes at the base (Node 1) and to guarantee that the path has no internal cycles, a standard sub-tour elimination constraint [

To make sure the VRP solution will make the UAVs cover the area modeled by graph

This constraint enforces that each UAV, having visited one of the nodes of a coverage row, must visit the other node of that row. This is possible given the way the nodes were numbered (see

To avoid the UAVs crossing the coverage area following an edge that is not parallel to the coverage rows, two optional constraints can be added to the optimization problem:

In practice, constraints in Equations (

Finally, to allow the number of UAVs used in the mission,

It is important to mention that constraints in Equations (

By solving the problem represented by the objective function in Equation (

The first one is a heuristic and depends on the adjustment of some constants. The idea is to change the utility cost function, so that it explicitly takes into account the number of UAVs and/or a combination of all UAV path costs. For example, the cost function

The second strategy, which will generate the optimal solution in terms of the number of UAVs and individual paths independently of parameter choices, is an iterative solution that consists of solving the optimization problem more than once. In the first iteration, the original graph is used, and the optimization problem to be solved is exactly the one previously presented. In the second iteration, the problem is reduced by removing the UAV assigned to the longest path in the first iteration, which is already optimal, and all nodes (except for the base) and associated edges that belong to its path. This procedure is repeated until all nodes, but the base, are removed from the graph. With this procedure, we have a better use of the available resources. It is then guaranteed that the optimal number of UAVs is found and that the paths for all UAVs are optimal without compromising the primary objective, which is to minimize the cost of the route with the highest cost.

In the next section, we present simulations that illustrate our methodology and the role of the constraints in the optimization problem.

This section intends to illustrate the proposed methodology using a series of simulations. All simulations were executed in MATLAB on an Intel Core i5 1.7 GHz computer with 4 GB of RAM. The optimization problem was solved using the Yalmip [

In our first simulation, we explore the cost function in Equation (

Effect of the cost function. (

Our second set of simulations explores the activation of constraint in Equation (

Effect of constraint in Equation (

The next simulation shows the effect of constraints in Equations (

Effect of constraints in Equations (

In what follows, we show the effects of constraint in Equation (

Two trivial solutions for the optimization problem. (

For the same coverage area and number of UAVs (

(

(

For the last set of simulations, we explore the effect of a number of operators larger than one and smaller than the number of available UAVs, using the same coverage area and number of UAVs (

We have tested our methodology in practice using two fixed-wing UAVs controlled by the 2128

Picture of one of the UAVs used in the experiments.

Coverage area used in the experiments overlaid on a satellite image.

In our first experiment, we use only one UAV (

Coverage of the area in

In the second experiment, we used two UAVs (

Coverage of the area in

For this specific area, it can be noticed that the gain in time to include an extra UAV was only

Coverage of the area in

This paper presented a methodology for the coverage and sensing of ground areas using fixed-wing UAVs. The main contribution of the method is that it explicitly and formally considers some practical problems that only appear during the deployment of the actual vehicles. The number of UAVs used in the task, for instance, is chosen as a function of the size and format of the area, the maximum flight time of the vehicles and, more importantly, the time needed to prepare and launch the UAV, which we call setup time. This time was never considered before in the solutions for this kind of problem, which frequently resulted in trivial solutions where the time of coverage is inversely proportional to the number of UAVs used. This is certainly not true in practice if the number of human operators is smaller than the number of UAVs to be launched.

It is important to mention that our methodology would not find a solution to the coverage problem in some situations, which include the ones where the number of UAVs and their battery life are small given the size of the area to be covered. In such a situation, it would be interesting to have a methodology that allows the UAVs to land, recharge and take-off again to complete the mission. This strategy is considered as future work.

It is also important to say that the UAV routing strategy proposed in this paper does not take into account possible collisions among the UAVs. To avoid collisions when the planned paths intersect, a velocity planner, such as the one proposed in [

The authors thank FINEP/Brazil, FAPEMIG/Brazil (Funding Agency for Research in Minas Gerais), and CNPq/Brazil (National Counsel of Technological and Scientific Development) for the financial support. The authors hold scholarships from CNPq/Brazil.

Gustavo Avellar was the main developer of the proposed methodology. He also performed experiments, analyzed the results and helped with writing this manuscript. Guilherme Pereira contributed with the methodology and was responsible for writing the manuscript. Luciano Pimenta contributed with the methodology and in the writing of the manuscript. Paulo Iscold participated in the experiments, analyzed the results and reviewed the manuscript.

The authors declare no conflict of interest.