Inter-Object Navigation of Unmanned Aerial Vehicles to Increase the Efficiency and Accuracy of Inspection of Power Lines

. The purpose of the work is to improve the accuracy and efficiency of a power line section inspection for a fault detection using unmanned aerial vehicles. The goal was achieved by using a unified computing and measurement platform on multicopter and aircraft drones and by simplifying the interaction between them and by using the inter-object navigation sensors. The most significant results were the development of a method of route planning by drones over different parts of the power grid and a method of inter-object navigation. The drone route planning problem was represented by a multi-agent variation of the classical traveling salesman problem and was solved by the ant colony method. The method of inter-object navigation was distinguished by the representation of the power grid topology by high and low intensity graphs, involving a different number and types of drones in the inspection process. The application of the developed methods made it possible to increase the accuracy of power line inspections by 27-73%, and the efficiency by 2-8 times. Solving the problem of multi-criteria optimization of the drone team flight route planning made it possible to reduce the cost of monitoring critical infrastructure facilities while improving its efficiency and accuracy. Thus, the conducted research has shown the effectiveness of the proposed approach for the monitoring of power facilities, route selection, number and composition of search teams. The direction for further research is to improve the ant algorithm.


INTRODUCTION
The development of modern civilization has entered the phase of smart cities construction.Their elaboration requires integration and the best usage in practice of several intellectual solutions in various regions.In this context, recently the studies of 'smart' power grids were carried out.This advanced generation of the energy systems must maintain the optimum output throughout all the cycle stages, including energy consumption and energy transmission.
Rapid economic development of territories and urbanization have led to an abnormal increase in demand for electricity consumption, which requires a high level of electrical supply reliability.High-voltage power transmission lines, as the connecting element between production and consumption nodes, play an important role in the overall performance of the electrical grid.
Most of the high-voltage transmission lines, for reasons of environmental protection, safety, cost savings in construction, etc., are located far from main roads, production, and residential centers.Therefore, the search for more efficient and cost-effective ways of inspecting transmission lines is one of the most important stages in electricity management.
To check electrical equipment, pedestrian patrols or helicopter surveys are usually carried out [1,2,3].The first method is quite slow and mainly ineffective.Helicopter inspections are much faster.However, since they cannot hover at a short distance from energy systems, it is quite problematic to get reliable measurements visually or with other sensors.
The rapid development of automation and artificial intelligence technologies in recent years has highlighted the inspection of transmission lines with unmanned aerial vehicles (UAVs) as a viable alternative method [4,5].
Power lines are extensively inspected using UAVs in China.In the provinces of Shandong and Ganzhou, intelligent control systems based on small drones equipped with HD cameras and infrared thermal imaging are successfully applied to 220 kV and 500 kV transmission lines [6].
To maintain optimal power network performance, it is necessary to reduce the time it takes to detect and repair faults on the network.Known power line inspection methods can be replaced or improved with the use of recent advances in science and technology.With this goal in mind, it is proposed to investigate the construction of a UAV-based robot for monitoring conditions and, if possible, carrying out some urgent maintenance procedures on various components of energy systems.
The aim of the article is to increase the accuracy and speed of inspecting a power network section to detect faults using UAVs.
We will consider existing approaches to solving similar problems.

PUBLISHED LITERATURE ANALYSIS
In most of the analyzed studies [7][8][9][10][11], the UAVs are only considered as an element of the system for checking the state of high-voltage transmission lines.If any defects are detected in them, no technical maintenance scenario is carried out.
Attempts have been made to determine the mission of the drone to improve its planning efficiency and pre-model the inspection [12].
Primitive methods of digital image processing are used to locate the connections of transmission lines: background subtraction and morphological operations.However, this method is considered unstable when consecutive images of the same scene from different scales or orientations are captured [7].
The Kalman filter and the Hough transform are used to track the state of transmission lines based on the flow of the video stream [9] Acceptable results were obtained in the study of the state of power grids using a multi-channel groundmatching BPL system relying on a laser radar [10].
When moving along cables to read the state of electrical components from close range and achieve the required maintenance quality, an alpine robot [13] is proposed.However, this type of platform is slow and has many mechanical difficulties when moving along lines located in the forest.
Recently, a hybrid alpine-flying robot has been proposed, which combines the advantages of UAV and ROW robots on one platform [14].
The verification of power transmission lines usually takes place in two stages: data collection and fault detection.The key direction of the research is the automation of the verification process.It is also carried out in two ways -a) selection of the type of robotic platform and b) development and modification of computer vision algorithms.
At the second stage, faults in the power line infrastructure [20] are usually detected at the base station using automation tools, specifically in electrical wires [21], supports [22], insulators, conductors, clamps, etc.
Currently, research on detecting power transmission lines themselves to identify sags and proximity to vegetation or man-made constructions is relevant.The image pre-processing strategy is to detect line candidates and segments search, which form the electric transmission lines' parts [22], [23] Some researchers have also focused on detecting and segmenting electrical poles on images [16] [17], [22], [23].Similarly to the detection of the electric transmission lines, the pre-processing stage in this case usually includes the determining of location of line sections on the image.
Therefore, the analysis conducted suggests the feasibility of using unmanned aerial vehicles to solve specific tasks in the energy sector.The unresolved issues remain the inter-object navigation of a group of unmanned aerial vehicles inspecting power lines to achieve the required speed and accuracy of the procedures.

Universal Computational Platform for Unmanned Aerial Vehicle
In any sufficiently developed electrical grid, there are extended stretches between base stations that sometimes reach hundreds of kilometers (Fig. 1).For automated inspection, a universal platform is proposed where all measurements and calculations are performed.The UAV is proposed to be implemented on two different flight schemes -multicopter and aircraft.This will allow for efficient inspection of fundamentally different parts of electrical grids.For long stretches of the network, the aircraft-type UAV is applicable due to its advantage in flight range without recharging.Short network sections and sections with complex interchanges and obstacles are proposed to be checked using multicopter UAVs due to their maneuverability advantage.The use of a group of UAVs allows for simultaneous inspection of various parts of the power grid.Accordingly, it is possible to find the number of UAVs (or kilometers of power line per UAV) that will allow for the most efficient detection of faults in a given area.To increase the accuracy of fault localization, a method described in [25] is proposed.
Navigation tasks are solved using a visual-inertial navigation system (VINS) [26], and UAV control is based on the PX4 autopilot [27].The PX4 hardware consists of an STM32 H7 MCU and a combined accelerometer and gyroscope IMU BMI088 with an 8GB memory card for logging.The IMU sensor is responsible for low-level position control and sending inertial sensor data to the highlevel navigation block.This block, performing localization, planning, high-level control, and other navigation functions, requires sufficient computing power.
In the proposed platform, the NVIDIA Xavier NX is used -a powerful computer for embedded and peripheral systems with a six-core processor, a 384core graphics processor, and 8 GB of RAM (Fig. 2).In experiments, except for multi-view video, the load on the processor and graphics processor was less than 40%.That is, there are significant computational reserves for additional potential use.The Intel Realsense D430 camera [28] outputs depth images for mapping and gray-scale stereo images for localization.The UWB module is a Nooploop LTPS with a DW1000 radio chip inside, which allows for the use of the UAV inter-object navigation method described in [25].The functional diagram of the proposed UAV is shown in Fig. 3. Inter-object navigation and the traveling salesman multi-agent task.
Traditionally, the UAV navigation system consists of a satellite navigation module, inertial measurement systems (accelerometer, gyroscope), barometer, and magnetometer.In recent years, SLAM (simultaneous localization and mapping) technologies, which use stereo cameras or a depth scanner and camera to build a model of the environment and determine their own location, are increasingly being used.
As an additional source of navigation information, we propose using UWB transceiver modules.The principle of this system is described in [25] based on [29][30][31][32].
With this set of modules, information exchange between UAVs is possible and the relative location can be determined with high accuracy.The location determination error is significantly less than in other navigation methods and does not exceed tens of centimeters.
But with this method, only the relative position can be determined.However, the known position of the UAV relative to the global navigation system and inertial sensors, using the Kalman's filter, allows us to compare the information and increase its accuracy [33].Let's imagine the UAV's position estimate as: x is the predicted state of the system; p is the position of the UAV; sis the velocity; F is the transition matrix; B is the control matrix; 1 k   is the monitoring vector at the previous moment of time;  is the process noise.The transition matrix F is necessary to map the traffic model to the object.Suppose there is a model that provides the position and velocity of an unaccelerated object.Then the new value of x and p over time t  is calculated as: ; .
Then matrix F will look like as follows: 1 .01 The control matrix B describes the changes in the state of an object through the influence of external or internal forces, such as gravity or friction.Now let's consider the equation for extrapolating the error covariance matrix: where T F is the transposed matrix of transition; Q is the noise matrix.Suppose the object changes direction of motion or may accelerate or decelerate.Therefore, after time t  the uncertainty will increase by Q .
Let's consider the step of updating the value of the UAV position.Let's start by describing the difference between the measured value and the predicted state value: , where z is the actual measurement value; H is the transition matrix;  x is the predicted state value.Matrix H is also known as the transition matrix.It can be used to discard unnecessary information from the predicted state value.Technically, H performs the same job as F in the extrapolation step.
Let's find the common error in determining the system state: where R is the noise measurement; K is the Kalman gain coefficient.Values of the Kalman gain coefficient are in the range from 0 to 1.If the error in measurement is large, the value of the coefficient is closer to 0. This means that the extrapolated value is closer to the real value than the measured one.If the error in extrapolation is large, the value of the coefficient is closer to 1, i.e., the measured value is closer to the real value than the extrapolated value.
We shall obtain the aposteriori estimates of the state vector and the error covariance matrix: The algorithm described above allows estimating the UAV vector based on the results of combining information on measurements and modeling results.
The choice of the navigation information source determines a different measurement error matrix R .This ultimately allows for a gain in measurement accuracy by combining heterogeneous observations.
The improvement of the efficiency of inspection of different parts of the power grid is achieved by using multiple UAVs.To solve the route planning problem for the UAVs, we will represent the power grid as a weighted graph (Fig. 4).Assuming that the arc weight includes the distance between the nodes of the power grid.Then the route planning problem becomes a classic traveling salesman problem with its multi-agent variant.As a solution option, let's consider the variation of the ant colony method for the multi-agent case [34].According to the rule of the ant colony method, the amount of pheromone deposited on the edges of the graph, the edges selected by each ant on its path, and the rate of evaporation of pheromone on each edge are determined.An ant k located in node i decides to move to node j using the "pseudo-random proportional rule" where  is the parameter monitoring q is the random variable with uniform law of distribution on section   0,1 ; 0 q is the parameter q initial value; J is the random node, selected according to the distribution law (9); i Nset of neighboring nodes of i node.

Probability
, ij p that the ant located in node i , occasionally decided to move to node j is From the analysis of formula (8), it follows that the ant makes the best possible move (marked by a large amount of pheromone) with probability 0 q .And it makes a random choice of a suboptimal arc with probability (1 − 0 q ).If 0 q = 0, it means that the focus is on searching for the best solution, avoiding convergence to the suboptimal as much as possible.
only probability ( 9) should be used to determine the transition in the proposed approach.
The best solutions should be marked by a large amount of pheromone along the path.Therefore, when k t determines a new path k V with cost k L , the ant will increase the strength of the pheromone on each edge of the tour by a value inversely proportional to the cost of the path: ,  = { 1/  if arc (, ) belongs to the way found   ; 0, where k Lcost of k path.
When an ant travels along a given path at a constant speed, it takes time proportional to the distance traveled.Pheromones are volatile substances.It will take the ant longer to travel a longer distance.Consequently, over a longer time, more pheromones will evaporate, implying better solutions that will be discovered in the future.It's evident that incorporating pheromone evaporation into the model can be useful for solving the traveling salesman problem.The path (arc) traveled by the ant is marked with pheromones.The update will also consider pheromone evaporation.The change in the amount of pheromones is taken into account as follows: , where  is the pheromone evaporation level, 01   .
For the probabilistic determination of the next step of the ants, formula ( 9) is used.Therefore, the arc with the highest pheromone content is chosen, i.e., the probability of exploring other paths is low.The solution consists in reducing the pheromone content on the arcs selected by the ants, i.e., applying a local evaporation process.This makes them less interesting for the ant, increasing the degree of exploration of still unselected arcs.Each time an ant crosses an arc, it uses local evaporation, updating the pheromone as follows: 1, where  is the local level of pheromone evaporation, 01   , 0  is the initial pheromone amount on each arc.
A good heuristic for initializing the pheromone trails is to set them to a value slightly higher than the amount of pheromone deposited by ants in one iteration.To approximate this value, we need to tune where n is the number of nodes and C is the cost of the path.Thus, if awg w is the average edge cost, then it can be set to awg C nw  . To monitor the impact of evaporation on the solutions, a pheromone update scheme that does not include evaporation is also considered.In this case, equations ( 11) and ( 12) are replaced with , , , .
Then the influence of local evaporation rate of pheromones is excluded and the amount of pheromones is determined according to equation (10).

Modeling the process of monitoring a group of unmanned aerial vehicles for object search
The accuracy of fault localization in the power supply system depends on the accuracy of determining the UAV's own coordinates.Taking into account the obtained information on the location of the UAV relative to other agents in the proposed inter-object navigation system significantly increases the accuracy of coordinate determination [25].
Modeling this navigation method was carried out with several restrictions: -the proposed navigation system includes up to four UAVs or stationary sensors; the effect of electromagnetic radiation on the stability of the systems was not taken into account; the technical specifications of the proposed navigation system correspond to the values claimed by the equipment manufacturer.
In order to obtain reliable results, 100 experiments were conducted with different numbers of UAVs (from 1 to 4) in the navigation system.Their locations relative to each other were selected randomly.
The results of the modeling in Matlab using the Navigation Toolbox are presented in Table 1.In the columns of the table are reflected: Nuavthe number of UAV navigation systems;  The analysis of the simulation results showed that with an increase in the number of sensors in the navigation system, the accuracy of determining the UAV's own coordinates increases.
The root mean square deviation of the measured position of the UAV from the true one at the minimum distance between the agents decreases.Thus, when using two agents, the RMSD of the measured position of the UAV from the true one at the minimum distance between them decreases by 1.39 times, three UAVsby 1.96 times, four UAVs -by 2.63 times.
With the maximum distance between navigation system agents, the standard deviation of their coordinates decreases by 1.37, 1.78, and 2.06 times, respectively, for the same number of UAVs.
That is, as the number of UAVs in the navigation system increases, the accuracy of determining their coordinates increases.This allows for more accurate localization of faults in the power system.
It is obvious that the growth in the number of drones improves the efficiency of power line inspection.Additionally, the efficiency of inspection is influenced by the topology of the energy system itself, the degree of connectivity of the graph describing the power system, the ratio of the number of short and long sections of the network, and the overall length of the power transmission lines.
In general, it is difficult to estimate the efficiency of power line inspection.Therefore, for mathematical modeling, the representation of the power grid as a weighted graph is adequate.The specifics of its application have predetermined the characteristics of defining a weakly and strongly connected graph, which differs from the classical one.
We will call a graph weakly connected if the average number of arcs attached to one vertex is 3 Based on the results of modeling, the assessment of the efficiency of inspecting the main varieties of schemes is presented in Table 2.The data in the table are normalized, and the inspection time by one UAV is taken to be one unit.In a strongly connected network, increasing the number of UAVs used for inspection sharply reduces the inspection time.Thus, the second UAV used effectively reduces the inspection time by two; UAVs reduce it by three times, and eight UAVs reduce it by 6.25 times.
For a weakly connected network, the observed dynamics are the same.Only at the initial stage is the reduction in inspection time less noticeable: for two UAVs it is reduced by 1.38 times; for four UAVs by 2.86 times; and for eight UAVs by 5.26 times.
The presence of 10 or more UAVs in the navigation system makes it possible to carry out an inspection equally efficiently for both highly and weakly connected power grids.The increase in the number of UAVs will only be determined by economic feasibility and the configuration of the power grid.
We introduce the ratio  -the number of short sections of the power grid to the total number of all sections (network topology): low ( 0,33

 
).During mathematical modeling, the following assumptions will be made: 1.A single sweep is carried out only by a multicopter UAV.
2. In a multi-agent system, long sections of the power grid use aircraft-type UAVs, while short sections use multi-copter UAVs.
3. The cruising speed of the aircraft-type UAV is 2 times higher than speed of the multi-copter device.
The results of modeling the inspection efficiency of the power system with different network topologies and different numbers of UAVs involved are shown in Table 3.The data is normalized, and the inspection time of one UAV is taken as one unit.The operational efficiency of inspecting the power grid is at a maximum when the low topology network is inspected.Increasing the number of UAVs used for monitoring leads to a significant reduction in inspection time.The topology of the power grid only significantly affects this indicator when 2-4 UAVs are used.Further increases in inspecting UAVs do not make a noticeable difference in the ratio of short segments of the power grid to the total number of all segments.The presence of more than 10 UAVs in the navigation system allows for equally efficient inspection of the power grids of different topologies.
Thus, from the analysis of the simulation results it follows: -The proposed inter-object navigation approach increases the accuracy of inspecting power transmission lines from 27% to 73% depending on the number of UAVs in the operation area of the system.
-The use of a heterogeneous group of UAVs allows for the inspection of power grids to be increased by 2 to 8 times, depending on the number of drones used and the configuration of the power system itself.The inspection efficiency is greatly influenced by the ratio of the cruising speeds of different types of drones.An increase in this ratio results in a greater time gain in inspection when there is a large number of extended sections of the power system.
-The inspection efficiency of a power grid varies widely depending on the ratio of the number of short sections to the total number of sections of the power system and the number of UAVs.Inspection of a network with a low topology is carried out in the most efficient manner.

CONCLUSIONS
This article is devoted to the task of increasing the efficiency and accuracy of inspecting power transmission lines.The use of a unified computing and measuring platform has simplified the interaction between the proposed types of UAVs: a multicopteron short sections with complex junctions and obstacles, and an unmanned aircraft with an airframe flight scheme -on long sections.
The increase in the efficiency of fault detection was achieved by simultaneous inspection of different parts of the network by several different types of UAVs.The use of inter-object navigation sensors of UAVs has increased the accuracy of determining the UAV's position in space and, accordingly, increased the accuracy of locating the site of the malfunction.

About authors.
Tymochko Oleksandr, Doctor of Technical Sciences, Professor, Head of the Department, Flight Academy of the National Aviation University, area of scientific interests: Decision support systems, motion control, automation, Е-mail: timochko.alex@gmail.com

Fustii Vadym
Adjunct, Kharkiv National Air Force University, area of research interests: UAV, decision support systems, E-mail: vadimfustie1995@gmail.com

Fig. 1 .
Fig. 1.An example of transmission line infrastructure in Newcastle, Australia.

Fig. 2 .
Fig. 2. External view of the hardware of the proposed UAV control system.

Fig. 4 .
Fig. 4. Image of the power supply system in the form of a weighted graph.
mean square deviation (RMSD) of the measured position of the UAV from the true one; Prop MIN  -RMSD of the measured position of the UAV from the true one at the minimum distance between the agents; Prop MAX  -RMSD of the measured position of the UAV from the true one at the maximum distance between the agents.

Table 2 .
Inspection efficiency of the electrical network with different number of UAVs and graph connectivity degree.

Table 3 .
Inspection efficiency of the power grid with different ratios of the number of short sections to the total number of all sections of the energy system and different numbers of UAVs.