Unmanned aerial vehicles (UAVs), commonly known as drones, have drawn significant consideration thanks to their agility, mobility, and flexibility features. They play a crucial role in modern reconnaissance, inspection, intelligence, and surveillance missions. Coverage path planning (CPP) which is one of the crucial aspects that determines an intelligent system’s quality seeks an optimal trajectory to fully cover the region of interest (ROI). However, the flight time of the UAV is limited due to a battery limitation and may not cover the whole region, especially in large region. Therefore, energy consumption is one of the most challenging issues that need to be optimized. In this paper, we propose an energy-efficient coverage path planning algorithm to solve the CPP problem. The objective is to generate a collision-free coverage path that minimizes the overall energy consumption and guarantees covering the whole region. To do so, the flight path is optimized and the number of turns is reduced to minimize the energy consumption. The proposed approach first decomposes the ROI into a set of cells depending on a UAV camera footprint. Then, the coverage path planning problem is formulated, where the exact solution is determined using the CPLEX solver. For small-scale problems, the CPLEX shows a better solution in a reasonable time. However, the CPLEX solver fails to generate the solution within a reasonable time for large-scale problems. Thus, to solve the model for large-scale problems, simulated annealing for CPP is developed. The results show that heuristic approaches yield a better solution for large-scale problems within a much shorter execution time than the CPLEX solver. Finally, we compare the simulated annealing against the greedy algorithm. The results show that simulated annealing outperforms the greedy algorithm in generating better solution quality.

Unmanned aerial vehicles (UAVs) have been widely adopted in civilian and military application domains [

The terrain coverage is one of the most essential tasks of drones, which has been engaged in many applications, such as disaster management, photography, and intelligent agriculture [

The goal of the CPP mechanism is to seek an optimal collision-free flight path so that full coverage of a given region is guaranteed under specific constraint conditions, which is considered as a complicated global optimum problem. It is noteworthy mentioning that the quality of area coverage alone is not the exact metric for achieving high-quality missions. Instead, several operational objective goals, constraints, and restrictions have to be jointly optimized. The constraints and objectives are the two aspects that underpin any mission planning. The overall outputs quality from a mission mainly depends on optimizing final planning to account for both constraints and objectives. These constraints and objectives are required in mission planning for deriving a detailed agenda for a drone in terms of how it should be traveling through an ROI.

Despite UAVs’ ample applications, the onboard energy has fundamentally limited UAV performance and endurance, which is practically finite [

Several applications have outgrown the capability of a single drone. Thus, coverage efficiency has been significantly improved by deploying multiple UAVs. This is because multi-UAV provides more significant advantages over a single UAV in CPP robustness enhancing and operational time minimization [

Although adapting the swarm of drones in coverage path planning achieves flexibility enhancement and cost reduction in practical applications development, carrying out their path planning in a complex and large-scale environment increases the complexity of collaborative control and decision-making systems [

For handling multiple constraints, many approaches in the literature have formulated the CPP problem based on mixed-integer linear programming (MILP) [

To handle this issue in a tractable manner, we propose a coverage path planning algorithm that aims to achieve full coverage of the ROI. To this end, in a large-scale problem size in which the exact solution fails to find a solution in a reasonable time, a heuristic approach is implemented to address a large-scale problem in a reasonable time. Most research has focused on obtaining the shortest path coverage and neglected the energy consumption, which depends mainly on acceleration, deceleration, distance, and speed of the drone. To fill this gap, a more accurate model with energy consumption constraints is provided to calculate the energy-efficient optimization trajectory. The problem is formulated as a MILP based optimization problem. The proposed approach composes of two phases. In the first phase, the AOI is decomposed into small cells, known as Point of Interests (PoIs), where the centers of these cells are called waypoints. The cells that constitute the ROI are covered in the second phase when a UAV passes through their centers.

The contribution of this work can be summarized as follows:

We develop an optimization formulation of single and multi-UAVs coverage path planning. Mixed-integer linear programming is utilized to formulate the CPP problem as a minimization problem, where the energy consumption is used as the objective to be minimized. The proposed approach can reduce energy consumption which in turn reduces the required number of drones to cover the ROI. Since the turns have a significant effect on energy conservation, the number of turns is included in the objective function to be minimized.

The collision avoidance mechanism is proposed to avoid collision with terrain obstacles by designing the required constraints in the proposed formulation. As a result, the proposed CPP approach not only determines the optimal flight path for UAVs but also avoids collision with region obstacles that guarantee to complete the task safely. The proposed CPP problem is solved using the exact approach, i.e., CPLEX solver, and a heuristic approach, i.e., simulated annealing and greedy approaches. The results are analyzed and compared.

The proposed approach considers small and large ROI and uses single and multiple drones. In a single UAV scenario, the proposed approach provides multiple trips for a large regional area. Particularly, if the energy of the UAV is not sufficient to cover the whole region, the UAV is allowed to return to the depot and recharges its battery to start the next trip till completing the coverage mission. For multiple UAVs, the proposed approach provides a decomposition mechanism to decompose the region into sub-regions and allocate the sub-regions to the available UAVs. The region allocation aims to balance the energy consumption and reduce the completion time. The sub-regions are created to minimize the overall energy consumption for coverage. For UAV safety, the proposed CPP approach provides an energy calculation or constraint so that the drone can safely return to the depot for recharging.

The remainder of this paper is structured as follow:

UAV’s coverage path planning problem has been studied extensively in the literature, including energy consumption, terrain shape, and internal obstacles. The optimization solutions for the energy-efficient coverage path planning problem aim to develop new control algorithms that reduce the UAV’s energy consumption during its mission. The flight time is extended, and the energy consumption is minimized through minimum-energy paths design followed by aerial vehicles. For real situations, it is specifically important to realize that UAV operates under a battery-powered limitation [

In [

In [

An energy-aware coverage path planning mechanism was proposed in [

The work in [

The heuristic mechanisms are widely studied in the literature for coverage path planning problems, such as particle swarm optimization [

In [

In most research, the authors have focused on obtaining the shortest path coverage and neglected the energy consumption, which depends mainly on acceleration, deceleration, distance, and speed of the drone. Some literature works achieved enhancement in the performance of region coverage, such as completion time, region coverage maximization, and energy consumption. However, the optimization of energy consumption is not fully addressed. Although fewer works consider the energy consumption, they neglect considering many aspects such as a swarm of UAVs, the number of turns in energy optimization objective, or collision avoidance. It is worth emphasizing that collision avoidance has a significant impact on energy consumption and might increase the number of turns to avoid colliding with the target obstacles. To fill these gaps, we propose an energy-efficient coverage path planning approach to fully cover the target region considering single and multiple drones with minimum energy consumption. To do so, a more accurate model with energy consumption constraints is provided to calculate the energy-efficient optimization collision-free trajectory. To further optimize the flight path and minimize energy consumption, the sub-region allocation is proposed to optimize the allocated sub-regions to the available drones so that the overall energy consumption is minimized.

In spite of significant features of UAVs, the full potential of their applications is still hindered. The limited lifetime of drones due to onboard battery-powered is considered the main limitation [

The energy model for a quadrotor drone in [

The flying vertically up or climbing energy for

The flying vertically down or descent energy for

The hovering in place energy from time

The flying horizontally is given as a function of velocity and can be expressed as follows:

The power and the time needed during rotations were measured. Besides, the angular speed

Therefore, the energy can be written as follows:

The total energy of a drone can be simply obtained as

The coverage path planning algorithm needs to find the optimal coverage path from a base station, i.e., depot, covering the target region and then returning to the depot. Specifically, the best order of the path waypoints is determined. To do so, the proposed coverage path planning approach composes of two stages. In the first stage, the ROI is decomposed into small cells, which need to be surveyed by UAV. Then the problem is formulated and solved using both exact and heuristic solvers in the second stage. The proposed coverage path planning framework is shown in

In the first stage, the proposed approach decomposes the target region into cells, called PoIs, based on the drone camera footprint. Then, the path is planned in the coverage path planning stage, i.e., second stage, where the problem is formulated based on MILP and solved by both exact and heuristic approaches. Due to the complexity of the exact solver, the maximum CPU time is set to a reasonable time, and the best solution of all (exact and heuristic) is selected. The output ofthe algorithm is a collision-free path that guarantees covering the target region. The pseudo-code of the proposed approach is described in Algorithm 1. It starts with the initialization part that receives the region boundaries and uses a decomposition strategy to generate the waypoints of the path, and then obtains the energy matrix. In the second stage, as shown in

To achieve a better coverage, the ROI is decomposed into cells. The cell size is determined by UAV’s camera footprint and can be fully covered when a UAV is passing through its center, as illustrated in

Given a ROI, depot, and UAVs, the aim is to minimize the energy consumption and maximize the coverage region simultaneously. The output of the proposed path planning algorithm is the optimal collision-free flight path with minimum energy consumption for all drones with the following requirements: UAVs can refuel at a depot, i.e., base station. Moreover, the UAVs take off and land at the depot. To this end, the following assumptions are made:

The flight trajectory for UAV is planned in a static manner. In other words, the path of a UAV is planned in advance, i.e., before the beginning of a mission.

The drone is equipped with a download-facing camera with its coverage capacity known in advance.

The drone flies at a fixed altitude, and thus, the problem has been simplified into 2D CPP problem.

The ROI can be any shape, squire, circle, polygon, etc.

The objective is to fully cover the ROI with minimum energy consumption. Hence the objective function is a minimization problem. Moreover, the decision variables are inspired by the classical MILP formulation.

Let

The decision variable

The objective of these constraints is to generate a collision-free path so that the ROI is fully covered with minimum energy consumption, i.e., minimization problem. Thus, the objective function considers both coverage and drone’s safety mission, i.e., collision avoidance with terrain obstacles.

With this definition, the formulations of MILP are listed below.

The objective function is a minimization problem and can be formulated as

Subject to the following constraints:

The objective function in

In multiple UAVs, the large region is decomposed depending on the available number of drones. This step aims to prevent drones from intra-collision and balance the energy consumption for different drones. To do so, the region is decomposed into M cells, which are grouped into N groups, i.e., N sub-regions, where the number of sub-regions is equal to the number of drones. The allocation algorithm is illustrated in Algorithm 2. The algorithm receives the region coordinates and the available number of drones, and return the optimal allocation of sub-region to the available UAVs. Without loss of generality, the sub-regions or groups are created as follows:

To elaborate, assume that two UAVs are available. The whole region is divided into two groups that are determined with different colors, as illustrated in

For further optimizing the energy consumption, we further optimize the assigned group to UAVs. To clarify, the waypoints in different positions are swapped and the crossover between different groups is done so that the overall energy cost is minimized as explained in Algorithm 2 (Optimize (SubR)). It has to be stressed that in multiple UAVs starting from the same depot as shown in

The problem formulation of the proposed coverage path planning approach is similar to Vehicle Routing Problem (VRP) which is an NP-Hard problem. The aim is to fully cover the ROI by passing through all waypoints, and minimizing energy consumption.

The exact solution will achieve the best trajectory for drones by completely exploring the solution space if no time limit is set. For small-scale problems, the solution can be obtained within acceptable time consumption. Unfortunately, the solution space is significantly exploding for large-scale and complex system problems, resulting in an inefficient application of such formulation due to the required time consumption. Therefore, the linear programming-based formulation efficiency is unacceptable, especially in large-scale cooperative real path planning. To handle this issue in a tractable manner, we propose implementing simulated annealing [

This section, will explain these meta-heuristic approaches to solve the formulated CPP problem.

One approximation approach for solving the large-scale coverage path planning is simulated annealing. The SA [

The SA starts with an initial part that is responsible for initializing the algorithm’s parameters such as initial temperature, stop temperature, and damping rate of the temperature. The initialization part is also responsible to create the initial path, i.e., sequence of waypoints to be followed. It receives parameters and constraints and the best path that achieves the full coverage of ROI with minimum energy consumption is returned. For each iteration, a new solution, i.e., path, is generated from the current solution neighborhood, and the feasibility of the new solution is checked for ensuring that no constraint is violated. Then, the feasible solution is assessed by the objective function and the best solution so far will be stored with the corresponding fitness, i.e., energy consumption. Otherwise, the feasible solution will be accepted as a new solution with probability

It has to be stressed that the order of two cells’ positions is randomly exchanged to generate a new solution. Then the transition will occur if the quality of the current solution, i.e., the energy consumption of the new path, is better than the best solution. In the Metropolis criterion, the iteration process is controlled by the temperature

The greedy algorithm is an iterative heuristic that obtains a local optimum at each iteration. It is used to address optimization problems, where a solution is constructed through a sequence of available choices. At every step, once the choice is made, subsequent steps are not changed [

In this section, the correctness and efficiency of the proposed approach are verified. The exact solution is compared against heuristic approaches, i.e., SA and greedy. The comparison includes execution time and energy consumption, important metrics in coverage path planning, for a different number of waypoints.

To investigate the ability of the three methods used in the proposed approach in finding the optimal solution of the coverage path planning problem, the execution time that represents a key factor for evaluating the performance, is tested. The average execution time for 10 replications is illustrated in

It can be observed that the execution time of the three methods goes up simultaneously as the ROI size increases, demonstrating the effect of problem size on execution time. It is worth emphasizing that the greedy obtains a locally optimal solution by looking for the best solution to find a globally optimal solution. Consequently, it needs a shorter time to generate the solution. On the other hand, the exact solution obtains the best solution for drones by thoroughly exploring the solution space.

For small-scale problems, the exact solution can be obtained within acceptable time consumption, while in large-scale and complex system problems, the solution space is significantly exploding, resulting in an inefficient application of such formulation due to the required time consumption to find the exact solution. This fact is depicted in

Energy consumption is recognized as an essential metric for evaluating the performance of algorithms. It reflects the ability of the proposed approach to generate an efficient collision-free path. The drone flies from the depot covering every waypoint and returns. The visited sequence of waypoints is selected so that the overall energy consumption is minimized while avoiding obstacles’ collision and intra-swarm collision (in the case of multi-UAVs). Firstly, we show how the proposed approach contributes in maximizing energy saving. The CPP problem is formulated as a minimization optimization problem where energy consumption is used as the objective to be minimized. Therefore, the proposed approach minimizes the energy consumption, i.e., maximizes the energy saving of drone, during iterations. At the end of the last iteration, the generated path guarantees minimum energy consumption. This claim is proved in

As can be clearly seen in

To analyze the optimal solution of the proposed model, the average energy consumption of 10 replications is shown in

For further analyzing the optimal solution of the proposed model, the optimality gaps between CPLEX solver and heuristics are calculated and the results are recorded in

Energy consumption | Gap% | ||||
---|---|---|---|---|---|

WP | CPLEX solver | SA | Greedy | SA | Greedy |

10 | 3320.9 | 3673.633 | 3769.768 | 9.61 | 13.51 |

20 | 6829.37 | 7286.015 | 8929.121 | 6.68 | 30.74 |

30 | 11061.58 | 11430.86 | 17521.43 | 3.34 | 58.39 |

40 | 25874.82 | 14264.6 | 24981.7 | −44.87 | −3.45 |

50 | 35200.95 | 17693.87 | 28894.24 | −51.30 | −18.97 |

Owing to the complexity of the CPLEX solver, i.e., exact solution model, the maximum CPU time is set to 3600 s. The average optimal solutions of 10, 20, 30, 40, and 50 waypoints are shown. Both greedy and SA could achieve the optimal solutions in a significantly shorter time than the CPLEX solver. For large scenarios where number of waypoints is greater than 30 waypoints, i.e., 40, 50 waypoints, the CPLEX solver cannot solve for optimality in reasonable time while heuristic approaches yield a solution with a gap of (44.8707% and 51.308%) for SA and (3.45% and 18.97%), for greedy. The percentage gap shows that in a small number of waypoints, i.e., small region, the CPLEX solver achieves a better solution than heuristics. The negative sign of Gap% indicates poor solution by CPLEX solver, when the number of waypoints exceeded 30 waypoints.

To further illustrate the impact of execution time on the quality of energy consumption, we plot the energy consumption with respect to number of waypoints, 10 to 50 waypoints, and the result is highlighted in

In this subsection, the terrain involves two static obstacles. The proposed approach generates a feasible collision-free path, which achieves the objective and satisfies all constraints. The generated collision-free path covers the whole region with minimum energy consumption, as illustrated in two-dimensional views in

It is worth noting that considering the collision avoidance with obstacles impacts the drone’s energy consumption and might increase the number of turns to avoid colliding with terrain obstacles. This fact can be easily seen in

To further analyze the effectiveness of the proposed region allocation approach on energy conservation, we discuss the impact of region allocation on reducing the energy consumption to cover the ROI. The optimal solutions of different region sizes are obtained and recorded in

Region area (m^{2}) |
No RA optimization | RA optimization | Improvement gap % |
---|---|---|---|

7168 | 19807.65263 | 19481.0597 | 1.648822 |

9072 | 24844.04037 | 24396.02768 | 1.8033 |

11200 | 29556.10933 | 28690.02266 | 2.930314 |

13552 | 35392.05027 | 34085.57421 | 3.691439 |

16128 | 42681.06277 | 41132.89634 | 3.627291 |

18928 | 49012.12125 | 48129.767 | 1.800278 |

21952 | 57948.43785 | 56950.48396 | 1.722141 |

25200 | 65112.06962 | 65101.67432 | 0.015965 |

28672 | 74981.2094 | 73353.79255 | 2.170433 |

32368 | 86464.31403 | 83104.89846 | 3.88532 |

36288 | 94563.97185 | 94120.23399 | 0.469246 |

To show the performance of the proposed approach in addressing small and large region areas, different scenarios involving single UAV and multi-UAV with the small and large region are presented.

Single UAV coverage path planning performance evaluation.
In this scenario, the drone is flying from the depot (we consider the starting waypoint of the coverage path as the depot), covering all waypoints, and then returns to the depot, i.e., the region is covered in one trip, as illustrated in

Multi-UAV coverage path planning performance evaluation.
In this scenario, three UAVs are assumed to be available. Thus, the ROI is divided into three parts, and each drone is tasked to cover a set of waypoints as explained above in

In this paper, we developed an energy-efficient coverage path planning approach that considered different region sizes. Firstly, an optimization formulation of single and multi-UAVs coverage path planning was formulated as a minimization problem, where energy consumption was used as the objective to be minimized. The number of turns was included in the objective function for further minimizing energy consumption. Furthermore, the collision avoidance mechanism was proposed to avoid collision with terrain obstacles by designing the required constraints in the proposed formulation. The exact formulation for CPP was proposed based on MILP to seek the optimal trajectories for drones so that the generated path minimizes the energy consumption and satisfies all constraints during the mission. The proposed approach was able to efficiently decompose the ROI into sub-regions. The proposed sub-regions allocation strategy contributed in reducing energy consumption. The MILP-based formulation was solved using CPLEX solver and heuristic approaches, i.e., simulated annealing and greedy algorithms. Several scenarios were studied to verify the correctness of the proposed approach. The results showed that in small problem sizes, both exact and heuristic approaches were able to generate collision-free paths for UAVs, and the CPLEX solver outperformed the heuristic approaches. However, in large-scale problems, the CPLEX failed to generate the optimal solution in a tractable time. Additionally, the results showed that simulated annealing with energy optimization used less energy consumption than the greedy mechanism. Furthermore, the results illustrated that energy conservation was more prominent as the region size increased.

In future work, the proposed model will be extended by considering multiple separated regions and different depot locations.

The authors would like to acknowledge the support of the Interdisciplinary Center of Smart Mobility and Logistics, and the Department of Computer Engineering at King Fahd University of Petroleum and Minerals for the support of this research.

This research was funded by Project Number

The authors declare that they have no conflicts of interest to report regarding the present study.