Global Path Planning Research Articles

Efficient micro-mobility path planning without using high-definition maps

Efficient path planning is crucial for the safe autonomous operation of micro-mobility vehicles in unknown environments. When planning paths for micro-mobility, factors, such as the changes in the user's intended destination and user comfort, must be considered. Moreover, for driving in unknown areas, the path planner should not rely on predetermined detailed information like High-Definition maps (HD maps). In this paper, we propose an innovative path planning algorithm for automated driving that solely uses basic perception data from RGB camera, IMU and GPS, thereby eliminating the dependency on HD maps. We initially convert perception data into an occupancy grid map. Subsequently, a global path planner, based on a modified A* algorithm, computes an efficient trajectory, particularly adept to navigation in unknown environments and to scenarios where goal position moves. Additionally, we developed a local planner that optimize multi-clothoid curves using designed constraints to predict the best trajectory. Our experiments, conducted in both simulated and real-world environments, validate the effectiveness of our approach for micro-mobility path planning using only perception data.

Research on Global Off-Road Path Planning Based on Improved A* Algorithm

In field driving activities, off-road areas usually lack existing paths that can be directly driven on by ground vehicles, but their surface environments can still satisfy the planning and passage requirements of some off-road vehicles. Additionally, the existing path planning methods face limitations in complex field environments characterized by undulating terrains and diverse land cover types. Therefore, this study introduces an improved A* algorithm and an adapted 3D model of real field scenes is constructed. A velocity curve is fitted in the evaluation function to reflect the comprehensive influences of different slopes and land cover types on the traffic speed, and the algorithm not only takes the shortest distance as the basis for selecting extension nodes but also considers the minimum traffic speed. The 8-neighborhood search method of the traditional A* algorithm is improved to a dynamic 14-neighborhood search method, which effectively reduces the number of turning points encountered along the path. In addition, corner thresholds and slope thresholds are incorporated into the algorithm to ensure the accessibility of path planning, and some curves and steep slopes are excluded, thus improving the usability and safety of the path. Experimental results show that this algorithm can carry out global path planning in complex field environments, and the planned path has better passability and a faster speed than those of the existing approaches. Compared with those of the traditional A* algorithm, the path planning results of the improved algorithm reduce the path length by 23.30%; the number of turning points is decreased by 33.16%; and the travel time is decreased by 38.92%. This approach is conducive to the smooth progress of various off-road activities and has certain guiding significance for ensuring the efficient and safe operations of vehicles in field environments.

Adaptive Deep Ant Colony Optimization–Asymmetric Strategy Network Twin Delayed Deep Deterministic Policy Gradient Algorithm: Path Planning for Mobile Robots in Dynamic Environments

Path planning is one of the main focal points and challenges in mobile robotics research. Traditional ant colony optimization (ACO) algorithms encounter issues such as low efficiency, slow convergence, and a tendency to become stuck in local optima and search stagnation when applied to complex dynamic environments. Addressing these challenges, this study introduces an adaptive deep ant colony optimization (ADACO) algorithm, which significantly improves efficiency and convergence speed through enhanced pheromone diffusion mechanisms and updating strategies, applied to global path planning. To adapt to dynamically changing environments and achieve more precise local path planning, an asymmetric strategy network TD3 algorithm (ATD3) is further proposed, which utilizes global path planning information within the strategy network only, creating a new hierarchical path planning algorithm—ADACO-ATD3. Simulation experiments demonstrate that the proposed algorithm significantly outperforms in terms of path length and number of iterations, effectively enhancing the mobile robot’s path planning performance in complex dynamic environments.

Hybrid Mobile Robot Path Planning Using Safe JBS-A*B Algorithm and Improved DWA Based on Monocular Camera

This paper addresses the formidable challenge of enabling autonomous navigation in Mobile Robots (MRs), focusing on the development of advanced path planning strategies. Despite their pivotal role in diverse applications, they face challenges in dynamic settings due to limitation in existing Global Path Planning (GPP) and Local Path Planning (LPP) techniques. In response to this, we propose an innovative hybrid path planning approach that enhances the A* algorithm with a risk-aware heuristic function and integrates the Jump Point Search (JPS) technique for route optimization. Additionally, B-spline smoothing is employed for perceptually global trajectory refinement. Our approach also includes an innovative improvement to the Dynamic Window Approach (DWA) to align with the proposed enhanced A* algorithm for effective local navigation. Acknowledging the importance of high-quality input in path planning, we present substantial improvements to the IRDC-Net, a monocular-image semantic-segmentation model that we studied previously. Novel improvements include the integration of quantization and the Adam optimizer, along with the implementation of the Balanced Cross-Entropy loss function. These enhancements not only elevate the output quality of IRDC-Net but also reduce the model’s training parameters. The experimental results demonstrate the performance and viability of the proposed algorithm. Ultimately, the hybrid MR’s path planning algorithm exhibits proficiency across various tasks, particularly in addressing the challenge of evading moving obstacles to ensure the robot’s safety while adhering to the global path.

Global path planning of unmanned ship island region based on improved A* algorithm

Abstract To solve the path planning problem for unmanned boats in island and reef areas, this paper introduces an adaptive heuristic function specifically for island and reef areas based on the traditional A* algorithm, in order to effectively handle the obstacle avoidance problem. A new cost function is designed to balance the relationship between path length and safety. The sea chart is converted into a path planning map by using the grid method, and the path planning is carried out. The paper compares the performance of the new path-planning algorithm with other path-planning algorithms through experiments, and the improved A* algorithm for global path planning of unmanned boats in island and reef areas shows excellent performance in various complex environments, effectively improving the island and reef area navigation efficiency.

Improved ACO algorithm fused with improved Q-Learning algorithm for Bessel curve global path planning of search and rescue robots

Addressing issues with traditional ant colony and reinforcement learning algorithms, such as low search efficiency and the tendency to produce insufficiently smooth paths that easily fall into local optima, this paper designs an improved ant colony optimization algorithm fusion with improved Q-Learning (IAC-IQL) algorithm for Bessel curve global path planning of search and rescue (SAR) robots. First, the heuristic function model in the ant colony algorithm is improved, the elite ant search strategy and the adaptive pheromone volatility factor strategy are introduced, and the initial path is searched in realize the motion environment with the help of the improved ant colony algorithm, and the initialized pheromone matrix is constructed. Second, the improved ant colony algorithm and Q-Learning (QL) algorithm are fused by utilizing the similarity between the pheromone matrix in the improved ant colony algorithm and the Q-matrix in the QL algorithm. A heuristic learning evaluation model is designed to dynamically adjust the learning factor and provide guidance for the search path. Additionally, a dynamic adaptive greedy strategy is introduced to balance the exploration and exploitation of the robot in the environment. Finally, the paths are smoothed using third-order Bessel curves to eliminate the problem of excessive steering angles. Through three sets of comparative simulation experiments conducted in Pycharm platform, the effectiveness, superiority, and practicality of the IAC-IQL algorithm were verified. The experimental results demonstrated that the IAC-IQL algorithm integrates the strong search capability of ant colony algorithm and the self-learning characteristics of QL algorithm. SAR robots equipped with the improved IAC-IQL algorithm exhibit significantly enhanced iterative search efficiency in grid simulation environment and image sampling simulation environment. The global path optimization indicators demonstrate high efficiency, and the paths are smoother.

Global path planning for inland vessels based on fast marching algorithm

Ship path planning is essential for enhancing navigation safety, shipping efficiency, cost savings and autonomy. This paper presents a path planning algorithm specifically designed for inland vessels, exemplified on the Western Scheldt waterway area from Hansweert to Bath in the Netherlands (known as the area of Schaar van Valkenisse). The algorithm utilizes the fast marching (FM) method to generate safe and cost-efficient paths for both autonomous and conventional navigation, considering factors such as water depth, distance to waterway borders, preferential navigation zones (e.g. starboard side and parallel routes), ship dimensions, and manoeuvring characteristics.The fast marching algorithm uses starting points and a velocity grid, generated based on the aforementioned factors, to produce an arrival time map. The velocity here represents preferences for deeper water, and wider and starboard navigation zones. Subsequently, a gradient descent algorithm is applied to determine the fastest route from the destination to the starting point on the arrival time map. To ensure the route is navigable, the optimal path is updated to a Dubins path that satisfies the ships’ dynamic constraints by using a so-called Dubins model filter.Case studies with various navigation scenarios demonstrate that the path planning tool can provide expected results with tunable parameters allowing for customized preferences. This work can further assist in predicting paths for a traffic study, designing fairways, aids to navigation and can possibly serve as an operational tool to assess the accessibility of a (alternative) fairway.

A-Star (A*) with Map Processing for the Global Path Planning of Autonomous Underwater and Surface Vehicles Operating in Large Areas

The global path planning system is one of the basic systems ensuring the autonomous operation of unmanned underwater vehicles (UUVs) and unmanned surface vehicles (USVs) in a complex aquatic environment. The A* path planning algorithm is one of the most well-known algorithms used to obtain an almost optimal path, avoiding obstacles even in a complex environment containing objects with specific shapes and non-uniform arrangements. The main disadvantage of this algorithm is the computational cost of path calculation. This article presents a new approach based on the image processing of the map before determining the path using A*. The results of numerical research based on a large-sized map expressing the port area confirm the proposed method’s effectiveness, which reduces the calculation time by over 500 times with a slight increase in the path length compared to the basic version of the A* algorithm. Based on the obtained results, the proposed approach also increases the path’s safety by designating narrow and risky areas as closed to vehicle movement. For this reason, the method seems suitable for use in global path planning for autonomous underwater vehicles (AUVs) and autonomous surface vehicles (ASVs) operating in large areas.

FF-RRT*: A Sampling-Based Planner for Multirobot Global Formation Path Planning

Abstract This article presents a collision-free global path planning approach for multirobot systems called flexible formation—rapidly exploring randomized trees* (FF-RRT*). The algorithm is based on RRT* and provides a flexible and efficient representation of the formation geometry independent of the number of robots. It is designed to generate optimal paths for multirobot systems in a five-dimensional configuration space comprising the formation centroid, orientation, and scaling. An affine transformation is used to convert the path in the configuration space to the workspace of the robots. The proposed method employs a new distance function that eliminates the need for tuning weights and a sampling scheme for scaling factors to avoid inter-robot collisions. FF-RRT* is experimentally demonstrated using nonholonomic wheeled mobile robots and is effective in planning the collective motion of the robots. Robots could collectively reach goals by squeezing through narrow gaps and splitting and merging around large obstacles.

Research on AGV Path Planning Integrating an Improved A* Algorithm and DWA Algorithm

With the rapid development of the economy and the continuous improvement of people’s living standards, the printing and packaging industry plays an increasingly important role in people’s lives. The traditional printing industry is a discrete manufacturing industry, relying on a large amount of manpower and manual operation, low production efficiency, higher labor costs, wasting of resources, and other issues, so the realization of printing factory intelligence to improve the competitiveness of the industry is an important initiative. Automatic guided vehicles (AGVs) are an important part of an intelligent factory, serving the function of automatic transportation of materials and products. To optimize the movement paths of AGVs, enhance safety, and improve transportation efficiency and productivity, this paper proposes an alternative implementation of the A* algorithm. The proposed algorithm improves search efficiency and path smoothness by incorporating the grid obstacle rate and enhancing the heuristic function within the A* algorithm’s evaluation function. This introduces the evaluation subfunction of the nearest distance between the AGV, the known obstacle, and the unknown obstacle in the global path in the dynamic window approach (DWA algorithm), and reduces the interference of obstacles with the AGV in global path planning. Finally, the two improved algorithms are combined into a new fusion algorithm. The experimental results show that the search efficiency of the fusion algorithm significantly improved and the transportation time shortened. The path smoothness significantly improved, and the closest distance to obstacles increased, reducing the risk of collision. It can thus effectively improve the productivity of an intelligent printing factory and enhance its flexibility.

Multi-Robot Navigation System Design Based on Proximal Policy Optimization Algorithm

The more path conflicts between multiple robots, the more time it takes to avoid each other, and the more navigation time it takes for the robots to complete all tasks. This study designs a multi-robot navigation system based on deep reinforcement learning to provide an innovative and effective method for global path planning of multi-robot navigation. It can plan paths with fewer path conflicts for all robots so that the overall navigation time for the robots to complete all tasks can be reduced. Compared with existing methods of global path planning for multi-robot navigation, this study proposes new perspectives and methods. It emphasizes reducing the number of path conflicts first to reduce the overall navigation time. The system consists of a localization unit, an environment map unit, a path planning unit, and an environment monitoring unit, which provides functions for calculating robot coordinates, generating preselected paths, selecting optimal path combinations, robot navigation, and environment monitoring. We use topological maps to simplify the map representation for multi-robot path planning so that the proposed method can perform path planning for more robots in more complex environments. The proximal policy optimization (PPO) is used as the algorithm for deep reinforcement learning. This study combines the path selection method of deep reinforcement learning with the A* algorithm, which effectively reduces the number of path conflicts in multi-robot path planning and improves the overall navigation time. In addition, we used the reciprocal velocity obstacles algorithm for local path planning in the robot, combined with the proposed global path planning method, to achieve complete and effective multi-robot navigation. Some simulation results in NVIDIA Isaac Sim show that for 1000 multi-robot navigation tasks, the maximum number of path conflicts that can be reduced is 60,375 under nine simulation conditions.

Navigating Intelligence: A Survey of Google OR‐Tools and Machine Learning for Global Path Planning in Autonomous Vehicles

We offer a new in‐depth investigation of global path planning (GPP) for unmanned ground vehicles, an autonomous mining sampling robot named ROMIE. GPP is essential for ROMIE's optimal performance, which is translated into solving the traveling salesman problem, a complex graph theory challenge that is crucial for determining the most effective route to cover all sampling locations in a mining field. This problem is central to enhancing ROMIE's operational efficiency and competitiveness against human labor by optimizing cost and time. The primary aim of this research is to advance GPP by developing, evaluating, and improving a cost‐efficient software and web application. We delve into an extensive comparison and analysis of Google operations research (OR)‐Tools optimization algorithms. Our study is driven by the goal of applying and testing the limits of OR‐Tools capabilities by integrating Reinforcement Learning techniques for the first time. This enables us to compare these methods with OR‐Tools, assessing their computational effectiveness and real‐world application efficiency. Our analysis seeks to provide insights into the effectiveness and practical application of each technique. Our findings indicate that Q‐Learning stands out as the optimal strategy, demonstrating superior efficiency by deviating only 1.2% on average from the optimal solutions across our datasets.

Global Path Planning of Unmanned Surface Vehicle in Complex Sea Areas Based on Improved Streamline Method

In this paper, an innovative method is proposed to improve the global path planning of Unmanned Surface Vehicles (USV) in complex sea areas, combining fluid mechanic calculations with an improved A* algorithm. This method not only generates smooth paths but also ensures feasible global solutions, significantly enhancing the efficiency and safety of path planning. Firstly, in response to the water depths limitation, this study set up safe water depths, providing strong guarantees for the safe navigation of USVs in complex waters. Secondly, based on the hydrological and geographical characteristics of the study sea area, an accurate ocean environment model was constructed using Ansys Fluent software and computational fluid dynamics (CFD) technology, thus providing USVs with a feasible path solution on a global scale. Then, the local sea area with complex obstacles was converted into a grid map to facilitate detailed planning. Meanwhile, the improved A* algorithm was utilized for meticulous route optimization. Furthermore, by combining the results of local and global planning, the approach generated a comprehensive route that accounts for the complexities of the maritime environment while avoiding local optima. Finally, simulation results demonstrated that the algorithm proposed in this study shows faster pathfinding speed, shorter route distances, and higher route safety compared to other algorithms. Moreover, it remains stable and effective in real-world scenarios.

A New Multimodal Map Building Method Using Multiple Object Tracking and Gaussian Process Regression

Recent advancements in simultaneous localization and mapping (SLAM) have significantly improved the handling of dynamic objects. Traditionally, SLAM systems mitigate the impact of dynamic objects by extracting, matching, and tracking features. However, in real-world scenarios, dynamic object information critically influences decision-making processes in autonomous navigation. To address this, we present a novel approach for incorporating dynamic object information into map representations, providing valuable insights for understanding movement context and estimating collision risks. Our method leverages on-site mobile robots and multiple object tracking (MOT) to gather activation levels. We propose a multimodal map framework that integrates occupancy maps obtained through SLAM with Gaussian process (GP) modeling to quantify the activation levels of dynamic objects. The Gaussian process method utilizes a map-based grid cell algorithm that distinguishes regions with varying activation levels while providing confidence measures. To validate the practical effectiveness of our approach, we also propose a method to calculate additional costs from the generated maps for global path planning. This results in path generation through less congested areas, enabling more informative navigation compared to traditional methods. Our approach is validated using a diverse dataset collected from crowded environments such as a library and public square and is demonstrated to be intuitive and to accurately provide activation levels.

A Multiple Environment Available Path Planning Based on an Improved A* Algorithm

The objective of the path planning for a mobile robot is to generate a collision-free path from a starting position to a target position, aiming to realize a higher quality of path planning, an improved A* algorithm and a hybrid approach incorporating the dynamic window algorithm have been proposed for robot path planning in various environments in this paper. In global path planning, first, a bidirectional search strategy was introduced into to improve the searching efficiency, and an adaptive heuristic function was designed to reduce redundant search nodes. In the meantime, a filtering function for key path nodes and an enhanced jump point optimization method help to remove redundant nodes in the path, reduce turning angles, greatly shorten the path length, and smooth the path using cubic B-spline curves. Furthermore, in local path planning, the combination of key path nodes and the dynamic window approach (DWA) algorithm is utilized to achieve obstacle avoidance in dynamic environments and adjust the heading angle of the section enables seamless locomotion of the robot. Finally, the simulation experiments and physical experiments on the robot were conducted to validate that the proposed improved algorithm significantly improves the speed of path planning while also reducing the length of the planned path and improve the reliability of the algorithm when compared with other algorithms.

Simulation of Dynamic Path Planning of Symmetrical Trajectory of Mobile Robots Based on Improved A* and Artificial Potential Field Fusion for Natural Resource Exploration

With the rapid development of new-generation artificial intelligence and Internet of Things technology, mobile robot technology has been widely used in various fields. Among them, the autonomous path-planning technology of mobile robots is one of the cores for realizing their autonomous driving and obstacle avoidance. This study conducts an in-depth discussion on the real-time and dynamic obstacle avoidance capabilities of mobile robot path planning. First, we proposed a preprocessing method for obstacles in the grid map, focusing on the closed processing of the internal space of concave obstacles to ensure the feasibility of the path while effectively reducing the number of grid nodes searched by the A* algorithm, thereby improving path search efficiency. Secondly, in order to achieve static global path planning, this study adopts the A algorithm. However, in practice, algorithm A has problems such as a large number of node traversals, low search efficiency, redundant path nodes, and uneven turning angles. To solve these problems, we optimized the A* algorithm, focusing on optimizing the heuristic function and weight coefficient to reduce the number of node traversals and improve search efficiency. In addition, we use the Bezier curve method to smooth the path and remove redundant nodes, thereby reducing the turning angle. Then, in order to achieve dynamic local path planning, this study adopts the artificial potential field method. However, the artificial potential field method has the problems of unreachable target points and local minima. In order to solve these problems, we optimized the repulsion field so that the target point is at the lowest point of the global energy of the gravitational field and the repulsive field and eliminated the local optimal point. Finally, for the path-planning problem of mobile robots in dynamic environments, this study proposes a hybrid path-planning method based on a combination of the improved A* algorithm and the artificial potential field method. In this study, we not only focus on the efficiency of mobile robot path planning and real-time dynamic obstacle avoidance capabilities but also pay special attention to the symmetry of the final path. By introducing symmetry, we can more intuitively judge whether the path is close to the optimal state. Symmetry is an important criterion for us to evaluate the performance of the final path.

Research on Intelligent Wheelchair Multimode Human–Computer Interaction and Assisted Driving Technology

The traditional wheelchair focuses on the “human-chair” motor function interaction to ensure the elderly and people with disabilities’ basic travel. For people with visual, hearing, physical disabilities, etc., the current wheelchairs show shortcomings in terms of accessibility and independent travel for this group. Therefore, this paper develops an intelligent wheelchair with multimodal human–computer interaction and autonomous navigation technology. Firstly, it researches the multimodal human–computer interaction technology of occupant gesture recognition, speech recognition, and head posture recognition and proposes a wheelchair control method of three-dimensional head posture mapping the two-dimensional plane. After testing, the average accuracy of the gesture, head posture and voice control modes of the motorized wheelchair proposed in this study reaches more than 95 percent. Secondly, the LiDAR-based smart wheelchair indoor autonomous navigation technology is investigated to realize the autonomous navigation of the wheelchair by constructing an environment map, using A* and DWA algorithms for global and local path planning, and adaptive Monte Carlo simulation algorithms for real-time localization. Experiments show that the position error of the wheelchair is within 10 cm, and the heading angle error is less than 5° during the autonomous navigation. The multimode human–computer interaction and assisted driving technology proposed in this study can partially compensate and replace the functional deficiencies of the disabled population and improve the quality of life of the elderly and disabled population.

A Fusion Approach for UAV Onboard Flight Trajectory Management and Decision Making Based on the Combination of Enhanced A* Algorithm and Quadratic Programming

The rapid advancement of unmanned aerial vehicle (UAV) technologies has led to an increasing demand for UAV operations in low-altitude, high-density, and complex airspace such as mountains or urban areas. In order to handle complex scenarios and ensure flight safety for UAVs with different flight missions beyond visual line of sight in such environments, a fusion framework of onboard autonomous flight trajectory management and decision-making system using global strategical path planning and local tactical trajectory optimization combination is proposed in this paper. The global strategical path planning is implemented by an enhanced A* algorithm under the multi-constraint of UAV positioning uncertainty and obstacle density to improve the safety and cost-effectiveness. The local tactical trajectory optimization is realized using quadratic programming to ensure smoothness, kinematic feasibility, and obstacle avoidance of the planned trajectory in dynamic environments. Receding-horizon control is used to ensure the flight path and trajectory planning efficiently and seamlessly. To assess the performance of the system, a terrain database and a navigation system are employed for environment and navigation performance simulation. The experimental results confirm that the fusion approach can realize better safety and cost-effectiveness through path planning with kino-dynamic feasible trajectory optimization.

Global path planning for autonomous construction vehicles in building construction: A comparative study with a focus on vehicle kinematic characteristics

Technological advancements in robotics and automation have led to a growing emphasis on integration into construction industry from a global research context. In particular, autonomous construction vehicles (ACVs) stand out as a pivotal innovation. One key aspect of successful deployment of ACVs on construction sites is the path planning technology, especially the global path planning (GPP) methods. Thus, this study conducted a comparative study of the six GPP algorithms from various underlying principles, including graph search methods (e.g. Dijkstra and A*), sampling-based methods (e.g. rapidly exploring random tree (RRT) and rapidly exploring random tree star (RRT*)), evolutionary computation (e.g. genetic algorithms (GAs)), and artificial intelligence (e.g. deep Q learning (DQN)), to reveal how GPP algorithms perform on the travel of ACVs. These algorithms were evaluated with consideration of the kinematic characteristics of typical construction vehicles, including truck-trailers and excavators, within a typical unstructured real-world building construction site and based on two tasks and eight criteria encompassing efficiency and safety. The findings were analysed from three perspectives, i.e. the planned global paths and travel paths of ACVs, the performance of algorithms in each metric, and the overall performance of each algorithm, to identify the strengths of each GPP algorithm. GAs excel in generating smoother travel paths than others, whereas the global paths from RRT and DQN exhibit unpredictable changes, leading to a meandering travel paths for ACVs. The quality of global paths induces a greater impact on differential-wheeled excavators compared to front-wheel steering truck-trailers. Practical guidance can therefore be provided to select and improve the GPP algorithms and thereby to enhance the safety and efficiency of ACVs on construction sites.

A Context-Aware Navigation Framework for Ground Robots in Horticultural Environments.

Environmental mapping and robot navigation are the basis for realizing robot automation in modern agricultural production. This study proposes a new autonomous mapping and navigation method for gardening scene robots. First, a new LiDAR slam-based semantic mapping algorithm is proposed to enable the robots to analyze structural information from point cloud images and generate roadmaps from them. Secondly, a general robot navigation framework is proposed to enable the robot to generate the shortest global path according to the road map, and consider the local terrain information to find the optimal local path to achieve safe and efficient trajectory tracking; this method is equipped in apple orchards. The LiDAR was evaluated on a differential drive robotic platform. Experimental results show that this method can effectively process orchard environmental information. Compared with vnf and pointnet++, the semantic information extraction efficiency and time are greatly improved. The map feature extraction time can be reduced to 0.1681 s, and its MIoU is 0.812. The resulting global path planning achieved a 100% success rate, with an average run time of 4ms. At the same time, the local path planning algorithm can effectively generate safe and smooth trajectories to execute the global path, with an average running time of 36 ms.