Probabilistic Roadmap Algorithm Research Articles

A comparative study of different radial basis function interpolation algorithms in the reconstruction and path planning of γ radiation fields

Accurate reconstruction of radiation field and path planning are very important for the safety of operators in the process of dismantling nuclear facilities. Based on radial basis function (RBF) interpolation algorithm, this paper discussed the application of inverse multiquadric radial basis Function (IMRBF) interpolation method to the reconstruction of gamma radiation field, and proved the feasibility of reconstructing a radiation field with multiple γ sources. The average relative errors of IMRBF interpolation results were 4.28% and 8.76%, respectively, for the experimental scenarios with single and double gamma sources. After comparing the consistency between the simulated scene and the experimental scene, IMRBF method and Cubic Spline method were respectively used to reconstruct the gamma radiation field by Geant4 simulation data. The results showed that the interpolation accuracy of IMRBF method was superior to that of Cubic Spline method. Further, more RBF interpolation algorithms were used to reconstruct the multi-γ source radiation field, and then the Probabilistic Roadmap (PRM) algorithm was used to optimize the human walking path in the radiation field reconstructed by different interpolation methods. The optimal paths in radiation fields generated by multiple interpolation methods were compared. The results herein contribute to a comprehensive understanding of RBF interpolation methods in reconstructing γ radiation fields and their application in optimizing paths in radiation environments. The insights may provide valuable information for decision-making in radiation protection during the decommissioning of nuclear facilities.

Grid-Based Non-Uniform Probabilistic Roadmap-Based AGV Path Planning in Narrow Passages and Complex Environments

In this paper, we propose a Grid-based Non-uniform Probability Density Sampling Probabilistic Roadmap algorithm (GN-PRM) in response to the challenges of difficult sampling in narrow passages and low-probability map generation in traditional Probabilistic Roadmap algorithms (PRM). The improved algorithm incorporates grid-based processing for map segmentation, employing non-uniform probability density sampling based on the different attributes of each block to enhance sampling probability in narrow passages. Additionally, considering the computational cost and frequent ineffective searches in traditional PRM algorithms during pathfinding, this paper optimizes the time required for query route planning by altering connection strategies to improve the algorithm’s runtime. Finally, the simulation results indicate that, with a reduction of over 50% in undirected line segments and a reduction of over 85% in runtime, the GN-PRM algorithm achieves a 100% success rate in complex planning scenarios with a sampling point value of K = 500. In comparison, the traditional PRM algorithm has a success rate of no more than 10%, with a sampling point value of K = 500.

On Hierarchical Multi-UAV Dubins Traveling Salesman Problem Paths in a Complex Obstacle Environment.

This article aims to solve a hierarchical multi-UAV Dubins traveling salesman problem (HMDTSP). Optimal hierarchical coverage and multi-UAV collaboration are achieved by the proposed approaches in a 3-D complex obstacle environment. A multi-UAV multilayer projection clustering (MMPC) algorithm is presented to reduce the cumulative distance from multilayer targets to corresponding cluster centers. A straight-line flight judgment (SFJ) was developed to reduce the calculation of obstacle avoidance. An improved adaptive window probabilistic roadmap (AWPRM) algorithm is addressed to plan obstacle-avoidance paths. The AWPRM improves the feasibility of finding the optimal sequence based on the proposed SFJ compared with a traditional probabilistic roadmap. To solve the solution to TSP with obstacles constraints, the proposed sequencing-bundling-bridging (SBB) framework combines the bundling ant colony system (BACS) and homotopic AWPRM. An obstacle-avoidance optimal curved path is constructed with a turning radius constraint based on the Dubins method and followed up by solving the TSP sequence. The results of simulation experiments indicated that the proposed strategies can provide a set of feasible solutions for HMDTSPs in a complex obstacle environment.

Comparative Analysis of GA-PRM Algorithm Performance in Simulation and Real-World Robotics Applications

Abstract: This paper presents a comprehensive analysis of the performance of the Genetic Algorithm Probabilistic Roadmap (GA-PRM) algorithm in both simulated and real-world robotic environments. The GA-PRM algorithm is a promising approach for robot path planning, and understanding its behavior in different settings is crucial for its practical applications. In simulations, we explore the advantages of controlled and reproducible test conditions, allowing for extensive parameter tuning and algorithm improvement. Real-world testing is employed to validate the algorithm's performance in actual robotic environments, taking into account the inherent complexities and uncertainties present. In our comparative analysis, we found that the GA-PRM algorithm demonstrates significant improvements in real-world scenarios compared to simulations. Specifically, the algorithm produced shorter paths in real-world robot testing, with an average length of 21.428 cm, as opposed to 25.6235 units in simulations. Moreover, the computational efficiency of the algorithm was notably enhanced in the real-world environment, where it took only 0.375 seconds on average to plan paths, compared to 0.6881 seconds in simulations. The algorithm also exhibited higher path smoothness in the real world, with an average smoothness score of 0.432, compared to 0.3133 in simulations. These results underscore the algorithm's adaptability to real-world conditions and its potential for efficient navigation in practical healthcare and automation applications. Our research bridges the gap between simulation and reality, facilitating the development of more reliable and adaptable robotic systems. The insights gained from this comparative evaluation contribute to a deeper understanding of the GA-PRM algorithm's behavior and its potentials.

Path planning of USV based on improved PRM under the influence of ocean current

Multi-extensibility and flexibility of unmanned surface vehicles (USVs) allow them perform many different tasks, further path planning technology is crucial to the safety, autonomy, and intelligent navigation of USVs. Firstly, this paper analyzes the impact of ocean currents and risk constraints on USV based on the electronic chart. Then take the optimal sailing time as the objective function and design a path planning algorithm based on an improved probabilistic roadmap (PRM) algorithm, in which a Gaussian space sampling algorithm based on edge detection is introduced. After building the network topology environment through improved PRM, then a Dijkstra algorithm based on great circle distance is used to solve the optimal path. Finally, the simulation experiment is designed through the MATLAB platform. By comparing the average and the three quartile lengths of the planned paths under three environments, the values of the designed Edge-Gaussion (E-G) PRM algorithm are smaller than Lazy PRM and Gaussian PRM algorithm, which shows that the improved PRM algorithm has better performance. When planning the USV path under the influence of current, compared with traditional length optimal path planning, although the navigation length planned by the designed algorithm is shorter by 972 m, sailing time is improved by 110 s, which efficiency shows the better application on the sea.

Data-Driven Approach Toward Airspace Design for Regional Air Mobility Operations in Korea

As the Korean government agencies have recently announced the first official road map for urban air mobility (UAM) with the aim of introducing a new aviation transportation system, many companies in South Korea have initiated projects to design airspace infrastructure for UAM operations at the early stage of development. Given that the agencies tentatively plan to expand UAM to regional air mobility (RAM) operations at the mature stage of development, this research specifically focuses on establishing airspace infrastructure for upcoming RAM operations in South Korea. The proposed methodology leverages three different algorithms: 1) a partitioning-based clustering algorithm for placing vertiport locations, 2) a density-based clustering algorithm for predicting areas of convective weather, and 3) the Latin hypercube sampling-based probabilistic road map (LHS-based PRM) algorithm for generating an adaptive airspace network. The resulting airspace, constructed by the proposed methodology, takes into account airspace restriction areas such as prohibited areas or military operation areas. The main contribution of this research is to employ a data-driven approach using machine learning and LHS-based PRM algorithms to dynamically establish airspace infrastructure to be potentially used for upcoming RAM operations in South Korea.

Ship route planning in the pirate area via hybrid probabilistic roadmap algorithm within the context of the Maritime Silk Road

The frequent occurrence of pirate accidents along the Maritime Silk Road has seriously affected the safety of ships. To guarantee navigation safety in pirate activity area, we present a hybrid probabilistic roadmap (HPRM) algorithm for ship route planning. Our HPRM algorithm consists of the improved learning phase and the enhanced exploration phase. Firstly, to improve the utilization of sampling points, the sampling point reset (SPR) function is introduced to generate new sampling points to replace the sampling points in the dangerous area. Secondly, to reduce the number of ship turns, the Douglas–Peucker (D–P) algorithm is utilized to extract the key waypoints (KWP) for generating the optimized route. Finally, the Euler spiral fitting is applied to smooth the route. Numerical cases verified that the ship route planned via the HPRM algorithm is shorter and smoother. This study is conducive to guarantee the safety of ship navigation in the pirate area and enhance ship navigation efficiency, which is of great practical significance for the advancement of the Maritime Silk Road Initiative.

Efficient ship weather routing using probabilistic roadmaps

This paper introduces the probabilistic roadmap (PRM) concept in maritime transportation for solving the ship weather routing (SWR) problem. SWR is a path finding problem that seeks for the optimum route (path) for a ship moving from an initial port to a final desired port considering the weather conditions (winds, waves, sea currents). PRM is an old effective algorithm for robot motion planning based on a systematic use of a graph-based map which represents the robot's workspace. Using this map PRM explores feasible paths around the obstacles until finding a collision-free path between the starting and goal configurations of the robot. Considering the digital map of the ship's navigation area as well as forecasting data (updated every 3 h) concerning the weather conditions, a modified PRM algorithm is presented for tackling SWR. The proposed algorithm starts by taking random samples across the ship's navigation area which follow a particular distribution. Then, it uses a local planner to construct a large undirected graph (a roadmap) with nodes all the generated sample points connected with feasible (collision-free) edges (paths). Each path is related with a weight estimated by considering the weather conditions in the corresponding sea's region. Finally, given the departure and desired arrival ports, a modified Dijkstra's algorithm is applied to the resulting graph to search for the optimal path in terms of both fuel consumption and travel time that connects the two ports in the roadmap. The proposed algorithm operates in real-time determining the best solution within less than 1 min. Simulation simulations over the Aegean archipelagos as well as the Mediterranean Sea demonstrate the efficiency of the developed algorithm.

Long-Range Risk-Aware Path Planning for Autonomous Ships in Complex and Dynamic Environments

Abstract Path planning and collision avoidance are common problems for researchers in vehicle and robotics engineering design. In the case of autonomous ships, the navigation is guided by the regulations for preventing collisions at sea (COLREGs). However, COLREGs do not provide specific guidance for collision avoidance, especially for multi-ship encounters, which is a challenging task even for humans. In short-range path planning and collision avoidance problems, the motion of target ships is often considered as moving at a constant velocity and direction, which cannot be assumed in long-range planning and complex environments. The research challenge here is how to factor in the uncertainty of the motion of the target ships when making long-range path plans. In this paper, we introduce a long-range path planning algorithm for autonomous ships navigating in complex and dynamic environments to reduce the risk of encountering other ships during future motion. Based on the information on the position, speed over ground, and course over ground of other ships, our algorithm can estimate their intentions and future motions based on the probabilistic roadmap algorithm and use a risk-aware A* algorithm to find the optimal path that has low accumulated risk of encountering other ships. A case study is carried out on real automatic identification systems (AIS) datasets. The result shows that our algorithm can help reduce multi-ship encounters in long-term path planning.

Online obstacle avoidance path planning and application for arc welding robot

• The system of online collision-free path planning for the arc welding robot is established. • An improved lazy-PRM algorithm with repulsion field is proposed to solve the path planning. • The collision-free path of the 7-DOF arc welding robot can be planned online. • The path quadratic optimization strategy is proposed to fine-tuning the pose and position of the welding gun. • Fast trajectory planning for each workpiece at any position during the welding process. The offline path planning problem for arc welding robots becomes increasingly difficult to achieve with the increasing product complexity and the open work environment, such as the welding tasks in ship formation. Most research considers the path planning problem without time limitations or other constraints that conform to the actual production process. During the welding process, the placement of workpieces seriously affects the efficiency of finding feasible paths for the welding robots for weld tasks that cannot be repeated accurately. Thus, in the flow welding workshop, the improved lazy Probabilistic Roadmap (PRM) algorithm based online collision-free path planning method is proposed to finish the welding tasks of general stiffened plates at an arbitrary position on the workbench within the robot's reach. The work environment is built with the grid method to reduce the computational dimension of collision detection. The local path planner is implemented by the lazy-PRM algorithm with the repulsive force field to rapidly search the collision-free path for the welding robot with specific safe distances. The robot posture adjustment strategy is also applied to the collision detection process to adjust some poses of the robot at candidate paths to be feasible. The improved path planning method is tested on both the simulated environment and actual application scenario and proved to be suitable for the path planning problem of the arc welding robot. The results of this study have been integrated into a computer approach, which can accelerate the motion planning process and reduce human efforts.

Development of Ship Route-Planning Algorithm Based on Rapidly-Exploring Random Tree (RRT*) Using Designated Space

Ship route planning is a crucial activity that must consider not only the safety of the ship but also the safe passage of nearby ships in the same space and time. This study aims to provide general route-planning guidance to shipping traffic by improving conventional sampling-based route-planning algorithms in accordance with the maritime environment from a ship operator’s perspective. The obstacle safety margin in a marine environment can be reflected in a binary image map space based on an electronic navigational chart. Consequently, an initial route was created using the probabilistic road map (PRM) algorithm in the configured map space to increase the speed of the conventional sampling-based route-planning algorithm. Based on the initial route created, a designated space—that is, a multi-elliptical area—was created to limit the route-search range. After searching the final route in the designated space based on the rapidly-exploring random tree (RRT*) algorithm, optimal route planning could be achieved by generating a collision-free space graph to remove unnecessary nodes from the searched final route. The simulation results showed that the route was shortened by approximately 33.7 km compared with the conventional RRT* algorithm, and the calculation time was shortened by approximately 2.5 times.

An Efficient Motion Planning Method with a Lazy Demonstration Graph for Repetitive Pick-and-Place.

Robotic systems frequently need to plan consecutive similar manipulation in some scenarios (e.g., pick-and-place tasks), leading to similar motion plans. Moreover, the workspace of a robot changes with the difference in operation actions, which affects subsequent tasks. Therefore, it is significant to reuse information from previous solutions for new motion planning instances to adapt to workplace changes. This paper proposes the Lazy Demonstration Graph (LDG) planner, a novel motion planner that exploits successful and high-quality planning cases as prior knowledge. In addition, a Gaussian Mixture Model (GMM) is established by learning the distribution of samples in the planning cases. Through the trained GMM, more samples are placed in a promising location related to the planning tasks for achieving the purpose of adaptive sampling. This adaptive sampling strategy is combined with the Lazy Probabilistic Roadmap (LazyPRM) algorithm; in the subsequent planning tasks, this paper uses the multi-query property of a road map to solve motion planning problems without planning from scratch. The lazy collision detection of the LazyPRM algorithm helps overcome changes in the workplace by searching candidate paths. Our method also improves the quality and success rate of the path planning of LazyPRM. Compared with other state-of-the-art motion planning algorithms, our method achieved better performance in the planning time and path quality. In the repetitive motion planning experiment of the manipulator for pick-and-place tasks, we designed two different experimental scenarios in the simulation environment. The physical experiments are also carried out in AUBO-i5 robot arm. Accordingly, the experimental results verified our method's validity and robustness.

Motion Planning in the Area of Robotics and Automation

Motion Planning is computational problem of geometry to find continuous and optimal path from source to destination in multidimensional environment. Today’s automation world for industry 4.0 works on multiple technologies where robotics is core part of industry 4.0. To achieve optimal solution with robotics and automation motion planning is crucial area of research. This paper proposes study about motion planning sampling-based algorithm and latest research and development of new variant of probabilistic roadmap algorithm in which researcher achieve optimal solution and reduce time complexity. Main logic behind PRM algorithm is learning phase and query phase. In learning phase, construction of basic road map take place and in query phase, different techniques are used to reach destination by optimal path for different environment.

An Optimized Probabilistic Roadmap Algorithm for Path Planning of Mobile Robots in Complex Environments with Narrow Channels.

In this paper, we propose a new path planning algorithm based on the probabilistic roadmaps method (PRM), in order to effectively solve the autonomous path planning of mobile robots in complex environments with multiple narrow channels. The improved PRM algorithm mainly improves the density and distribution of sampling points in the narrow channel, through a combination of the learning process of the PRM algorithm and the APF algorithm. We also shortened the required time and path length by optimizing the query process. The first key technology to improve the PRM algorithm involves optimizing the number and distribution of free points and collision-free lines in the free workspace. To ensure full visibility of the narrow channel, we extend the obstacles through the diagonal distance of the mobile robot while ignoring the safety distance. Considering the safety distance during movement, we re-classify the all sampling points obtained by the quasi-random sampling principle into three categories: free points, obstacle points, and adjacent points. Next, we transform obstacle points into the free points of the narrow channel by combining the APF algorithm and the characteristics of the narrow channel, increasing the density of sampling points in the narrow space. Then, we include potential energy judgment into the construction process of collision-free lines shortening the required time and reduce collisions with obstacles. Optimizing the query process of the PRM algorithm is the second key technology. To reduce the required time in the query process, we adapt the bidirectional A* algorithm to query these local paths and obtain an effective path to the target point. We also combine the path pruning technology with the potential energy function to obtain a short path without collisions. Finally, the experimental results demonstrate that the new PRM path planning technology can improve the density of free points in narrow spaces and achieve an optimized, collision-free path in complex environments with multiple narrow channels.

Path Planning for UAV Based on Improved PRM

In this paper, an improved probabilistic roadmap (IPRM) algorithm is proposed to solve the energy consumption problem of multi-unmanned aerial vehicle (UAV) path planning with an angle. Firstly, in order to simulate the real terrain environment, a mathematical model was established; secondly, an energy consumption model was established; then, the sampling space of the probabilistic roadmap (PRM) algorithm was optimized to make the obtained path more explicit and improve the utilization rate in space and time; then, the sampling third-order B-spline curve method was used to curve the rotation angle to make the path smoother and the distance shorter. Finally, the results of the improved genetic algorithm (IGA), PRM algorithm and IPRM algorithm were compared through a simulation. The data analysis shows that the IGA has significant advantages over other algorithms in some aspects, and can be well applied to the path planning of UAVs.

On Free Velocity Cones of Narrow Passages of High-DoF Kinematic Chains

Narrow passages in free space pose great challenges to many sampling-based motion planners. In problems with high-dimensional configuration spaces (C-spaces), narrow passages in free space (C-free) can be hard to find and navigate and, sometimes, even counterintuitive. In this article, we present an algorithm to construct cones of available instantaneous velocities (“free velocity cones” or, briefly, “free cones”) on the boundary of C-free to facilitate finding and navigating narrow passages. This is accomplished by first developing free cones and associated measures of local C-space narrowness for a single rigid link. These results are then extended to kinematic chains (open and closed) of arbitrary degrees of freedom. It turns out that the degeneracy of the free cones dictates the existence of C-space narrow passages, and the locations and orientations of the links in the workspace relate intimately to the corresponding connected component of C-free. This observation leads us to a modified probabilistic roadmap (M-PRM) algorithm and a modified rapidly exploring random vine (M-RRV) algorithm of combining the enumeration of topological components and random sampling of the free cones. Experimental results from applying our algorithms to several challenging examples show that our new algorithms are more efficient than some variants of the PRM algorithms, and several variants of the rapidly exploring random tree (RRT) algorithms, such as RRT-CONNECT and RRV.

Planning and visual-servoing for robotic manipulators in ROS

This article presents a probabilistic road map (PRM) and visual servo control (visual-servoing) based path planning strategy that allows a Motoman HP20D industrial robot to move from an initial positional to a random final position in the presence of fixed obstacles. The process begins with an application of the PRM algorithm to take the robot from an initial position to a point in space where it has a free line of sight to the target, to then apply visual servoing and end up, finally, at the desired position, where an image captured by a camera located at the robot’s end effector matches a reference image, located on the upper surface of a rectangular prismatic object. Algorithms and experiments were developed in simulation, specifically, the visual servo control that includes the dynamic model of the robot and the image sensor subject to realistic lighting were developed in robot operating system (ROS) environment.

A modified probabilistic roadmap algorithm for efficient mobile robot path planning

Aiming to address the shortcomings of conventional algorithms in mobile robot path planning, such as long paths, random sampling and high collision risk, a novel probabilistic roadmap algorithm, or node reduction-based search algorithm, is proposed. A decision-making strategy is developed to identify the suitable node, which depends on the distance error to the nearby obstacles and goal and the Gaussian cost function, which improves path efficiency by eliminating unwanted nodes. Then, an optimal path is selected based on the weight of the edges. The comparative analysis is conducted in five different test cases with differing complexity. Different performance parameters are measured to validate the effectiveness of the proposed algorithm. The outcomes acquired from the different test cases indicate that the proposed algorithm outperforms the state-of-the-art algorithms, with a maximum improvement of 13.51% in path length, 66.82% in execution time, 28.5% in smoothness and 38.05% in collision risk value.

Real-Time Path Planning for Robot Using OP-PRM in Complex Dynamic Environment.

During task execution, the autonomous robots would likely pass through many narrow corridors along with mobile obstacles in dynamically complex environments. In this case, the off-line path planning algorithm is rather difficult to be directly implemented to acquire the available path in real-time. Hence, this article proposes a probabilistic roadmap algorithm based on the obstacle potential field sampling strategy to tackle the online path planning, called Obstacle Potential field-Probabilistic Roadmap Method (OP-PRM). The obstacle potential field is introduced to determine the obstacle area so as to construct the potential linked roadmap. Then the specific range around the obstacle boundary is justified as the target sampling area. Based on this obstacle localization, the effectiveness of the sampling points falling into the narrow corridors can be increased greatly for feasible roadmap construction. Furthermore, an incremental heuristic D* Lite algorithm is applied to search the shortest paths between the starting point and the target point on the roadmap. Simulation experiments demonstrate that the OP-PRM path planning algorithm can enable robots to search the optimal path fast from the starting point to the destination and effectively cross narrow corridors in complex dynamic environments.

Helical5AM: Five-axis parametrized helical additive manufacturing

Additive manufacturing (AM) commonly utilizes slicing techniques to create layers of a model, in which material is deposited layer-by-layer. However, slicing method directly affects the mechanical properties of the printed parts. This paper introduces a new AM technique (named as Helical5AM ), which employs print-paths having helical geometry for five-axis AM. Given an object to be printed, a base (supporting helical print-paths) with a center curve and helix parameters (such as lead angle and turn direction), a complete volumetric coverage using helical print-paths is obtained. A collision-free tool orientation is then generated using a probabilistic roadmap algorithm for depositing material along the helical print-paths by avoiding tool interference with obstacles. As a proof of concept, print-paths (of models) with orientation information obtained using the proposed algorithms are simulated using a five-axis AM simulation software, and material deposition process in Helical5AM is demonstrated using a five-axis AM machine. Furthermore, compression tests are performed on the printed parts for evaluating the effects of helix lead angles of the helical print-paths on mechanical properties of the printed parts. It has been confirmed that mechanical behavior of a printed part is predictable and tunable according to the helix lead angles of the print-paths. Helical5AM can potentially empower engineers to obtain AM parts with desirable mechanical properties.