Planning the Shortest Path in Cluttered Environments: A Review and a Planar Convex Hull-Based Approach

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Time Complexity ◽  
Optimal Path ◽  
Optimal Solution ◽  
Free Graph ◽  
Worst Case ◽  
Cluttered Environments ◽  
Planar Convex ◽  
Polyhedral Obstacles

Abstract Routing or path-planning is the problem of finding a collision-free and preferably shortest path in an environment usually scattered with polygonal or polyhedral obstacles. The geometric algorithms oftentimes tackle the problem by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra’s can then be applied to find an optimal path on the created graph. Previously developed methods to construct the collision-free graph, without loss of generality, explore the entire workspace of the problem. For the single-source single-destination planning problems, this results in generating some unnecessary information that has little value and could increase the time complexity of the algorithm. In this paper, first a comprehensive review of the previous studies on the path-planning subject is presented. Next, an approach to address the planar problem based on the notion of convex hulls is introduced and its efficiency is tested on sample planar problems. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points. Hence, we are able to reduce the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles in a planar workspace are intersecting, the algorithm yields a time complexity of O(n log(n/f)), with n being the total number of vertices and f being the number of obstacles. The computational complexity of the algorithm outperforms the previous attempts in reducing the size of the graph yet generates the exact solution.

Path Planning for Manipulator Robots in Cluttered Environments

2005 ◽  
Author(s):  
Samir Lahouar ◽  
Said Zeghloul ◽  
Lotfi Romdhane
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Planning Method ◽  
Search Process ◽  
Grid Cells ◽  
Heuristic Function ◽  
Search Mode ◽  
Cluttered Environments ◽  
Grid Sampling ◽  
Cluttered Environment

In this paper we propose a new path planning method for robot manipulators in cluttered environments, based on lazy grid sampling. Grid cells are built while searching for the path to the goal configuration. The proposed planner acts in two modes. A depth mode, while the robot is far from obstacles, makes it evolve toward its goal. While a width search mode becomes active when the robot gets close to an obstacle. This method provides the shortest path to go around the obstacle. It also reduces the gap between pre-computed grid methods and lazy grid methods. No heuristic function is needed to guide the search process. An example dealing with a robot in a cluttered environment is presented to show the efficiency of the method.

CELLULAR AUTOMATA AND OPTIMAL PATH PLANNING

1996 ◽  
Vol 06 (03) ◽  
pp. 603-610 ◽  
Author(s):  
M. STÄMPFLE
Keyword(s):  
Cellular Automata ◽  
Path Planning ◽  
Optimal Path ◽  
Shortest Paths ◽  
Optimal Solution ◽  
Starting Position ◽  
Optimal Path Planning ◽  
Time Space ◽  
Neural Network Theory ◽  
Optimal Configurations

Cellular automata are deterministic dynamical systems in which time, space, and state values are discrete. Although they consist of uniform elements, which interact only locally, cellular automata are capable of showing complex behavior. This property is exploited for solving path planning problems in workspaces with obstacles. A new automaton rule is presented which calculates simultaneously all shortest paths between a starting position and a target cell. Based on wave propagation, the algorithm ensures that the dynamics settles down in an equilibrium state which represents an optimal solution. Rule extensions include calculations with multiple starts and targets. The method allows applications on lattices and regular, weighted graphs of any finite dimension. In comparison with algorithms from graph theory or neural network theory, the cellular automaton approach has several advantages: Convergence towards optimal configurations is guaranteed, and the computing costs depend only linearly on the lattice size. Moreover, no floating-point calculations are involved.

Three-Dimensional Shortest Path Planning in the Presence of Polyhedral Obstacles

1996 ◽  
Vol 210 (4) ◽  
pp. 373-381 ◽  
Author(s):  
K Jiang ◽  
L D Seneviratne ◽  
S W E Earles
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Shortest Path ◽  
Turning Points ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Visibility Graph ◽  
Three Dimensions ◽  
View Point ◽  
Polyhedral Obstacles

A new algorithm is presented for solving the three-dimensional shortest path planning (3DSP) problem for a point object moving among convex polyhedral obstacles. It is the first non-approximate three-dimensional path planing algorithm that can deal with more than two polyhedral obstacles. The algorithm extends the visibility graph concept from two dimensions to three dimensions. The two main problems with 3DSP are identifying the edge sequence the shortest path passes through and the turning points of the shortest path. A technique based on projective relationships is presented for identifying the set of visible boundary edges (VBE) corresponding to a given view point over which the shortest path, from the view point to the goal, will pass. VBE are used to construct an initial reduced visibility graph (RVG). Optimization is used to revise the position of the turning points and hence the three-dimensional RVG (3DRVG) and the global shortest path is then selected from the 3DRVG. The algorithm is of computational complexity O(n3vk), where n is the number of verticles, v is the maximum number of vertices on any one obstacle and k is the number of obstacles. The algorithm is applicable only with polyhedral obstacles, as the theorems developed for searching for the turning points of the three-dimensional shortest path are based on straight edges of the obstacles. It needs to be further developed for dealing with arbitrary-shaped obstacles and this would increase the computational complexity. The algorithm is tested using computer simulations and some results are presented.

Finding the Shortest Path for a Mobile Robot With Two Actuated Spoke Wheels Based on Variable Kinematic Configurations

2010 ◽  
Author(s):  
Ya Wang ◽  
Dennis Hong
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Shortest Path ◽  
Optimal Path ◽  
Curvature Radius ◽  
Planning Strategy ◽  
Optimal Path Planning ◽  
Path Geometry ◽  
Motion Characteristics ◽  
Motion Strategy

Strategies for finding the shortest path for a mobile robot with two actuated spoke wheels based on variable kinematic configurations are presented in this paper. The optimal path planning strategy proposed here integrate the traditional constrained path planning tools and the unique kinematic configuration spaces of the mobile robot IMPASS (Intelligent Mobility Platform with Actuated Spoke System). IMPASS utilizes a unique mobility concept of stretching in or out individually actuated spokes in order to perform variable curvature radius steering using changing kinematic configuration during its movement. Due to this unique motion strategy, various kinematic topologies produce specific motion characteristics in the way of curvature radius-variable steering. Instead of traditional differential drive or Ackerman steering locomotion, combinational path geometry methods, Dubins’ curve and Reeds and Shepp’s curve are applied to classify optimal paths into known permutations of sequences consisting of various kinematic configurations. Numerical simulation is given to verify the analytical solutions provided by using Lagrange Multiplier.

scholarly journals Two-degree-of-freedom manipulator path planning based on zeroing neural network

2020 ◽  
Vol 309 ◽  
pp. 04005
Author(s):  
Yan Li ◽  
Keping Liu
Keyword(s):  
Neural Network ◽  
Path Planning ◽  
Shortest Path ◽  
Lyapunov Method ◽  
Optimal Path ◽  
Shortest Path Problem ◽  
Optimal Planning ◽  
Optimal Path Planning ◽  
The Stability ◽  
Two Degree Of Freedom

In this paper, the shortest path problem of manipulator path planning is transformed into a linear programming problem, and solved by zeroing neural network (ZNN). Firstly, the method of constructing the zeroing neural dynamics is given, and the ZNN model is constructed for shortest path problem of manipulator. Then, the Lyapunov method is utilized to prove the stability of the ZNN model. Finally, the ZNN model is applied to the path planning of manipulator to generate an optimal planning path. The simulation results show that the proposed method can effectively realize the optimal path planning of the manipulator.

scholarly journals AGV optimal path planning based on improved ant colony algorithm

2018 ◽  
Vol 232 ◽  
pp. 03052 ◽  
Author(s):  
Chengwei He ◽  
Jian Mao
Keyword(s):  
Path Planning ◽  
Ant Colony Algorithm ◽  
Optimal Path ◽  
Optimal Solution ◽  
Ant Colony ◽  
Undirected Network ◽  
Optimal Path Planning ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Improved Ant Colony Algorithm

Using the traditional Ant Colony Algorithm for AGV path planning is easy to fall into the local optimal solution and lacking the capability of obstacle avoidance in the complex storage environment. In this paper, by constructing the MAKLINK undirected network routes and the heuristic function is optimized in the Ant Colony Algorithm, then the AGV path reaches the global optimal path and has the ability to avoid obstacles. According to research, the improved Ant Colony Algorithm proposed in this paper is superior to the traditional Ant Colony Algorithm in terms of convergence speed and the distance of optimal path planning.

scholarly journals An Improved Ant Colony Algorithm and Its Application in Vehicle Routing Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Min Huang ◽  
Ping Ding
Keyword(s):  
Path Planning ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Transition Probability ◽  
Optimal Path ◽  
Optimal Solution ◽  
Planning Method ◽  
Ant Colony ◽  
Routing Problem

Optimal path planning is an important issue in vehicle routing problem. This paper proposes a new vehicle routing path planning method which adds path weight matrix and save matrix. The method uses a new transition probability function adding the angle factor function and visibility function, while setting penalty function in a new pheromone updating model to improve the accuracy of the route searching. Finally, after each cycle, we use 3-opt method to update the optimal solution to optimize the path length. The results of comparison also confirm that this method is better than the traditional ant colony algorithm for vehicle routing path planning method. The result of computer simulation confirms that the method can plan a more rational rescue path focused on the real traffic situation.

scholarly journals Warehouse-Oriented Optimal Path Planning for Autonomous Mobile Fire-Fighting Robots

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yong-tao Liu ◽  
Rui-zhi Sun ◽  
Tian-yi Zhang ◽  
Xiang-nan Zhang ◽  
Li Li ◽  
...  
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Inflection Point ◽  
Optimal Path ◽  
Fire Fighting ◽  
Turning Angle ◽  
Grid Map ◽  
Smooth Path ◽  
Inflection Points ◽  
Planning Algorithm

In order to achieve the fastest fire-fighting purpose, warehouse autonomous mobile fire-fighting robots need to make an overall optimal planning based on the principle of the shortest time for their traveling path. A∗ algorithm is considered as a very ideal shortest path planning algorithm, but the shortest path is not necessarily the optimal path for robots. Furthermore, the conventional A∗ algorithm is affected by the search neighborhood restriction and the theoretical characteristics, so there are many problems, which are closing to obstacles, more inflection points, more redundant points, larger total turning angle, etc. Therefore, A∗ algorithm is improved in eight ways, and the inflection point prior strategy is adopted to compromise Floyd algorithm and A∗ algorithm in this paper. According to the criterion of the inflection point in this paper, the path inflection point arrays are constructed and traveling all path nodes are replaced by traveling path inflection points for the conventional Floyd algorithm backtracking, so it greatly reduces the backtracking time of the smooth path. In addition, this paper adopts the method of the extended grid map obstacle space in path planning safety distance. According to the relationship between the actual scale of the warehouse grid map and the size of the robot body, the different safe distance between the planning path and the obstacles is obtained, so that the algorithm can be applied to the safe path planning of the different size robots in any map environments. Finally, compared with the conventional A∗ algorithm, the improved algorithm reduces by 7.846% for the path length, reduces by 71.429% for the number of the cumulative turns, and reduces by 75% for the cumulative turning angle through the experiment. The proposed method can ensure robots to move fast on the planning path and ultimately achieve the goal of reducing the number of inflection points, reducing the cumulative turning angle, and reducing the path planning time.

scholarly journals LAV Path Planning by Enhanced Fireworks Algorithm on Prior Knowledge

2016 ◽  
Vol 1 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Li Bing ◽  
You Ning ◽  
Du YeHong
Keyword(s):  
Path Planning ◽  
Prior Knowledge ◽  
Optimal Path ◽  
Optimal Solution ◽  
Search Space ◽  
Intelligent Algorithm ◽  
Fireworks Algorithm ◽  
Dynamic Path Planning ◽  
Minimum Probability ◽  
Dynamic Path

AbstractPath planning plays an extremely important role in the design of LAVs (Loitering Air Vehicles) to accomplish the air combat task fleetly and reliably. The planned path should ensure that LAVs reach the destination along the optimal path with minimum probability of being found and minimal consumed fuel. Traditional methods tend to find local best solutions due to the large search space. So it takes a lot of time and consumes a lot of computing resources. In this paper, a new young intelligent algorithm-fireworks algorithm is introduced, and EFWA (enhanced fireworks algorithm)-its enhanced version is used to find the optimal solution. At the same time, the battlefield prior knowledge is fully utilized to predict the existence space of the potential optimal trajectory. Greatly the search space reduced, plan planning efficiency is significantly improved. Path planning method effectiveness in this paper has further been improved compared with FACPSO. Moreover, the EFWA on prior knowledge performs well on the application of dynamic path planning when the threats cruise randomly than FAC-PSO.

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