Search results for: path planning

Authors: Divya Agarwal, Pushpendra S. Bharti

Abstract:

Autonomous mobile robots (AMR) are expected as smart tools for operations in every automation industry. Path planning and obstacle avoidance is the backbone of AMR as robots have to reach their goal location avoiding obstacles while traversing through optimized path defined according to some criteria such as distance, time or energy. Path planning can be classified into global and local path planning where environmental information is known and unknown/partially known, respectively. A number of sensors are used for data collection. A number of algorithms such as artificial potential field (APF), rapidly exploring random trees (RRT), bidirectional RRT, Fuzzy approach, Purepursuit, A* algorithm, vector field histogram (VFH) and modified local path planning algorithm, etc. have been used in the last three decades for path planning and obstacle avoidance for AMR. This paper makes an attempt to review some of the path planning and obstacle avoidance algorithms used in the field of AMR. The review includes comparative analysis of simulation and mathematical computations of path planning and obstacle avoidance algorithms using MATLAB 2018a. From the review, it could be concluded that different algorithms may complete the same task (i.e. with a different set of instructions) in less or more time, space, effort, etc.

Keywords: Autonomous mobile robots, obstacle avoidance, path planning, and processing time.

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Authors: Lana Dalawr Jalal

Abstract:

This paper addresses the problem of offline path planning for Unmanned Aerial Vehicles (UAVs) in complex threedimensional environment with obstacles, which is modelled by 3D Cartesian grid system. Path planning for UAVs require the computational intelligence methods to move aerial vehicles along the flight path effectively to target while avoiding obstacles. In this paper Modified Particle Swarm Optimization (MPSO) algorithm is applied to generate the optimal collision free 3D flight path for UAV. The simulations results clearly demonstrate effectiveness of the proposed algorithm in guiding UAV to the final destination by providing optimal feasible path quickly and effectively.

Keywords: Obstacle Avoidance, Particle Swarm Optimization, Three-Dimensional Path Planning Unmanned Aerial Vehicles.

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Authors: Neda Shahidi, Hadi Esmaeilzadeh, Marziye Abdollahi, Caro Lucas

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In this paper, the problem of finding the optimal collision free path for a mobile robot, the path planning problem, is solved using an advanced evolutionary algorithm called memetic algorithm. What is new in this work is a novel representation of solutions for evolutionary algorithms that is efficient, simple and also compatible with memetic algorithm. The new representation makes it possible to solve the problem with a small population and in a few generations. It also makes the genetic operator simple and allows using an efficient local search operator within the evolutionary algorithm. The proposed algorithm is applied to two instances of path planning problem and the results are available.

Keywords: Path planning problem, Memetic Algorithm, Representation.

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Authors: Takahiro Takayama, Takao Kawamura, Toshihiko Sasama, Kazunori Sugahara

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Recently, web services to access from many type devices are often used. We have developed the shortest path planning system called "Bus-Net" in Tottori prefecture as a web application to sustain the public transport. And it used the same user interface for both devices. To support both devices, the interface cannot use JavaScript and so on. Thus, we developed the method that use individual user interface for each device type to improve its convenience. To be concrete, we defined formats of condition input to the path planning system and result output from it and separate the system into the request processing part and user interface parts that depend on device types. By this method, we have also developed special device for Bus-Net named "Intelligent-Bus-Stop".

Keywords: Bus, Path planning, Public transport, User interface

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Authors: Rong-Jong Wai, Chia-Ming Liu

Abstract:

Generally speaking, the mobile robot is capable of sensing its surrounding environment, interpreting the sensed information to obtain the knowledge of its location and the environment, planning a real-time trajectory to reach the object. In this process, the issue of obstacle avoidance is a fundamental topic to be challenged. Thus, an adaptive path-planning control scheme is designed without detailed environmental information, large memory size and heavy computation burden in this study for the obstacle avoidance of a mobile robot. In this scheme, the robot can gradually approach its object according to the motion tracking mode, obstacle avoidance mode, self-rotation mode, and robot state selection. The effectiveness of the proposed adaptive path-planning control scheme is verified by numerical simulations of a differential-driving mobile robot under the possible occurrence of obstacle shapes.

Keywords: Adaptive Path Planning, Mobile Robot ObstacleAvoidance

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Authors: Zeyu Zhang, Guisheng Yin, Ziying Zhang, Liguo Zhang

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This paper mainly studies the path planning method based on ant colony optimization (ACO), and proposes heuristic integration ant colony optimization (HIACO). This paper not only analyzes and optimizes the principle, but also simulates and analyzes the parameters related to the application of HIACO in path planning. Compared with the original algorithm, the improved algorithm optimizes probability formula, tabu table mechanism and updating mechanism, and introduces more reasonable heuristic factors. The optimized HIACO not only draws on the excellent ideas of the original algorithm, but also solves the problems of premature convergence, convergence to the sub optimal solution and improper exploration to some extent. HIACO can be used to achieve better simulation results and achieve the desired optimization. Combined with the probability formula and update formula, several parameters of HIACO are tested. This paper proves the principle of the HIACO and gives the best parameter range in the research of path planning.

Keywords: Ant colony optimization, heuristic integration, path planning

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Authors: In-Geun Lim, Jin-Soo Kim, Chirl-Hwa Lee

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This paper presents a constrained valley detection algorithm. The intent is to find valleys in the map for the path planning that enables a robot or a vehicle to move safely. The constraint to the valley is a desired width and a desired depth to ensure the space for movement when a vehicle passes through the valley. We propose an algorithm to find valleys satisfying these 2 dimensional constraints. The merit of our algorithm is that the pre-processing and the post-processing are not necessary to eliminate undesired small valleys. The algorithm is validated through simulation using digitized elevation data.

Keywords: valley, width, depth, path planning.

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Authors: Ellips Masehian, Golnaz Habibi

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This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.

Keywords: 3D C-space, Binary Integer Programming (BIP), Delaunay Tessellation, Robot Motion Planning.

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Authors: Ethar H. Khalil, Bahaa I. Kazem

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In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.

Keywords: Mobile robot, path planning, Bezier curve.

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Authors: K. Oh, J. P. Hwang, E. Kim, H. Lee

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This paper presents an algorithm which extends the rapidly-exploring random tree (RRT) framework to deal with change of the task environments. This algorithm called the Retrieval RRT Strategy (RRS) combines a support vector machine (SVM) and RRT and plans the robot motion in the presence of the change of the surrounding environment. This algorithm consists of two levels. At the first level, the SVM is built and selects a proper path from the bank of RRTs for a given environment. At the second level, a real path is planned by the RRT planners for the given environment. The suggested method is applied to the control of KUKA™,, a commercial 6 DOF robot manipulator, and its feasibility and efficiency are demonstrated via the cosimulatation of MatLab™, and RecurDyn™,.

Keywords: Path planning, RRT, 6 DOF manipulator, SVM.

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Authors: Siliang Wang, Minghui Wang, Jun Hu

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A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: Seiichi Tamagawa, Takao Kawamura, Toshihiko Sasama, Kazunori Sugahara

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Route bus system is one of fundamental transportation device for aged people and students, and has an important role in every province. However, passengers decrease year by year, therefore the authors have developed the system called "Bus-Net" as a web application to sustain the public transport. But there are two problems in Bus-Net. One is the user interface that does not consider the variety of the device, and the other is the path planning system that dose not correspond to the on-demand bus. Then, Bus-Net was improved to be able to utilize the variety of the device, and a new function corresponding to the on-demand bus was developed.

Keywords: Route Bus, Path Planning System, User Interface, Ondemandbus, Reservation system.

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Authors: Penghui Zhang, Hua Zhang, Jun-Bo Wang, Cheng Zeng, Zijian Cao

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With the development of software-defined networks and programmable data planes, in-band network telemetry (INT) has become an emerging technology in communications because it can get accurate and real-time network information. However, due to the expansion of the network scale, existing telemetry systems, to the best of the authors’ knowledge, have difficulty in meeting the common requirements of low overhead, low latency and full coverage for traffic measurement. This paper proposes a network-wide telemetry system with a low-latency low-overhead path planning (INT-LLPP). This paper builds a mathematical model to analyze the telemetry overhead and latency of INT systems. Then, we adopt a greedy-based path planning algorithm to reduce the overhead and latency of the network telemetry with the full network coverage. The simulation results show that network-wide telemetry is achieved and the telemetry overhead can be reduced significantly compared with existing INT systems. INT-LLPP can control the system latency to get real-time network information.

Keywords: Network telemetry, network monitoring, path planning, low latency.

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Authors: Sohrab Khanmohammadi, Raana Soltani Zarrin

Abstract:

In this paper, a heuristic method for simultaneous rescue robot path-planning and mission scheduling is introduced based on project management techniques, multi criteria decision making and artificial potential fields path-planning. Groups of injured people are trapped in a disastrous situation. These people are categorized into several groups based on the severity of their situation. A rescue robot, whose ultimate objective is reaching injured groups and providing preliminary aid for them through a path with minimum risk, has to perform certain tasks on its way towards targets before the arrival of rescue team. A decision value is assigned to each target based on the whole degree of satisfaction of the criteria and duties of the robot toward the target and the importance of rescuing each target based on their category and the number of injured people. The resulted decision value defines the strength of the attractive potential field of each target. Dangerous environmental parameters are defined as obstacles whose risk determines the strength of the repulsive potential field of each obstacle. Moreover, negative and positive energies are assigned to the targets and obstacles, which are variable with respects to the factors involved. The simulation results show that the generated path for two cases studies with certain differences in environmental conditions and other risk factors differ considerably.

Keywords: Artificial potential field, GERT, path planning

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Authors: U. Yerlikaya, R. T. Balkan

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In this research, a method is developed to obtain high-dimensional configuration space for path planning problems. In typical cases, the path planning problems are solved directly in the 3-dimensional (D) workspace. However, this method is inefficient in handling the robots with various geometrical and mechanical restrictions. To overcome these difficulties, path planning may be formalized and solved in a new space which is called configuration space. The number of dimensions of the configuration space comes from the degree of freedoms of the system of interest. The method can be applied in two ways. In the first way, the point clouds of all the bodies of the system and interaction of them are used. The second way is performed via using the clearance function of simulation software where the minimum distances between surfaces of bodies are simultaneously measured. A double-turret system is held in the scope of this study. The 4-D configuration space of a double-turret system is obtained in these two ways. As a result, the difference between these two methods is around 1%, depending on the density of the point cloud. The disparity between the two forms steadily decreases as the point cloud density increases. At the end of the study, in order to verify 4-D configuration space obtained, 4-D path planning problem was realized as 2-D + 2-D and a sample path planning is carried out with using A* algorithm. Then, the accuracy of the configuration space is proved using the obtained paths on the simulation model of the double-turret system.

Keywords: A* Algorithm, autonomous turrets, high-dimensional C-Space, manifold C-Space, point clouds.

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Authors: T.C. Manjunath,

Abstract:

This paper features the trajectory planning design of a indigenously developed 4-Axis SCARA robot which is used for doing successful robotic manipulation task in the laboratory. Once, a trajectory is being designed and given as input to the robot, the robot's gripper tip moves along that specified trajectory. Trajectories have to be designed in the work space only. The main idea of this paper is to design a continuous path trajectory model for the indigenously developed SCARA robot arm during its maneuvering from one point to another point (during pick and place operations) in a workspace avoiding all the obstacles in its path of motion.

Keywords: SCARA, Trajectory, Planning.

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Authors: I. Sahul Hamid, Abraham V. M.

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A decomposition of a graph G is a collection ψ of subgraphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path or an induced cycle in G, then ψ is called an induced path decomposition of G. The minimum cardinality of an induced path decomposition of G is called the induced path decomposition number of G and is denoted by πi(G). In this paper we initiate a study of this parameter.

Keywords: Path decomposition, Induced path decomposition, Induced path decomposition number.

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Authors: Johan Segeborn, Johan S. Carlson, Robert Bohlin, Rikard Söderberg

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This paper presents a method to support dynamic packing in cases when no collision-free path can be found. The method, which is primarily based on path planning and shrinking of geometries, suggests a minimal geometry design change that results in a collision-free assembly path. A supplementing approach to optimize geometry design change with respect to redesign cost is described. Supporting this dynamic packing method, a new method to shrink geometry based on vertex translation, interweaved with retriangulation, is suggested. The shrinking method requires neither tetrahedralization nor calculation of medial axis and it preserves the topology of the geometry, i.e. holes are neither lost nor introduced. The proposed methods are successfully applied on industrial geometries.

Keywords: Dynamic packing, path planning, shrinking.

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Authors: Azali Saudi, Jumat Sulaiman

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Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: Doraid Dalalah

Abstract:

A topologically oriented neural network is very efficient for real-time path planning for a mobile robot in changing environments. When using a recurrent neural network for this purpose and with the combination of the partial differential equation of heat transfer and the distributed potential concept of the network, the problem of obstacle avoidance of trajectory planning for a moving robot can be efficiently solved. The related dimensional network represents the state variables and the topology of the robot's working space. In this paper two approaches to problem solution are proposed. The first approach relies on the potential distribution of attraction distributed around the moving target, acting as a unique local extreme in the net, with the gradient of the state variables directing the current flow toward the source of the potential heat. The second approach considers two attractive and repulsive potential sources to decrease the time of potential distribution. Computer simulations have been carried out to interrogate the performance of the proposed approaches.

Keywords: Mobile robot, Path Planning, Mesh, Potential field.

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Authors: Amir Reza Saffari Azar Alamdari

Abstract:

In this paper, a model of self-organizing spiking neural networks is introduced and applied to mobile robot environment representation and path planning problem. A network of spike-response-model neurons with a recurrent architecture is used to create robot-s internal representation from surrounding environment. The overall activity of network simulates a self-organizing system with unsupervised learning. A modified A* algorithm is used to find the best path using this internal representation between starting and goal points. This method can be used with good performance for both known and unknown environments.

Keywords: Mobile Robot, Path Planning, Self-organization, Spiking Neural Networks.

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: Path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart.

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Authors: Miloš Šeda

Abstract:

Finding the shortest path between two positions is a fundamental problem in transportation, routing, and communications applications. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of visibility graphs in point-to-point motion planning in the Euclidean plane and an alternative approach using Voronoi diagrams that decreases the probability of collisions with obstacles. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the plane using either only straight connections between pairs of points (minimum spanning tree) or allowing the addition of auxiliary points to the set to obtain shorter spanning networks (minimum Steiner tree).

Keywords: motion planning, spanning tree, Steiner tree, Delaunay triangulation, Voronoi diagram.

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Authors: Jean Berger, Mohamed Barkaoui

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Discrete search path planning in time-constrained uncertain environment relying upon imperfect sensors is known to be hard, and current problem-solving techniques proposed so far to compute near real-time efficient path plans are mainly bounded to provide a few move solutions. A new information-theoretic –based open-loop decision model explicitly incorporating false alarm sensor readings, to solve a single agent military logistics search-and-delivery path planning problem with anticipated feedback is presented. The decision model consists in minimizing expected entropy considering anticipated possible observation outcomes over a given time horizon. The model captures uncertainty associated with observation events for all possible scenarios. Entropy represents a measure of uncertainty about the searched target location. Feedback information resulting from possible sensor observations outcomes along the projected path plan is exploited to update anticipated unit target occupancy beliefs. For the first time, a compact belief update formulation is generalized to explicitly include false positive observation events that may occur during plan execution. A novel genetic algorithm is then proposed to efficiently solve search path planning, providing near-optimal solutions for practical realistic problem instances. Given the run-time performance of the algorithm, natural extension to a closed-loop environment to progressively integrate real visit outcomes on a rolling time horizon can be easily envisioned. Computational results show the value of the approach in comparison to alternate heuristics.

Keywords: Search path planning, false alarm, search-and-delivery, entropy, genetic algorithm.

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Authors: P. K. Panigrahi, Saradindu Ghosh, Dayal R. Parhi

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Now-a-days autonomous mobile robots have found applications in diverse fields. An autonomous robot system must be able to behave in an intelligent manner to deal with complex and changing environment. This work proposes the performance of path planning and navigation of autonomous mobile robot using Gravitational Search Algorithm (GSA), Simulated Annealing (SA) and Particle Swarm optimization (PSO) based intelligent controllers in an unstructured environment. The approach not only finds a valid collision free path but also optimal one. The main aim of the work is to minimize the length of the path and duration of travel from a starting point to a target while moving in an unknown environment with obstacles without collision. Finally, a comparison is made between the three controllers, it is found that the path length and time duration made by the robot using GSA is better than SA and PSO based controllers for the same work.

Keywords: Autonomous Mobile Robot, Gravitational Search Algorithm, Particle Swarm Optimization, Simulated Annealing Algorithm.

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Authors: Jürgen Beyer

Abstract:

In association with path dependence, researchers often talk of institutional “lock-in", thereby indicating that far-reaching path deviation or path departure are to be regarded as exceptional cases. This article submits the alleged general inclination for stability of path-dependent processes to a critical review. The different reasons for path dependence found in the literature indicate that different continuity-ensuring mechanisms are at work when people talk about path dependence (“increasing returns", complementarity, sequences etc.). As these mechanisms are susceptible to fundamental change in different ways and to different degrees, the path dependence concept alone is of only limited explanatory value. It is therefore indispensable to identify the underlying continuity-ensuring mechanism as well if a statement-s empirical value is to go beyond the trivial, always true “history matters".

Keywords: path dependence, increasing returns, historicalinstitutionalism, lock-in.

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Authors: Jean Berger, Nassirou Lo, Martin Noel

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Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: Search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization.

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Authors: C. Tung, P.-L. Tso

Abstract:

This paper presents a complete procedure for tool path planning and blade machining in 5-axis manufacturing. The actual cutting contact and cutter locations can be determined by lead and tilt angles. The tool path generation is implemented by piecewise curved approximation and chordal deviation detection. An application about drive surface method promotes flexibility of tool control and stability of machine motion. A real manufacturing process is proposed to separate the operation into three regions with five stages and to modify the local tool orientation with an interactive algorithm.

Keywords: 5-axis machining, tool orientation, lead and tilt angles, tool path generation.

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Authors: Almutasim Billa A. Alanazi, Hal S. Tharp

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Artificial Intelligence (AI), specifically Reinforcement Learning (RL), has proven helpful in many control path planning technologies by maximizing and enhancing their performance, such as navigation systems. Since it learns from experience by interacting with the environment to determine the optimal policy, the optimal policy takes the best action in a particular state, accounting for the long-term rewards. Most navigation systems focus primarily on "arriving faster," overlooking safety and efficiency while estimating the optimum path, as safety and efficiency are essential factors when planning for a long-distance journey. This paper represents an RL control model that proposes a control mechanism for improving navigation systems. Also, the model could be applied to other control path planning applications because it is adjustable and can accept different properties and parameters. However, the navigation system application has been taken as a case and evaluation study for the proposed model. The model utilized a Q-learning algorithm for training and updating the policy. It allows the agent to analyze the quality of an action made in the environment to maximize rewards. The model gives the ability to update rewards regularly based on safety and efficiency assessments, allowing the policy to consider the desired safety and efficiency benefits while making decisions, which improves the quality of the decisions taken for path planning compared to the conventional RL approaches.

Keywords: Artificial intelligence, control system, navigation systems, reinforcement learning.

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Authors: Chang-le Lu, Yong Chen

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The shortest path question is in a graph theory model question, and it is applied in many fields. The most short-path question may divide into two kinds: Single sources most short-path, all apexes to most short-path. This article mainly introduces the problem of all apexes to most short-path, and gives a new parallel algorithm of all apexes to most short-path according to the Dijkstra algorithm. At last this paper realizes the parallel algorithms in the technology of C # multithreading.

Keywords: Dijkstra algorithm, parallel algorithms, multi-thread technology, most short-path, ratio.

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