Unmanned aerial vehicle based low carbon monitoring planning
Introduction
Traditionally, there are two methods to monitor an area. The first one is monitoring by patrol agents. This method is very flexible and easy to implement. However, it has two significant drawbacks. The first drawback is that some areas are difficult to access or dangerous, limiting the applicability of monitoring by patrol agents. The other problem is the high manpower costs of safety specialists, especially in developed countries. The second method to monitor is to use video cameras, e.g., at the entrance of residential buildings and at metro stations. Using video cameras can reduce the manpower costs, as a person in a central control room can monitor the scenes in several cameras at the same time. Moreover, video cameras can conduct monitoring tasks on a 24/7 basis. A shortcoming of using video cameras is that the locations of video cameras are fixed. Even though some video cameras can rotate and shoot in many directions, they can still monitor only a limited region. It is practically impossible to install so many cameras that all corners of an area of conern are monitored. By contrast, patrol agents can monitor a much larger area, though not on a 24/7 basis. Another drawback of using video cameras is that they can effectively work only with sufficient light in the monitored area.
In recent years, using unmanned aerial vehicles (UAVs) that carry video cameras to carry out monitoring tasks integrates the advantages of the above two approaches [13], [11]. UAVs equipped with cameras can provide a bird-view of locations and acquire image data efficiently, and thus are able to monitor a large area with low manpower costs. Due to these advantages, UAVs, as a low-cost low-carbon alternative to carry out monitoring tasks, have been used in a number of applications. When a natural disaster occurs, UAVs can be used to monitor the affected area and obtain data on the extent of damage [14]. UAVs can patrol land borders and shorelines between two countries [8]. In agriculture, UAVs can inspect farm conditions for soil and yield analysis [15]. In built environment, UAVs equipped with infrared imaging are used to monitor the heat transfer of building blocks [16]. In this study, we will develop models to plan a UAV for carrying out monitoring tasks.
A building block in UAV routing is obtaining the flying time between two points. Li et al. [9] examined a three-dimensional UAV path planning problem in which a UAV travels from one point to another point in an indoor environment while keeping a certain distance from obstacles. They developed A*-based algorithms to identify the shortest path and the path whose height above the floor and stairs is minimized.
Some researchers have concentrated on optimizing UAV routes for monitoring a set of nodes, arcs, or an area. In the category on node monitoring, Kim and Lim [8] proposed a UAV border monitoring concept in which electrification line systems to wirelessly charge drones are deployed. Drones must visit a sequence of nodes considering battery capacity constraints. A mixed-integer linear programming model is developed to determine the locations to install the electrification line systems. Zhen et al. [26] investigated a routing problem in which UAVs monitor a set of nodes with different accuracy requirements, and in which the height at which a UAV visits each node is optimized as it affects the accuracy level of monitoring. A tabu search metaheuristic approach is developed for the problem. Xia et al. [22] examined the routing of a fleet of UAVs for monitoring air emissions from a set of vessels (nodes). Different from many routing studies, the vessels are moving rather than standing still. A space–time network model is developed to formulate the problem, which is solved by a Lagrangian relaxation-based method. Shen et al. [17] have developed path planning models for multi-UAVs to detect air pollution from ships in ports.
In some situations UAVs monitor not nodes, but arcs, such as road segments, power transmission lines, and territorial borders. Chow [4] and Li et al. [10] have studied the routing of a fleet of UAVs to monitor vehicle traffic on a set of road segments (arcs) over multiple periods. The problem is formulated as a mixed-integer linear program and solved by approximate dynamic programming in Chow [4] and a local branching algorithm in Li et al. [10]. Campbell et al. [1] pointed out that an arc can be monitored by more than one UAV because UAVs can travel directly between any two points.
Some studies have examined the routing of UAVs to monitor an area. Yang et al. [24] studied the design of a UAV route to monitor a target area with the aim of minimizing the total flying distance. They divided the area into discrete squares, whose side length is small enough to ensure a UAV can monitor a whole square when it flies along its center line. A modified ant colony optimization algorithm is developed to design the UAV route that passes all the discrete squares. Wang et al. [21] examined the routing of UAVs to monitor disjoint areas over an extended time horizon, in which each area is divided into a number of cells and must be revisited within a time period. The problem is solved by a multiobjective evolutionary algorithm.
UAV monitoring planning is also related to the locations of airbases. Vural et al. [20] considered the problem of determining the locations of airbases of UAVs that are used for surveillance. The functioning of the airbases depends on the weather conditions, which are random by nature. They developed a two-stage stochastic integer linear program to determine the locations of airbases considering uncertainty.
Given that UAVs have very limited flying time and distance, vehicles are used to transport and launch UAVs, improving the overall efficiency. Carlsson and Song [2] examined the coordination between a truck and a UAV. Hu et al. [7] proposed a vehicle-assisted multiple-drone routing problem and designed a heuristic solution approach.
In the above studies, the flying speed of the UAVs is assumed known and constant. We complement these studies by focusing on optimizing the speed of a UAV. Cheng et al. [3] modeled drone energy consumption as a function of payload, which is not applicable to our setting of surveillance. Yi and Sutrisna [25] examined a drone speed optimization problem based on dynamic programming, whereas our solution approach has elegantly taken advantage of the problem structure, offering new insights into the problem.
Section snippets
Objectives and contributions
The objective of this research is to propose a model for planning the speed of a UAV to ensure effective monitoring. We consider a UAV that flies along a fixed path and optimize the flying speed of the UAV. The flying speed of the UAV is optimized to ensure that the UAV spends the most time monitoring important segments on the path, subject to constraints that the UAV completes the path without depleting its battery. The contribution of the paper is that we propose an infinite-dimensional
Problem description and optimization model
A UAV flies along a fixed path to monitor an area of interest. We use Fig. 1 to illustrate an area of a construction site and use Fig. 2 to illustrate the fixed path. The length of the path is (m), where the starting and ending points are both the depot of the UAV.
The UAV must complete the monitoring tasks along the path in time (s). The minimum flying speed of the UAV is (m/s) and the maximum flying speed is (m/s). The battery of the UAV has an energy capacity of (kWh), and the
Solution method
Model [P1] is challenging to solve because its decisions are not scalars or vectors but functions. In other words, model [P1] is an infinite-dimensional optimization problem. Moreover, there are integration operations in the objective function (1) and constraints (2), (4), and (5), which all add to the complexity of the problem. To address the challenges, we examine the properties of the problem and develop a tailored solution method based on these properties.
Computational experiments
We carry out a case study to demonstrate the applicability of the proposed model and algorithm. The layout of the construction site is shown in Fig. 1, the path of the UAV is shown in Fig. 2, and the path is divided into 11 segments, as shown in Fig. 3. The lengths of the 11 segments are shown in Table 2. Segments 2, 4, 6, 8, and 10 correspond to Building II, rebar bending yard, material storage area, carpentry workshop, and Building I, respectively. Therefore, these five segments require
Conclusions
This study has proposed a UAV monitoring planning problem in which a UAV flies on a fixed path. The flying speed of the UAV is optimized to ensure that the UAV spends the most time monitoring important segments of the path while ensuring that the UAV completes the path within a certain time and without depleting its battery. The contribution of the paper is that we propose an infinite-dimensional optimization model for the UAV monitoring problem and transform the model into a linear programming
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This study is supported by Massey University Research Fund (MURF) RM20721.
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