Inspection Points Research Articles

UAV Inspection Trajectory Planning Method for High-Precision Tower Models

To accurately complete the inspection task of transmission lines, a UAV inspection trajectory planning method for high-precision tower models is discussed. By using GIM three-dimensional modeling technology, high-precision models of power towers and transmission lines are obtained, and then the coordinates of target points during the UAV inspection process are obtained. A target model based on the inspection point coordinates is established to plan the trajectory path. A trajectory planning model based on particle swarm algorithm and beetle whisker algorithm is established to improve the algorithm model’s ability to escape from difficulties. In response to sudden obstacles during UAV inspections, a wall-walking strategy is introduced to prevent UAVs from falling into static traps. Through experimental verification, the improved algorithm can effectively reduce the flight distance by 2.81[Formula: see text]km and improve the efficiency of UAV operation. The verification of sudden static and dynamic threats has been conducted, and the experimental results show that this method can effectively ensure the effectiveness of the UAV power inspection process.

Route Planning Method of UAV Patrol Based on High Precision Tower Model

The high-precision positioning technology of industrial Unmanned Aerial Vehicle (UAV) plays a vital role in intelligent trajectory planning in power inspection. First, the information on power facilities is collected and processed to form a planning grid to optimize the flight path and correct the trajectory of UAV. However, the preparatory work is more complex, and the algorithm model which needs more detailed and complex terrain database data is not universal enough. To improve the safety of UAV and the efficiency of path planning, we establish a three-dimensional model of the power tower, calculate the coordinate position of the inspection work according to the information of the high-voltage transmission tower, and then determine the corresponding relationship between the inspection point and the flight trajectory combined with the safe distance. Based on the set of random interference semaphores and model rasterization, the discrete error strategy and Euler method are introduced to improve the performance. In each iteration, the best solution is first updated using the execution strategy. We continue to calculate the spatial coordinates of all reference points and provide the coordinate position distribution for the flight mission. The solution of equipment inspection trajectory optimization is realized by using dynamic obstacle perception. The proposed discrete measurement error self-correction algorithm is deployed on the flight platform to guide UAV inspection tasks according to the point cloud coordinate model of transmission equipment in the power system and to correct the flight route in time. To verify the research results, the Algorithm Artemisinin optimization and Whale Optimization Algorithm test verify that the ability of the proposed algorithm to get rid of local optimization is improved by 8.94% and, 12.42% respectively compared with other optimization algorithms. The convergence accuracy is 12.4% and 7.9% higher than other schemes, and it has a better effect in solving numerical problems. The research results using the embedded system to complete the task deployment and unloading provide a reference for trajectory planning and task design in different application scenarios.

A Comprehensive Survey on Visual Perception Methods for Intelligent Inspection of High Dam Hubs.

There are many high dam hubs in the world, and the regular inspection of high dams is a critical task for ensuring their safe operation. Traditional manual inspection methods pose challenges related to the complexity of the on-site environment, the heavy inspection workload, and the difficulty in manually observing inspection points, which often result in low efficiency and errors related to the influence of subjective factors. Therefore, the introduction of intelligent inspection technology in this context is urgently necessary. With the development of UAVs, computer vision, artificial intelligence, and other technologies, the intelligent inspection of high dams based on visual perception has become possible, and related research has received extensive attention. This article summarizes the contents of high dam safety inspections and reviews recent studies on visual perception techniques in the context of intelligent inspections. First, this article categorizes image enhancement methods into those based on histogram equalization, Retinex, and deep learning. Representative methods and their characteristics are elaborated for each category, and the associated development trends are analyzed. Second, this article systematically enumerates the principal achievements of defect and obstacle perception methods, focusing on those based on traditional image processing and machine learning approaches, and outlines the main techniques and characteristics. Additionally, this article analyzes the principal methods for damage quantification based on visual perception. Finally, the major issues related to applying visual perception techniques for the intelligent safety inspection of high dams are summarized and future research directions are proposed.

Seasonal dynamics of cereal aphid population

Goal. To compare the seasonal dynamics of cereal aphid abundance in the Steppe and Forest-Steppe zones during 2023 and to determine the factors that influenced it. Methods. To assess the state of the cereal aphid population on cereal crops, we used the results of personally conducted entomological phytosanitary monitoring of crops (according to generally accepted methods) in the farms of the Steppe and Forest-Steppe zones; information from current reports from the places where field experiments were conducted directly by the forecasting laboratory, as well as other laboratories of the IPP of NAAS, which is also confirmed by the materials of decadal reports of regional plant protection stations and signalization and forecasting points of the State Inspection of Plant Protection, confirmed by information on the phytosanitary status of regional state research stations. Cereal aphid adults and larvae were counted in populations of populations (in the crop phase, the end of the tube emergence is earing). Results. The state of cereal aphid populations on crops of cereal spiked crops in 2023 was studied, both in general in Ukraine and separately in the Steppe and Forest-Steppe zones. The dynamics of their number in farms of different natural and climatic zones was investigated, and an analysis of its peculiarities in the conditions of the year was carried out. Conclusions. In 2023, the harmfulness of cereal aphids on cereal crops remained at the level of long-term averages. The expansion of their harmful zone and an increase in their number was noted during the earing period (milk ripeness). On winter cereal crops, phytophages prevailed in the Steppe zone. In the Forest-Steppe zone, the phytophage was more damaging to winter cereals than to spring cereals. The results of entomological monitoring in Mykolaiv region (State Enterprise «Experimental Farming «Zori nad Bugom») showed that during the accounting period the bulk of aphids were concentrated on winter wheat crops, and winter barley was damaged in small numbers. On the contrary, the surveys conducted in Kyiv region (State Enterprise «Experimental Farming «Salyvonkivske») showed that in the second half of June — the first decade of July, the number of aphids on spring barley crops was approximately twice as high as on spring wheat. As a result of the study, it was practically confirmed that the optimal temperature regime for the development of cereal aphids is 16—20°C, and the relative humidity is 60—80%.

핵심역량 기반의 비교과 프로그램 성과 분석 연구

Objectives The purpose of this study is to determine the impact of extra-curricular program on strengthening core competencies of universities, based on the results of a satisfaction survey of the writing clinic using competency-based survey questions. In addition, this study seeks to present problems and improvement plans in the performance analysis of the current competency-based extra-curricular program. Methods For this purpose, a satisfaction survey was analyzed among S University students who participated in the writing clinic. The S University writing clinic is a program linked to the university writing class called <Thoughts and Expression>, and is an individual instruction course that helps students taking the class write academic writing. Satisfaction surveys prior to 2022 were not linked to university core competencies, so it was not possible to measure the impact of extracurricular program on improving core competencies. For this reason, we developed questions linked to S University's core competencies and conducted a satisfaction survey in the second semester of 2022. After finding problems and revising the questions, we conducted and analyzed a satisfaction survey in the first and second semesters of 2023. Results The results of the satisfaction survey showed that the writing clinic was helpful in cultivating all of S University’s core competencies, and among them, the cultivation scores for ‘competence in practicing ethics’ and ‘competence in exploring professional knowledge’ were high. This result is understood to be a phenomenon that occurred because the target was ‘academic writing’, which was an assignment in the <Thinking and Expression> class, and was influenced by the type of writing that was the target of the writing clinic and the instructors’ inspection points during the clinic process. Conclusions As a result of analyzing the case of S University, it is clear that extra-curricular program contribute to cultivating the university’s core competencies, but it is problematic to uniformly apply the core competencies set by the university to all programs. Therefore, it is suggested to apply it selectively, focusing on competencies with high suitability. In addition, how to link the university's core competencies and writing competencies and introduce them into performance management will be a future task.

Vertical Switching Algorithm for Unmanned Aerial Vehicle in Power Grid Heterogeneous Communication Networks

The rapid development of wireless network technology has led to the coexistence of various heterogeneous wireless networks (HWNs). To ensure that users enjoy normal and diversified services, research on vertical switching technology has become an inevitable trend. However, most current vertical switching algorithms only consider static situations or single services, which are not suitable for power grid scenarios. This paper studies the vertical switching problem of wireless heterogeneous networks for unmanned aerial vehicles (UAVs) performing inspection tasks in power grid scenarios. In this model, a UAV for power grid inspection needs to plan its flight trajectory, avoid obstacles, and find the optimal trajectory to reach each inspection point. Throughout the UAV inspection process, we must ensure the quality of communication services for the UAV. The UAV dynamically selects different networks for access at different locations, presenting a dynamic network selection and vertical switching problem. This paper proposes a method that combines trajectory planning and network selection, which first utilizes the A-star algorithm to obtain suitable trajectories, and then evaluates and judges networks based on the Fuzzy Analytic Hierarchy Process (FAHP) to determine the most appropriate network. It is worth noting that this paper considers three service requirements and seven network attributes under three types of heterogeneous wireless networks. Numerical results show that this method can better meet the requirements of UAV inspection tasks and reduce the number of switches, thus addressing the issue of terminal vertical switches in power grid scenarios.

Development of fatigue prediction system for bogie frame using a dynamic analysis model based on high‐speed and high‐precision stress estimation method

AbstractDespite ensuring the integrity of bogie frames for railway vehicles via nondestructive inspections during periodic maintenance, the possibility of fatigue cracks occurring at locations other than the predetermined inspection points cannot be dismissed. Therefore, fatigue cracks can be prevented more efficiently by assessing the overall degree of fatigue damage to the entire bogie frame and determining the results via nondestructive inspections. In this study, dynamic stresses in the bogie frame during running were estimated via finite element dynamic analysis by using the axle box acceleration as input, and the degree of fatigue damage and life were calculated from the waveform of the estimated stresses. Furthermore, we developed a bogie frame fatigue prediction system based on a high‐speed and high‐precision stress calculation method. The developed system visualized the overall relative life.

Balanced task allocation and motion planning of a multi-robot system under fuzzy time windows

PurposeA fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.Design/methodology/approachThe paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.FindingsThe computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.Originality/valueThis paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.

Efficacy of plasma treatment for surface cleansing and osseointegration of sandblasted and acid-etched titanium implants.

This study was conducted to evaluate the effects of plasma treatment of sandblasted and acid-etched (SLA) titanium implants on surface cleansing and osseointegration in a beagle model. For morphological analysis and XPS analysis, scanning electron microscope and x-ray photoelectron spectroscopy were used to analyze the surface topography and chemical compositions of implant before and after plasma treatment. For this animal experiment, twelve SLA titanium implants were divided into two groups: a control group (untreated implants) and a plasma group (implants treated with plasma). Each group was randomly located in the mandibular bone of the beagle dog (n = 6). After 8 weeks, the beagle dogs were sacrificed, and volumetric analysis and histometric analysis were performed within the region of interest. In morphological analysis, plasma treatment did not alter the implant surface topography or cause any physical damage. In XPS analysis, the atomic percentage of carbon at the inspection point before the plasma treatment was 34.09%. After the plasma treatment, it was reduced to 18.74%, indicating a 45% reduction in carbon. In volumetric analysis and histometric analysis, the plasma group exhibited relatively higher mean values for new bone volume (NBV), bone to implant contact (BIC), and inter-thread bone density (ITBD) compared to the control group. However, there was no significant difference between the two groups (P > .05). Within the limits of this study, plasma treatment effectively eliminated hydrocarbons without changing the implant surface.

Prevalence and Risk Factors of Scabies: Observational Study in Nurul Ilmi Darunnajah 14 Islamic Boarding School Students in Serang, Banten, Indonesia

Scabies is a contagious skin condition triggered by Sarcoptes scabiei varietas hominis. It is prevalent globally, particularly in tropical regions with low economic resources. The condition is commonly observed in densely populated environments characterized by close physical contact, such as Islamic boarding schools. This cross-sectional research was conducted in December 2023 at the Nurul Ilmi Darunnajah 14 Islamic Boarding School. This research involved 120 students who met the inclusion criteria. The questionnaire contains informed consent, personal identity, 15 questions to assess the level of personal hygiene, 15 questions to assess the respondent's level of knowledge, 8 statements, and 2 inspection points related to scabies diagnostic criteria. The data obtained will then be analyzed and researched according to the diagnostic criteria of the 2020 International Alliance for the Control of scabies consensus criteria for the diagnosis of scabies. The prevalence of scabies in this Islamic boarding school is 22.5% (27/120), with the risk factor for scabies being the level of personal hygiene, which includes individual cleanliness, environmental cleanliness, direct contact, ventilation, and humidity of the bedroom.

On Non-Occurrence of the Inspection Paradox

The well-known inspection paradox or waiting time paradox states that, in a renewal process, the inspection interval is stochastically larger than a common interarrival time having a distribution function F, where the inspection interval is given by the particular interarrival time containing the specified time point of process inspection. The inspection paradox may also be expressed in terms of expectations, where the order is strict, in general. A renewal process can be utilized to describe the arrivals of vehicles, customers, or claims, for example. As the inspection time may also be considered a random variable T with a left-continuous distribution function G independent of the renewal process, the question arises as to whether the inspection paradox inevitably occurs in this general situation, apart from in some marginal cases with respect to F and G. For a random inspection time T, it is seen that non-trivial choices lead to non-occurrence of the paradox. In this paper, a complete characterization of the non-occurrence of the inspection paradox is given with respect to G. Several examples and related assertions are shown, including the deterministic time situation.

Production Risk Analysis and Key Points for Field Inspection of Medical Electron Linear Accelerator

The medical electron linear accelerator（LINAC） has the characteristics of complex system structure, many core components and high precision control requirements, which puts forward higher requirements for product quality control and regulation. This study puts forward the main points of field inspection through the analysis of the technical characteristics and production risk of LINAC, combined with the requirements of the good manufacturing practice of medical devices. It has certain reference significance for quality management personnel and field inspectors.

Automated mission planning for aerial large‐scale power plant thermal inspection

AbstractClose‐range aerial inspection of large‐scale industrial facilities such as power plants is complex. It is characterized by a few areas suitable for safe landing, many obstacles, complicated radio communication, and so forth. The paper presented a new offline approach for automated mission planning in such conditions. It is based on novel concepts of ‐shaped flight profile and safe altitude map. These concepts reduce the mission planning task to a multiple traveling salesmen problem on a two‐dimensional map, which is solved using rapidly exploring random tree and genetic algorithms. A computational fluid dynamics‐based local turbulence map concept was proposed to avoid turbulence zones during inspection flights. As an advantage, this map can be generated at least 6.8× faster than the known approaches. Our new multicopter flight time prediction model provides an error of less than 10% in most cases and significantly outperforms those implemented in commercial mission planning software. All the proposed solutions were verified during a 2400‐MW power plant inspection. Our algorithms managed to plan to visit all the inspection points in six routes, approximately 15 min long each. This mission set has a comparable overall duration but better safety and even battery usage compared with the routes planned by a qualified operator. Moreover, the designed aerial inspection system provides higher quality images than manually from the ground using a thermal camera with two times higher sensitivity and equipped with more advanced optics. To our knowledge, this research is the first to report the successful implementation of autonomous unmanned aerial vehicle‐based power equipment diagnostics on a large‐scale thermal power plant.

ВОССТАНОВЛЕНИЕ ДВИЖЕНИЯ ПОСЛЕ ОТКАЗОВ С ПРИМЕНЕНИЕМ ВИРТУАЛЬНОЙ СЦЕПКИ ПОЕЗДОВ

The article examines the influence of group automatic train operation technology (virtual coupling) on accelerating the process of restoring traffic after a failure with a break in traffic on a railway section. Possible train-to-train intervals have been determined: calculated and statistical estimates taking into account real traffic conditions on the section and using virtual coupling technology. At the same time, the influence of energy supply shortage was not considered; it is assumed that in the process of mass implementation of group automatic train operation technology, the energy supply system will be strengthened to ensure the capabilities of automation systems. Simulation modeling of the operation of a railway section in the IMETRA system (macromodeling system for transport junctions and grounds) was carried out in order to comprehensively assess the impact of the introduction of group automatic train operation on the performance of the section in normal operation and after restoration of traffic in the case of a long-term (8 hours) failure of technical means. The possibility of strengthening technical inspection points with additional teams has been considered to speed up the restoration of traffic after failure of technical means.

Integrated Forward and Reverse Cross-Docking with Vehicle Routing and Scheduling Under the Uncertainty of Inspection Results: A Genetic-Mathematic Algorithm

Despite the recognized advantages of cross-docking in forward logistics, very few studies have investigated reverse cross-docking, and these studies do not consider the operational uncertainties of returned products in the reverse flow, which is required in practice. This paper introduces a vehicle routing and scheduling problem for the integration of forward and reverse logistics, in which the cross-docking facility is employed as (i) the distribution center in forward flow and (ii) the collection and dispatching center of returned products in reverse flow. We present two modes based on the inspection point: (i) retailer site or (ii) cross-dock. A deterministic mixed integer linear programming model is presented for the retailer-site inspection mode to minimize the total operational costs. For the second mode, a robust optimization counterpart of the modified deterministic model is formulated to account for the uncertainties arising from the inspection results revealed at the cross-dock. A genetic-mathematic algorithm is proposed to solve the large-sized instances. Through numerical studies, we evaluated the performance of the algorithm and demonstrated cost reductions and truck utilization improvements as benefits of integration. Moreover, in sensitivity analyses using a quasi-real case of a personal electronic device supply chain, and employing simulation, the price of robustness of the second model was evaluated by considering various budget sets, which justified the full robustness and application of the cross-dock as the inspection point in the closed-loop supply chain.

Yield strength evaluation of 3D-printed Ti–6Al–4V components based on non-contact eddy-current measurement

The demand for metal additive manufacturing (AM), also known as three-dimensional (3D) printing, is increasing owing to its ability to produce components with complex shapes, heterogeneous material properties, low material waste, etc. However, for broader acceptance of metal AM, quality assurance of mechanical properties, such as elastic (Young's) modulus, Poisson's ratio, and ductility, is becoming critical in additively manufactured components. This study proposes a non-contact, non-destructive and automated eddy-current technique for yield strength estimation of additively manufactured Ti–6Al–4V components with the potential for online operation during metal AM. After conducting the eddy-current measurement at a specific inspection point within the Ti–6Al–4V component, the relationship between the eddy-current phase value and electrical conductivity is established. Subsequently, the yield strength of the Ti–6Al–4V component is estimated by utilizing the analytical relationship between yield strength and electrical conductivity, which is based on Andrew's research and the Hall–Petch relationship. For experimental validation, Ti–6Al–4V test specimens with different electrical conductivities (yield strengths) were fabricated by adjusting the cooling rate during metal direct energy deposition AM. Then, the yield strengths estimated using the proposed technique were compared with those obtained using conventional destructive tensile tests. The results show that the proposed technique can estimate the yield strength with an error rate of less than 8%. The uniqueness of this study lies in (1) the theoretical derivation of the relationship between the eddy-current phase value and yield strength, (2) non-destructive, non-contact, and automated estimation of the yield strength using eddy-current measurements, and (3) performance evaluation using additively manufactured Ti–6Al–4V specimens with different yield strengths.

Autonomous GPU-based UAS for inspection of confined spaces: Application to marine vessel classification

Inspection of confined spaces poses a series of health risks to human surveyors, and therefore a need for robotic solutions arises. In this paper, we design and demonstrate a real-time system for collecting 3D structural and visual data from a series of inspection points within a prior map of a confined space. The system consists of a GPU accelerated 3D point cloud registration and a visual inertial odometry estimate fused in an Unscented Kalman Filter. Using the state-of-the-art deep learning-based feature descriptors, FCGF –and the robust Teaser++ 3D registration algorithm– point clouds from a narrow field of view, time-of-flight, camera can be registered to a prior map of the environment, to provide accurate cm-level absolute pose estimates. The uncertainty of the system is furthermore estimated on the basis of the novel GPU-based Stein ICP algorithm. Visual defects, represented by augmented reality fiducial markers, are automatically detected during inspection, and their positions are estimated in the map frame of the confined space. The performance of the system has been evaluated in realtime onboard a small UAV, within a mock-up model of a water ballast tank from a marine vessel, where the UAV was able to navigate and inspect the ambiguous and featureless environment. All defects were estimated within ＋/−10 cm of their actual position.

Efficient Autonomous Path Planning for Ultrasonic Non-Destructive Testing: A Graph Theory and K-Dimensional Tree Optimisation Approach

Within the domain of robotic non-destructive testing (NDT) of complex structures, the existing methods typically utilise an offline robot-path-planning strategy. Commonly, for robotic inspection, this will involve full coverage of the component. An NDT probe oriented normal to the component surface is deployed in a raster scan pattern. Here, digital models are used, with the user decomposing complex structures into manageable scan path segments, while carefully avoiding obstacles and other geometric features. This is a manual process that requires a highly skilled robotic operator, often taking several hours or days to refine. This introduces several challenges to NDT, including the need for an accurate model of the component (which, for NDT inspection, is often not available), the requirement of skilled personnel, and careful consideration of both the NDT inspection method and the geometric structure of the component. This paper addresses the specific challenge of scanning complex surfaces by using an automated approach. An algorithm is presented, which is able to learn an efficient scan path by taking into account the dimensional constraints of the footprint of an ultrasonic phased-array probe (a common inspection method for NDT) and the surface geometry. The proposed solution harnesses a digital model of the component, which is decomposed into a series of connected nodes representing the NDT inspection points within the NDT process—this step utilises graph theory. The connections to other nodes are determined using nearest neighbour with KD-Tree optimisation to improve the efficiency of node traversal. This enables a trade-off between simplicity and efficiency. Next, movement restrictions are introduced to allow the robot to navigate the surface of a component in a three-dimensional space, defining obstacles as prohibited areas, explicitly. Our solution entails a two-stage planning process, as follows: a modified three-dimensional flood fill is combined with Dijkstra’s shortest path algorithm. The process is repeated iteratively until the entire surface is covered. The efficiency of this proposed approach is evaluated through simulations. The technique presented in this paper provides an improved and automated method for NDT robotic inspection, reducing the requirement of skilled robotic path-planning personnel while ensuring full component coverage.

An adaptive crack inspection method for building surface based on BIM, UAV and edge computing

Unmanned aerial vehicle (UAV) and building information modeling (BIM) have been applied to inspect building surfaces to improve efficiency and reduce labor costs. However, most of the current research focus on the inspection mode of “first collect and then identify” with limited intelligence. Therefore, this study proposes a “global-local” adaptive inspection method for building surfaces by integrating BIM, UAV (with multifunction camera), and edge computing, enabling real-time synchronization of crack data collection and analysis. First, the building surface area to be inspected is extracted from BIM to generate global inspection points using the selected camera's field of view (FOV) and considering coordinates transformation between BIM and reality. Then, A star algorithm integrating with genetic algorithm (GA) is used to optimize the global flight path based on generated inspection points. Finally, the coordinates of the inspection points based on BIM are converted into real-world coordinates, and the flight parameters such as the flight yaw angle (FYA) and the gimbal yaw angle (GYA) are calculated to generate the inspection mission. During global inspection, a local adaptive inspection is proposed for each FOV through real-time local crack identification and flight replanning using edge computing and zoom camera. In addition, multiple battery supply points are automatically added considering the endurance of the UAV. A real building has been used to validate the proposed “global-local” adaptive inspection method. The experiment results show that the inspection time has been significantly reduced compared with the traditional method, and the crack identification of building surfaces can be implemented with high efficiency, precision, quality, and low cost.

Trajectory Synthesis for the Coordinated Inspection of a Spacecraft with Safety Guarantees

As outer space becomes increasingly congested, there exists a growing need for auxiliary spacecraft to perform support missions for existing satellites with guarantees for safety and mission success. We focus on a multispacecraft inspection mission, wherein a team of “deputy” spacecraft inspect a passive “chief” spacecraft by traveling to a set of inspection points while satisfying a set of safety constraints, namely, that they avoid aligning themselves with the sun, that they avoid colliding with one another, and that they avoid colliding with the chief. We model the deputy dynamics using the Clohessy–Wiltshire–Hill equations, and subsequently discretize the environment by exploiting elliptical natural motion trajectories. Using this finite state space, we construct a Markov decision process (MDP) model of the environment and determine the optimal sequence of inspection points for each deputy to visit by solving a vehicle routing problem. To ensure that the deputies satisfy the safety constraints, we form the product MDP of the original MDP and a nondeterministic Büchi automaton that encodes the sensing task and safety constraints. Using this product MDP, we propose a pair of decentralized algorithms that each seeks to minimize the weighted combination of the time and fuel required to safely complete the mission. The first is an offline algorithm that synthesizes a safe trajectory for each deputy that requires no communication at runtime, while the second is an online algorithm that enforces safety at runtime by leveraging communication between the deputies. We provide numerical examples demonstrating the efficacy of both proposed algorithms.