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Articles 121 - 150 of 844
Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering
Research On Experimental Method Of Joint Operation Simulation Based On Human-Machine Hybrid Intelligence, Ma Jun, Jingyu Yang, Wu Xi
Research On Experimental Method Of Joint Operation Simulation Based On Human-Machine Hybrid Intelligence, Ma Jun, Jingyu Yang, Wu Xi
Journal of System Simulation
Abstract: In view of the difficulties that the joint operation simulation experiment methods are mainly for guiding equipment evaluation and demonstration, which is difficult to effectively support the research of operation problems, a joint operation simulation experiment method based on human-machine hybrid intelligence is proposed. The classification, generation and accumulation process of the knowledge in joint operation simulation experiment are clarified. Through the detailed descriptions of experimental interaction process, experimental operation process, experimental driving mode, simulation operation mode, supporting system structure, etc., a joint operation simulation experiment framework based on man-machine hybrid intelligence is constructed. It provides a new method …
Reusability Analysis And Application For Complex System Simulation Model, Zhu Feng, Yiping Yao, Wenjie Tang, Li Jin
Reusability Analysis And Application For Complex System Simulation Model, Zhu Feng, Yiping Yao, Wenjie Tang, Li Jin
Journal of System Simulation
Abstract: Model reuse is an important way to improve the development efficiency of complex system simulation application. At present, there are few researches on the reusability of simulation model and its impact on the development efficiency of complex system simulation application integration by using qualitative/quantitative methods. A simulation model reusability analysis method is proposed. By introducing the simulation application integration development speedup ratio, the simulation model reusability analysis mathematical model is constructed, and the requirements of model interface, model testing and information description for improving model reusability are analyzed qualitatively. Through two typical case studies, the influence of reusable simulation …
Research On Path Tracking Control Strategy Of Four-Wheel Steering Intelligent Vehicle, Jingbo Zhao, Liangpeng Zhu, Chengye Liu
Research On Path Tracking Control Strategy Of Four-Wheel Steering Intelligent Vehicle, Jingbo Zhao, Liangpeng Zhu, Chengye Liu
Journal of System Simulation
Abstract: Aiming at the instability of path tracking control of intelligent vehicle at high speed, a path tracking control strategy of four-wheel steering combined with differential braking is proposed. In the upper layer, the front wheel active steering controller is designed based on the path tracking model. In the lower layer, the integrated controller of active rear steering and additional yaw moment is designed using the sliding mode control method. The additional yaw moment is transformed into the control of single wheel by designing differential braking distribution strategy. Simulation results show that the tracking accuracy of the combined control strategy …
Fixed-Time Event-Triggered Formation Control For Multiple Uavs, Ye Shuai, Guoping Jiang, Yingjiang Zhou, Liu Shang
Fixed-Time Event-Triggered Formation Control For Multiple Uavs, Ye Shuai, Guoping Jiang, Yingjiang Zhou, Liu Shang
Journal of System Simulation
Abstract: To solve the quadrotor UAV formation control problem, an event-triggered fixed time formation control algorithm of multi quadrotor UAV system is studied. For the attitude loop control problem of UAV, the switching fixed time sliding surface is selected to make the system reach the equilibrium point in a fixed time when the system state is on the sliding surface. A fixed-time sliding mode controller is designed so that the system state which is not on the sliding surface can reach the sliding surface within a fixed time. In view of the position loop control problem of UAV, the event-driven …
Virus Propagation And System Simulation Based On Cellular Automata Model, Lijuan Zhang, Fuchang Wang, Zhengang Li
Virus Propagation And System Simulation Based On Cellular Automata Model, Lijuan Zhang, Fuchang Wang, Zhengang Li
Journal of System Simulation
Abstract: A susceptible-latent-infected-cured-immune virus spreading model is established according to the characteristics of epidemic transmission and the actual urban spatial map model. Individuals in the environment are regarded as agents, and the spreading mechanism is established according to the principle of cellular. The effects of different strategies and different characteristics of virus spreading on epidemic have been studied. The role and effect of important factors on epidemic prevention and control method are discussed, and the model is validated taking Shijiazhuang epidemic as an example . The results show that the number of initial latent, the infectivity of disease, vaccination proportion …
Research On Accurate Gesture Recognition Algorithm In Complex Environment Based On Machine Vision, Xu Sheng, Wenyu Feng, Zhicheng Liu, Xintao Tu, Minrui Fei, Kun Zhang
Research On Accurate Gesture Recognition Algorithm In Complex Environment Based On Machine Vision, Xu Sheng, Wenyu Feng, Zhicheng Liu, Xintao Tu, Minrui Fei, Kun Zhang
Journal of System Simulation
Abstract: To address the issue of cross infection caused by elevator public buttons during COVID-19, a software algorithm based on machine vision for non-contact control of public buttons by gesture recognition is designed. In order to improve the accuracy of gesture recognition, an improved YOLOv4 algorithm is proposed. A Ghost module is designed based on attention mechanism, and the ResBlock module in YOLOv4 is improved to Ghost module. The experimental results show that, in the task of gesture recognition, the detection speed is improved by 14% and the detection accuracy is improved by 0.1% compared with the original model. The …
Simulation Of Civil Aircraft Takeoff Scenario Based On Mbse, Liangyu Zhao, Junjie Ye, He Qi, Guo Wei, Zhao Yong
Simulation Of Civil Aircraft Takeoff Scenario Based On Mbse, Liangyu Zhao, Junjie Ye, He Qi, Guo Wei, Zhao Yong
Journal of System Simulation
Abstract: Aiming at the interactions and flaws of design being difficult to be fully discovered, the requirements being hard to be traced, the early verification of system design being difficult to be realized and so on, a Model-Based System Engineering (MBSE) method is adopted to realize the simulation of civil aircraft take-off scenario. Based on the analysis of civil aircraft takeoff scenario requirements, the civil aircraft takeoff scenario simulation architecture, take-off scenario discrete logic model, and continuous physical simulation model are established. The method of fusing the SysML model and Simulink model and the 3D visualization of simulation data …
An Equivalent Method Of Uav Simulating High-Altitude Reconnaissance Equipment Optical Imaging, Jiangang Tu, Xu Cheng, Wang Hui, Zenghui Shen
An Equivalent Method Of Uav Simulating High-Altitude Reconnaissance Equipment Optical Imaging, Jiangang Tu, Xu Cheng, Wang Hui, Zenghui Shen
Journal of System Simulation
Abstract: Aiming at the situation that the actual image of enemy reconnaissance equipment is difficult to be obtained, and the process of using similar equipment of our army is complicated and expensive in the detection of the camouflage effect of our important military targets, an equivalent detection method of using the UAV aerial photography to generate the high-altitude optical reconnaissance images is proposed. The number of pixels in the equivalent image is determined by comparing the acquisition height and the optical imaging device’s parameters of the UAV and the high-altitude reconnaissance equipment. The compressed pixel value is calculated through the …
Joint Distribution Location-Routing Problem And Large Neighborhood Search Algorithm, Zhenping Li, Yuwei Zhao, Yuwei Zhang, Lining Xing, Ren Teng
Joint Distribution Location-Routing Problem And Large Neighborhood Search Algorithm, Zhenping Li, Yuwei Zhao, Yuwei Zhang, Lining Xing, Ren Teng
Journal of System Simulation
Abstract: Based on the characteristics of two-echelon, multi-center, and heterogeneous fleets in urban logistics joint distribution system, the two-echelon joint distribution location routing problem is studied. The problem is formulated into a mixed integer programming model to minimize the total costs. An adaptive large neighborhood search algorithm (ALNS) for solving the model with multiple deletion and insertion operators is proposed to obtain neighborhood solution. The selection probability of each operator is adjusted according to the neighborhood solution to accelerate the convergence speed. Several test examples are generated based on the benchmark of location-routing problem. Both ALNS algorithm and Gurobi software …
An Application Of An Unequal-Area Facilities Layout Problem With Fixed-Shape Facilities, Alan Mckendall, Artak Hakobyan
An Application Of An Unequal-Area Facilities Layout Problem With Fixed-Shape Facilities, Alan Mckendall, Artak Hakobyan
Faculty & Staff Scholarship
The unequal-area facility layout problem (UA-FLP) is the problem of locating rectangular facilities on a rectangular floor space such that facilities do not overlap while optimizing some objective. The objective considered in this paper is minimizing the total distance materials travel between facilities. The UA-FLP considered in this paper considers facilities with fixed dimension and was motivated by the investigation of layout options for a production area at the Toyota Motor Manufacturing West Virginia (TMMWV) plant in Buffalo, WV, USA. This paper presents a mathematical model and a genetic algorithm for locating facilities on a continuous plant floor. More specifically, …
Thin Safety Margin: The Sefor Super-Prompt-Critical Transient Experiments, Ozark Mountains, Arkansas 1970–1971, Jerry Havens, Collis Geren
Thin Safety Margin: The Sefor Super-Prompt-Critical Transient Experiments, Ozark Mountains, Arkansas 1970–1971, Jerry Havens, Collis Geren
Arkansas Scholarly Editions
Thin Safety Margin charts the history of SEFOR, a twenty-megawatt reactor that operated for three years in the rural Ozark Mountains of Arkansas as part of an internationally sponsored program designed to demonstrate the Doppler effect in plutonium-oxide-fueled fast reactors. Authors Jerry Havens and Collis Geren draw upon this history to assess the accidental explosion risk inherent in using fast reactors to reduce the energy industry’s carbon dioxide emissions.
If a sufficiently powerful fast-neutron explosion were to cause the containment of a reactor such as SEFOR’s to fail, the reactor’s radiotoxic plutonium fuel could vaporize and escape into the surrounding …
Manufacturing: The Qualitative Study Of A Transition To A Green Facility, Brandon David Staves
Manufacturing: The Qualitative Study Of A Transition To A Green Facility, Brandon David Staves
Masters Theses & Specialist Projects
This qualitative study focused on answering three core questions: How have facilities reduce pollutions in regards to the quality of air, water, land, light and noise? Which Types of pollution reduction projects are more or less successful to implement? What types of pollution are facilities focusing on and why? The results of the 15 companies surveyed show a variety of projects that facilities have used to reduce pollution, it also shows that cost is a major factor in the unsuccessful projects, and that facilities are actively focused on reducing Air, Land, and Water pollution. While the data shows a variety …
Model Optimization For Resource Allocation In A Consulting Firm, Riad Alharithi, Karthik Manjunath, Sara Ferdousi, Vladislav Ruchin, Jennifer Lynn Zeitouni
Model Optimization For Resource Allocation In A Consulting Firm, Riad Alharithi, Karthik Manjunath, Sara Ferdousi, Vladislav Ruchin, Jennifer Lynn Zeitouni
Engineering and Technology Management Student Projects
Assigning employees with multiple skill sets to projects at the right time has long been a challenge in professional settings. Whether it is assigning a salesperson to a product, an employee to a task, or a company to a project, many variables affect such decisions and make them taxing for managers and owners. In this project, an optimization issue observed in a team member’s workplace is being addressed.. The aim is to efficiently allocate employees to different concurrent projects. The firm's organizational structure is similar to a Project Management Office (PMO) that has an employee pool with varying skill sets …
Autonomous Farming With Uavs, Pallavi Agrawal, Karthik Manjunath, Cherokee Rawls, Sujitha Raj Rajagopal, Riad Alharithi, Kamal Thapa
Autonomous Farming With Uavs, Pallavi Agrawal, Karthik Manjunath, Cherokee Rawls, Sujitha Raj Rajagopal, Riad Alharithi, Kamal Thapa
Engineering and Technology Management Student Projects
As the global need for food grows, agriculture is adapting autonomous farming techniques to scale in response. One of the most useful tools are UAVs (Unmanned Autonomous Vehicles), which are providing invaluable information and assistance to farmers. In some countries, UAVs are being rapidly embraced, while in others this progress is much slower. For a number of reasons, the United States has not broadly adopted this technology in assisting agricultural practices. In this article, we focus on the challenges companies and farmers are facing in making use of UAVs and what might be done to push this technology into widespread …
Tourism Route Optimization For Portland, Oregon, Duane Murray, Mohammed Thawab, Adnan Binmahfood, Mohammed Zaid, Colin Owens
Tourism Route Optimization For Portland, Oregon, Duane Murray, Mohammed Thawab, Adnan Binmahfood, Mohammed Zaid, Colin Owens
Engineering and Technology Management Student Projects
The city of Portland, Oregon has experienced an unprecedented reduction in tourism due to the COVID-19 pandemic. This reduction in tourism has had a negative impact on all businesses in the area. This paper provides a methodology and tool that can be used to help local businesses potentially gain patrons, and at the same time help visitors in maximizing their time while minimizing costs. when visiting the city after the pandemic abates. To accomplish this, first, an itinerary of selected attractions are filtered by the visitor. Next, a linear programming method using a travelling salesman problem (TSP) algorithm is implemented …
A Methodology For Reliability-Based Selection Of System Of Systems, Justin Brown
A Methodology For Reliability-Based Selection Of System Of Systems, Justin Brown
Operations Research and Engineering Management Theses and Dissertations
Currently, Department of Defense (DoD) systems underperform and have inadequate reliability compared to acquisition expectations. Additionally, System of Systems (SoS) complexity and non-quantifiable approaches to selecting systems to perform a mission cause challenges for the decision-maker. Beyond DoD, mission-critical scenarios exist where responses are not data-driven, such as hurricane response, wildfire response, and littoral search and research missions. Optimization of these missions within a short amount of time can not only increase the probability of success and reduce the cost of performing the mission but allow systems to be used for additional missions.
This dissertation presents solution methodologies to address …
Resource Allocation With Sigmoidal Demands: Mobile Healthcare Units And Service Adoption, Andres Alban, Philippe Blaettchen, Harwin De Vries, Luk Van Wassenhove
Resource Allocation With Sigmoidal Demands: Mobile Healthcare Units And Service Adoption, Andres Alban, Philippe Blaettchen, Harwin De Vries, Luk Van Wassenhove
Research Collection Lee Kong Chian School Of Business
Problem definition: Achieving broad access to health services (a target within the sustainable development goals) requires reaching rural populations. Mobile healthcare units (MHUs) visit remote sites to offer health services to these populations. However, limited exposure, health literacy, and trust can lead to sigmoidal (S-shaped) adoption dynamics, presenting a difficult obstacle in allocating limited MHU resources. It is tempting to allocate resources in line with current demand, as seen in practice. However, to maximize access in the long term, this may be far from optimal, and insights into allocation decisions are limited. Academic/practical relevance: We present a formal model of …
Design Of A Two-Echelon Freight Distribution System In Last-Mile Logistics Considering Covering Locations And Occasional Drivers, Vincent F. Yu, Panca Jodiawan, Ming-Lu Hou, Aldy Gunawan
Design Of A Two-Echelon Freight Distribution System In Last-Mile Logistics Considering Covering Locations And Occasional Drivers, Vincent F. Yu, Panca Jodiawan, Ming-Lu Hou, Aldy Gunawan
Research Collection School Of Computing and Information Systems
This research addresses a new variant of the vehicle routing problem, called the two-echelon vehicle routing problem with time windows, covering options, and occasional drivers (2E-VRPTW-CO-OD). In this problem, two types of fleets are available to serve customers, city freighters and occasional drivers (ODs), while two delivery options are available to customers, home delivery and alternative delivery. For customers choosing the alternative delivery, their demands are delivered to one of the available covering locations for them to pick up. The objective of 2E-VRPTW-CO-OD is to minimize the total cost consisting of routing costs, connection costs, and compensations paid to ODs …
Quantum-Inspired Algorithm For Vehicle Sharing Problem, Whei Yeap Suen, Chun Yat Lee, Hoong Chuin Lau
Quantum-Inspired Algorithm For Vehicle Sharing Problem, Whei Yeap Suen, Chun Yat Lee, Hoong Chuin Lau
Research Collection School Of Computing and Information Systems
Recent hardware developments in quantum technologies have inspired a myriad of special-purpose hardware devices tasked to solve optimization problems. In this paper, we explore the application of Fujitsu’s quantum-inspired CMOS-based Digital Annealer (DA) in solving constrained routing problems arising in transportation and logistics. More precisely in this paper, we study the vehicle sharing problem and show that the DA as a QUBO solver can potentially fill the gap between two common methods: exact solvers like Cplex and heuristics. We benchmark the scalability and quality of solutions obtained by DA with Cplex and with a greedy heuristic. Our results show that …
Challenges And Reflection On Next-Generation Large-Scale Computer Wargame System, Guangya Si, Yanzheng Wang
Challenges And Reflection On Next-Generation Large-Scale Computer Wargame System, Guangya Si, Yanzheng Wang
Journal of System Simulation
Abstract: In view of the systematic, networked and intelligent characteristics of the future war, the major challenges of the new generation of large computer warfare system are proposed, and the next-generation large-scale computer wargame system is constructed. The key technologies of building a new generation of large computer warfare systems, such as intelligent war modeling, architecture integration, resource service management and human-computer interaction are researched.
Fault Diagnosis Of Industrial Process Based On Lle And K-Means Clustering Algorithm, Li Yuan, Zewei Geng
Fault Diagnosis Of Industrial Process Based On Lle And K-Means Clustering Algorithm, Li Yuan, Zewei Geng
Journal of System Simulation
Abstract: Because of the similarity of various types of data in the industrial process. The fault diagnosis using the K-means algorithm has a large error rate. A K-means clustering algorithm based on Locally Linear Embedding (LLE) is proposed. the normal data is reduced by the LLE algorithm and the projection matrix is obtained. The projection matrix is used to map the original fault data to the low-dimensional space and the K-means algorithm clusters is used to carry out the data to establish a detection and diagnosis model. The method is applied to the fault detection and diagnosis in the TE …
Exploring Formal Model Transformation Techniques Within Model Driven Engineering, Zhu Zhi, Lei Sen, Yonglin Lei
Exploring Formal Model Transformation Techniques Within Model Driven Engineering, Zhu Zhi, Lei Sen, Yonglin Lei
Journal of System Simulation
Abstract: With the increasing complexity of simulation system and the wide use of simulation models, the higher requirements of the efficiency and quality for simulation models are needed. Currently, model-driven engineering is mostly applied in many simulation software tools, which cannot really carry out the formal analysis at the model level. Based on model driven engineering, the domain specific language with metamodeling and engineering model continuity is designed. Taking a group fire control channel system as the example, the domain specific language is designed and the conceptual models are transformed into other precise semantics to carry out the final executable …
Research And Implementation Of A High Performance Distributed Object-Oriented Simulation Engine, Xiaodong Huang, Kongshu Xie
Research And Implementation Of A High Performance Distributed Object-Oriented Simulation Engine, Xiaodong Huang, Kongshu Xie
Journal of System Simulation
Abstract: Simulation engine is the core of simulation platform and the operating system of simulation field. On the basis of the reflection-based object-oriented simulation modeling framework and programing specification, aiming at the developing integration and operation requirements for the large-scale multi-granularity computation intensive simulation system, a High-performance Distributed Object-oriented Simulation Engine (HDOSE) is developed. Combined with the brief review of HDOSE development, on the basis of expounding the HDOSE function services and architecture, the key technology, large-scale multi-granularity parallel computation, programming model and interface, parameterized componentized modeling and so on are mainly introduced. The HDOSE typical application cases …
Modeling Research Of Cognition Behavior For Intelligent Wargaming, Xiaoyuan He, Shengming Guo, Wu Lin, Li Dong, Xu Xiao, Li Li
Modeling Research Of Cognition Behavior For Intelligent Wargaming, Xiaoyuan He, Shengming Guo, Wu Lin, Li Dong, Xu Xiao, Li Li
Journal of System Simulation
Abstract: Aiming at the problem of cognitive behavior modeling in the construction and application of intelligent wargaming system, one modeling framework based on Actor-Operations-Scene (AOS) was proposed for C2 agent in wargaming. Then the realization of cognitive behavior modeling method for C2 agent was explored, including the modeling for the scenario oriented knowledge graph, intelligent situation awareness, operational planning, integrated operational control. It provides a feasible scheme for the construction and application of intelligent wargaming system.
Trajectory Planning Of 6-Dof Manipulator Based On Inverse Multi-Objective Optimization, Xianyin Duan, Can Zhang, Zerun Zhu, Zhaoyang Sun, Guozhang Jiang, Xiang Feng
Trajectory Planning Of 6-Dof Manipulator Based On Inverse Multi-Objective Optimization, Xianyin Duan, Can Zhang, Zerun Zhu, Zhaoyang Sun, Guozhang Jiang, Xiang Feng
Journal of System Simulation
Abstract: In order to optimize the machining quality and production efficiency of manipulator, an inverse multi-objective determination method based on the optimization of manipulator stiffness and global travel is proposed. Establishing the forward kinematics model of manipulator, the inverse kinematics is solved by using behaviour tree. The stiffness performance evaluation index and the mathematical model of total stroke of joint angle are constructed to carry out the inverse solution multi-objective optimization. The 7-5-7 order polynomial joint space interpolation algorithm is designed for the trajectory planning. Compared with the commonly used cubic polynomial programming method, the manipulator trajectory obtained by …
Whole Ship Simulation Training Platform Based On Virtual Reality, Jiawen Sun, Hongxiang Ren, Fangbing Xiao, Xiaobin Jiang
Whole Ship Simulation Training Platform Based On Virtual Reality, Jiawen Sun, Hongxiang Ren, Fangbing Xiao, Xiaobin Jiang
Journal of System Simulation
Abstract: Under the current navigation education mode, it is common that trainees lack the overall navigation knowledge and the operation practice on onboard equipment and instruments. It is necessary to develop a whole ship simulation training platform that is not limited by time and sites. The six-degree freedom mathematical model of ship motion is established by using the separation modeling theory of ship maneuverability. The flexible object simulation technology, the modeling and rendering of ocean wave technology, and the reverse dynamics technology are adopted to realize the ship scene roaming and equipment interaction. The simulation results show that …
Intelligent Wargaming System: Change Needed By Next Generation Need To Be Changed, Xiaofeng Hu, Dawei Qi
Intelligent Wargaming System: Change Needed By Next Generation Need To Be Changed, Xiaofeng Hu, Dawei Qi
Journal of System Simulation
Abstract: The future direction of wargaming system is intelligent, and the most significant feature of intelligence is the modeling of cognition. The main problems of wargaming system are summarized, the main difficulties of modeling brought by cognition and the overall framework of intelligent wargaming system design are discussed, the technical ways of transformation and upgrading based on the existing wargaming system are given from four aspects of model construction, system design, wargaming ecology and test inspection. It provides direction and reference to the development and construction of the next generation intelligent wargaming system.
Study On Next-Generation Strategic Wargame System, Wu Xi, Xianglin Meng, Jingyu Yang
Study On Next-Generation Strategic Wargame System, Wu Xi, Xianglin Meng, Jingyu Yang
Journal of System Simulation
Abstract: Strategic wargame is an important support to the strategic decision. The research status and challenges of the strategic wargame are analyzed, and the influence of big data and artificial intelligence technology on the strategic wargame system is studied. The prospects and key technologies of the next-generation strategic wargame system are studied, including the construction of event association graph for strategic topics, generation of strategic decision sparse samples based on generative adversarial nets, gaming strategy learning of human-in-loop hybrid enhancement, and public opinion dissemination modeling technology based on social network. The development trend of the strategic wargame is proposed.
Optimization Algorithm Of Mine Ventilation Based On Sa-Ipso, Liangshan Shao, Wang Zhen, Changming Li
Optimization Algorithm Of Mine Ventilation Based On Sa-Ipso, Liangshan Shao, Wang Zhen, Changming Li
Journal of System Simulation
Abstract: A non-linear optimization mathematical model aiming at the minimum total power of the mine ventilation network is established, in which SA-IPSO algorithm is applied for the optimization. The mutation operation is introduced in the PSO algorithm, in which a new inertia weight is proposed and a new particle selection method is constructed to control the number of particles violating the constraints, and the ability of the PSO algorithm to find boundaries is improved. The constraint conditions of the mine ventilation law are transformed into the penalty term of the objective function. IPSO optimizes the objective function and uses SA …
Multi-Uav Trajectory Planning Simulation Based On Adaptive Extended Potential Field, Wang Ning, Jiyang Dai, Ying Jin, Yeding Li, Liangliang Lu
Multi-Uav Trajectory Planning Simulation Based On Adaptive Extended Potential Field, Wang Ning, Jiyang Dai, Ying Jin, Yeding Li, Liangliang Lu
Journal of System Simulation
Abstract: To address the defects of the traditional artificial potential field method, such as unreachable targets, easy to fall into local minimums, inability to avoid obstacles, and lack of trajectory optimization strategies, and to solve the problem of slow planning rate due to more layers in the layered potential field algorithm, the model of the UAV is established, in which the influence factor of the attractive and repulsive force is introduced into the layered potential field function to solve the problem of unreachable targets, and the " auxiliary force" is introduced to solve the problem of easily falling into local …