Shortest Path Evaluation with Enhanced Linear Graph and Dijkstra Algorithm

In this paper a novel combination of data structures and algorithms is presented as a fast and efcient practical approach to path planning for unmanned vehicles. This approach utilizes an architecture that integrates effective obstacle representation using an efcient Quadtree data structure, with path planning based on a modied Rapidly-exploring Random Tree (RRT) algorithm, and a path pruning technique based on Dijkstra’s algorithm, resulting in rapid discovery of sub-optimal feasible paths. One of the computationally expensive steps of the RRT algorithm is checking RRT segments for collision with obstacles. To address this problem, an efcient obstacle representation using Quadtrees is implemented enabling fast segment checks. While the RRT approach is guaranteed to nd a feasible path through complex obstacle elds with the probability of discovery approaching one as the number of iterations increases, the resulting paths may be far from optimal as the only criterion embedded in the RRT search is feasibility. For this reason, the paths generated by the RRT algorithm are passed through Dijkstra algorithm that nds a shortest obstacle-free path among the points on the path. Dijkstra algorithm that re-samples the segments of the path and nds the shortest path among the new points is implemented resulting in paths that are very close to the optimal ones. To speed up the computation, the basic search algorithm is implemented as a dual RRT from the initial and nal points. To account for motion transients along the path, a suitable size corridor is introduced, assuring that the vehicle has enough room for maneuvering among the obstacles. This computationally efcient architecture lends itself to real-time implementation for both pre-planning with known obstacles as well as rapid reactive re-planning in the presence of new pop-up obstacles. The proposed technique is evaluated using several challenging path-planning examples characterized by a large number of non-convex constraints arising in cluttered obstacle elds with known and unknown obstacles. A modication that allows an easy way to introduce vehicle dynamics constraints or actuation failures is also implemented. Algorithms have been implemented for two as well as three dimensional path planning applications.

Autonomous unmanned aerial vehicles (UAVs) need to dynamically re-plan paths online to avoid newly detected obstacles and no-fly zones. Existing 3D path planning methods are either too computationally intensive for online use or have practical limitations for actual applications. We propose a new method based on visibility graphs that is both computationally efficient for online use and is suitable for actual applications. We consider the 3D space to be composed of many 2D planes that all pass through the current position of the UAV and the destination point. Finding the shortest collision-free path in each plane is a 2D path planning problem which can be solved by using existing visibility graph algorithms. We then collect all the shortest paths generated from each 2D plane and find the shortest path in the whole 3D space. We present the results of the proposed 3D path planning algorithm for two cases to demonstrate that the proposed method is effective.

This paper proposes a parallel shortest path-searching algorithm and implements it on a newly structured parallel reconfigurable processor, DAPDNA-2 (IPFlex Inc). Routing determines the shortest paths from the source to the ultimate destination through intermediate nodes. In open shortest path first (OSPF), Dijkstra's shortest path algorithm, which is the conventional one, finds the shortest paths from the source on a program counter-based processor. The calculation time for Dijkstra's algorithm is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) when the number of nodes is N. When the network scale is large, calculation time required by Dijkstra's algorithm increases rapidly. It's very difficult to compute Dijkstra's algorithm in parallel because of the need for previous calculation results, so Dijkstra's algorithm is unsuitable for parallel processors. Our proposed scheme finds the shortest paths using a simultaneous multi-path search method. In contrast with Dijkstra's algorithm, several nodes can be determined at one time. Moreover, we partition the network into different groups (network groups) and find the all-node pair's shortest path in each group using a pipeline operation. Networks can be abstracted, and the shortest paths in very large networks can be found easily. The proposed scheme can decrease calculation time from O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(N) using a pipeline operation on DAPDNA-2. Our simulations show that the proposed algorithm uses 99.6% less calculation time than Dijkstra's algorithm. The proposed algorithm can be applied to the very large Internet network designs of the future.

Graph-based approaches for simulating pedestrian dynamics in building models

This paper presents a new method to design the shortest smooth 3D path for multiple Autonomous Underwater Vehicles (AUVs) to visit multiple targets. This path planning method can be separated into the target assignment problem and path designing problem. For the target assignment problem, we compare the genetic algorithm and ant colony optimization algorithm to get target sequence for each AUV with less distance cost. For the given target sequence for each AUVs, the path designing problem is to design shortest smooth path for visiting each target with constraint of G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> continuity. This paper designs 3D Bezier curves by selecting the control points along the incoming and out-going heading direction. Each two-target segment has a set of discrete in-coming and out-going heading direction. For multi-target path planning, the in-coming heading direction and the out-going heading direction at each target have to be the same and the shortest path is selected via back propagation algorithm. It is proved that the combined 3D cubic Bezier curves ensure G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> continuity along the entire multi-target path. Back propagation algorithm is applied to find the shortest curve sequence for multiple targets.

Existing path planning algorithms are capable of finding physically feasible, shortest, and energy-efficient paths for mobile robots navigating on uneven terrains. However, shortest paths on uneven terrains are often energy inefficient while energy-optimal paths usually take long time to be traversed. Therefore, due to time and energy constraints imposed on mobile robots, these shortest and energy-optimal paths might not be applicable. We propose a multiobjective path planner that can find pareto-optimal solutions in terms of path length and energy consumption. It is based on NAMOA* search algorithm that utilizes a proposed monotone heuristic cost function. The simulation results show that nondominated path options found by the proposed path planner can be very useful in many real-world applications.

The use of unmanned aerial vehicles (UAV) is increasing today. UAVs can be divided into two parts, which are remote controlled and can travel automatically due to a certain battery problem. Recent research has also focused on the development and application of new algorithms to autonomously control these vehicles and determine the shortest flight paths. Together with these researches, UAVs are used in many civil activities such as weather forecasts, environmental studies and traffic control. Three-dimensional (3D) path planning is an important issue for autonomously moving UAVs. The shortest path for Unmanned Aerial Vehicles (UAV) is determined by using two-dimensional (2D) path planning algorithms using the obstacles in the environment, and allows UAVs to perform their environmental tasks as soon as possible. The purpose of this study is to determine the shortest path to the target point and avoiding obstacles for UAVs using the Dijkstra algorithm. It was developed to evaluate the arrival time of the UAVs in the path planning algorithm with the simulation performed in the MATLAB program. In this study, the obstacles were defined for the purpose of the building with different heights and different widths and 2D and 3D models were carried out, assuming that the UAV flies at certain heights. In addition, the flight of the UAVs in the route planning determined in the real applications was carried out and the data such as battery consumption, amount of battery spent, speed, amount of travel were examined.

Autonomous Mobile Robots (AMRs) are utilized for handling goods and workpieces in factories and warehouses. The advantages of AMRs are completing automated tasks, reducing labour costs, improving efficiency and increasing convenience. In order to enable AMRs to navigate and move faster in all directions, this study focuses on the implementation of an AMR equipped with four Mecanum wheels to execute path planning tasks for a human-robot collaboration work. To achieve the path planning tasks, the AMR employs a Simultaneous Localization and Mapping (SLAM) algorithm based on the Robot Operating System (ROS) and light detection and ranging (LIDAR) sensors are used for mapping. With omnidirectional mobility of the AMR, a global path planning method is crucial to ensure the AMR’s navigation in the environment. This study adopts the A* algorithm and Voronoi diagram as the global path planning method; it can find the shortest path for navigation of the AMR. To improve the efficiency of AMR path planning, the Voronoi diagram is used to describe the map and the shortest path is built by Dijkstra algorithm. The collision-free A* algorithm will avoid collisions effectively and find the optimal path according to the shortest path tree. Voronoi algorithm is more suitable for use in factory environments with obstacles. Data fusion technology significantly improves positioning accuracy through the integration of visual odometers, IMUs, and traditional odometers.

Since its inception in 1959, Dijkstra's algorithm has long been regarded as the optimal solution for graph theory's single-source shortest path problem. Over the past seven decades, it has permeated daily life, underpinning applications in traffic navigation, geographic information systems (GIS), robotics, and communication networks. However, amid rapid technological advancement, the rise of smart cities and real-time systems has exposed critical limitations of traditional approachesnamely, inadequate scalability, poor dynamic adaptability, and exponential degradation in computational efficiency with increasing scale. Leveraging extensive literature, this paper systematically analyzes the algorithm's evolution across five dimensions: static optimizationheuristic extensiondynamic update3D integrationengineering deployment. The salient results encompass: refined data structures, such as Net-Arc dual-table compression, facilitating O(1) adjacency-edge access; augmented heuristic algorithms that markedly improve search efficacy while preserving solution optimality (or with negligible concession); dynamic weight update protocols diminishing computational complexity to O(|Q| log|Q|); the incorporation of three-dimensional modeling, enhancing Unmanned Aerial Vehicle (UAV) ranging precision by 8.72 meters; and pragmatic implementations, exemplified by optimal railway route determination. Future research must address negative-weight edges, distributed computing for ultra-large graphs (&gt;10 nodes), and real-time path planning integrated with digital twins.

With the development of urbanization and the rise of commercial center, the complex internal structure of public commercial buildings and the high density of people make the evacuation of people more aimless, and accurate path planning plays an important role in escape and evacuation. Dijkstra algorithm can only satisfy the single point to single point shortest path planning situation and cannot actually solve the shortest path planning problem with many source points and sink points. Thus, this paper studies the shortest path of escape with multi-source/multi-sink, and proposes an improved Dijkstra algorithm, which can solve the shortest path planning task of escape from multi-source point to multi-sink point and has fast and efficient characteristics of the original Dijkstra algorithm, thus improving the escape efficiency of personnel. In the end, this paper simulates the improved algorithm using the data of different distribution density of different people. The experimental results show that the proposed algorithm is more practical for the shortest path planning from multi-source to multi-sink under the condition of relatively dispersed personnel.

Path planning is an important area of mobile robot research, and the ant colony optimization algorithm is essential for analyzing path planning. However, the current ant colony optimization algorithm applied to the path planning of mobile robots still has some limitations, including early blind search, slow convergence speed, and more turns. To overcome these problems, an improved ant colony optimization algorithm is proposed in this paper. In the improved algorithm, we introduce the idea of triangle inequality and a pseudo-random state transfer strategy to enhance the guidance of target points and improve the search efficiency and quality of the algorithm. In addition, we propose a pheromone update strategy based on the partition method with upper and lower limits on the pheromone concentration. This can not only improve the global search capability and convergence speed of the algorithm but also avoid the premature and stagnation phenomenon of the algorithm during the search. To prevent the ants from getting into a deadlock state, we introduce a backtracking mechanism to enable the ants to explore the solution space better. Finally, to verify the effectiveness of the proposed algorithm, the algorithm is compared with 11 existing methods for solving the robot path planning problem, including several ACO variants and two commonly used algorithms (A* algorithm and Dijkstra algorithm), and the experimental results show that the improved ACO algorithm can plan paths with faster convergence, shorter path lengths, and higher smoothness. Specifically, the algorithm produces the shortest path length with a standard deviation of zero while ensuring the most rapid convergence and the highest smoothness in the case of the shortest path in four different grid environments. These experimental results demonstrate the effectiveness of the proposed algorithm in path planning.

Path planning is an important area in the control of autonomous mobile robots. Recent work has focused on aspects reductions in processing time than the memory requirements. A dynamic environment uses a lot of memory and hence the processing time increases too. Our approach is to reduce the processing time by the use of a pictorial approach to reduce the number of data used. In this paper, we present a path planning approach that operates in three steps. First, a construction of the visibility tree is performed. The following treatments are not performed on the original image but on the result tree whose elements are specific points of the environment linked by the relationship of visibility. We construct thereafter a visibility graph which one seeks the shortest path. This approach has a great interest because of its fast execution speed. The path search is extended also for the case where obstacles can move. The moving obstacles may be other mobile robots whose trajectories and speeds are known initially. At the end, some applications are provided on solving similar problem such civil aviation in order to guide plane avoiding collisions.

Path planning aims to enable autonomous robots to navigate safely and efficiently from a starting point to a target point in challenging and dynamic environments. Path planning in robotics is highly significant and still an ongoing subject of research. The increasing use of robots in various applications such as industrial automation, service robotics, and autonomous vehicles has brought forth the need for reliable and efficient path planning algorithms. The inherent capability of Voronoi diagrams to partition space based on proximity makes them an effective framework for research in path planning. Ant colony optimization, a bio-inspired optimization technique, is based on the foraging behavior of ants and is commonly employed to address the traveling salesman problem and various other combinatorial optimization problems. A hybrid method was adopted in this study by combining a Voronoi diagram and an ant colony algorithm. To create paths for the robot where it can stay as far away from obstacles as possible, a Voronoi diagram was utilized. Additionally, to find the shortest path from the starting point to the destination among these paths, ant colony optimization was employed. The main contribution of the study lies in the combination of the Voronoi diagram for obstacle avoidance and ant colony optimization for finding the optimal path. The combination of these techniques makes an effective contribution to robotic path planning by focusing on ensuring safety by avoiding obstacles while optimizing the shortest path. Experimental studies show that the hybrid method produces successful results for the desired purpose.

Mobile robots are mostly used in many industrial and military applications. Researches in the path planning is one of the most important aspects in mobile robot researches. Path planning for a mobile robot need to find a collision free path through the robot's environment with obstacles from the specified start location to a desired(target) goal location while satisfying certain optimization conditions. Existing path planning methods like graphical methods such as visibility graph, the potential field and the cell decomposition are designed for static environments, in which there are stationary obstacles. In practical systems such as Marine Science Research, Robots in Industry, and military combat applications, robots usually face dynamic environments where both moving and stationary obstacles exist. This project proposes a heuristic based method to search the feasible initial path efficiently. The heuristic based method is then combined into the simulated annealing algorithm based approach for dynamic robot path planning. Therefore the quality of the solution is characterised by the length of the planned path and it is improved with the combined heuristic method in the simulated annealing based approach for both runtime and offline path planning.

Door to door space-time path planning of intercity multimodal transport network using improved ripple-spreading algorithm