Success Rate Of Planning Research Articles

Integrated Scale-Adaptive Adjustment Factor-Enhanced BlendMask Method for Pineapple Processing System

This study addresses the challenge of efficiently peeling pineapples, which have a distinct elliptical form, thick skin, and small eyes that are difficult to detect with conventional automated methods. This results in significant flesh waste. To improve the process, we developed an integrated system combining an enhanced BlendMask method, termed SAAF-BlendMask, and a Pose Correction Planning (PCP) method. SAAF-BlendMask improves the detection of small pineapple eyes, while PCP ensures accurate posture adjustment for precise path planning. The system uses 3D vision and deep learning technologies, achieving an average precision (AP) of 73.04% and a small object precision (APs) of 62.54% in eye detection, with a path planning success rate reaching 99%. The fully automated electromechanical system was tested on 110 real pineapples, demonstrating a reduction in flesh waste by 11.7% compared to traditional methods. This study highlights the potential of advanced machine vision and robotics in enhancing the efficiency and precision of food processing.

A deep residual reinforcement learning algorithm based on Soft Actor-Critic for autonomous navigation

The problem of autonomous navigation has attracted significant attention from robotics research community in the last few decades. In this paper, we address the problem of low data utilization due to the large amount of episode experience value data. A maximum entropy algorithm based on prioritized experience replay (Learning Good Experience based on Soft Actor-Criti, LGE-SAC) is proposed to quickly reproduce past good experience episodes. As the deep reinforcement learning method is susceptible to failure to plan ahead and explore the target position in a long sequence environment, a deep Residual Soft Actor-Critic (RSAC) is proposed to alleviate this problem. The reinforcement learning policy is fused with the Artificial Potential Field method to improve the generalization ability of the proposed algorithm, thus improving robot adaptation in new test environments. In order to validate the effectiveness of the proposed algorithm, we conducted simulation experiments in Gazebo simulator environment and real experiments on a Turtlebot3 robot equipped with LiDAR sensor. Simulation and experiment results show that the proposed algorithm effectively avoids obstacles and succeeds in reaching the goal compared to other obstacle avoidance algorithms. In comparison with the Artificial Potential Field method, the planning success rate of the proposed RSAC algorithm in the test environment is increased by 30%, and at the same time, the number of planning steps is reduced by half, and the generalization ability is improved.

GVP-RRT: a grid based variable probability Rapidly-exploring Random Tree algorithm for AGV path planning

In response to the issues of low solution efficiency, poor path planning quality, and limited search completeness in narrow passage environments associated with Rapidly-exploring Random Tree (RRT), this paper proposes a Grid-based Variable Probability Rapidly-exploring Random Tree algorithm (GVP-RRT) for narrow passages. The algorithm introduced in this paper preprocesses the map through gridization to extract features of different path regions. Subsequently, it employs random growth with variable probability density based on the features of path regions using various strategies based on grid, probability, and guidance to enhance the probability of growth in narrow passages, thereby improving the completeness of the algorithm. Finally, the planned route is subjected to path re-optimization based on the triangle inequality principle. The simulation results demonstrate that the planning success rate of GVP-RRT in complex narrow channels is increased by 11.5–69.5% compared with other comparative algorithms, the average planning time is reduced by more than 50%, and the GVP-RRT has a shorter average planning path length.

3D-AMM: a 3D artificial moment method for path planning of manipulator in multiple obstacles scenario

PurposeIn response to the issue of traditional algorithms often falling into local minima or failing to find feasible solutions in manipulator path planning. The purpose of this paper is to propose a 3D artificial moment method (3D-AMM) for obstacle avoidance for the robotic arm's end-effector.Design/methodology/approachA new method for constructing temporary attractive points in 3D has been introduced using the vector triple product approach, which generates the attractive moments that attract the end-effector to move toward it. Second, distance weight factorization and spatial projection methods are introduced to improve the solution of repulsive moments in multiobstacle scenarios. Third, a novel motion vector-solving mechanism is proposed to provide nonzero velocity for the end-effector to solve the problem of limiting the solution of the motion vector to a fixed coordinate plane due to dimensionality constraints.FindingsA comparative analysis was conducted between the proposed algorithm and the existing methods, the improved artificial potential field method and the rapidly-random tree method under identical simulation conditions. The results indicate that the 3D-AMM method successfully plans paths with smoother trajectories and reduces the path length by 20.03% to 36.9%. Additionally, the experimental comparison outcomes affirm the feasibility and effectiveness of this method for obstacle avoidance in industrial scenarios.Originality/valueThis paper proposes a 3D-AMM algorithm for manipulator path planning in Cartesian space with multiple obstacles. This method effectively solves the problem of the artificial potential field method easily falling into local minimum points and the low path planning success rate of the rapidly-exploring random tree method.

A Random Path Sampling-Based Method for Motion Planning in Many Dimensions

In this paper, we present GRPMP (Gaussian Random Paths Motion Planner), a method for solving robot motion planning problems. Compared with traditional sampling-based methods which build large-scale random trees or roadmaps by sampling random nodes in configuration-spaces, GRPMP generates a set of smooth random paths discretized into sparse nodes, using a random path sampler based on Gaussian process, to reduce resource space occupation and improve planning success rate. Employing the high-quality path selecting strategy with the lazy collision checking technique, GRPMP can fast select the collision-free high-quality path that has the lowest cost in the set of smooth random paths, so as to improve the efficiency and quality of the motion planning. We present challenging experiments with GRPMP on pick-and-place tasks, using a humanoid robot, to show that GRPMP has the ability to find high-quality paths with efficiency and stability.

Path Planning of a Mobile Robot for a Dynamic Indoor Environment Based on an SAC-LSTM Algorithm.

This paper proposes an improved Soft Actor-Critic Long Short-Term Memory (SAC-LSTM) algorithm for fast path planning of mobile robots in dynamic environments. To achieve continuous motion and better decision making by incorporating historical and current states, a long short-term memory network (LSTM) with memory was integrated into the SAC algorithm. To mitigate the memory depreciation issue caused by resetting the LSTM's hidden states to zero during training, a burn-in training method was adopted to boost the performance. Moreover, a prioritized experience replay mechanism was implemented to enhance sampling efficiency and speed up convergence. Based on the SAC-LSTM framework, a motion model for the Turtlebot3 mobile robot was established by designing the state space, action space, reward function, and overall planning process. Three simulation experiments were conducted in obstacle-free, static obstacle, and dynamic obstacle environments using the ROS platform and Gazebo9 software. The results were compared with the SAC algorithm. In all scenarios, the SAC-LSTM algorithm demonstrated a faster convergence rate and a higher path planning success rate, registering a significant 10.5 percentage point improvement in the success rate of reaching the target point in the dynamic obstacle environment. Additionally, the time taken for path planning was shorter, and the planned paths were more concise.

Multiple Unmanned Aerial Vehicle Autonomous Path Planning Algorithm Based on Whale-Inspired Deep Q-Network

In emergency rescue missions, rescue teams can use UAVs and efficient path planning strategies to provide flexible rescue services for trapped people, which can improve rescue efficiency and reduce personnel risks. However, since the task environment of UAVs is usually complex, uncertain, and communication-limited, traditional path planning methods may not be able to meet practical needs. In this paper, we introduce a whale optimization algorithm into a deep Q-network and propose a path planning algorithm based on a whale-inspired deep Q-network, which enables UAVs to search for targets faster and safer in uncertain and complex environments. In particular, we first transform the UAV path planning problem into a Markov decision process. Then, we design a comprehensive reward function considering the three factors of path length, obstacle avoidance, and energy consumption. Next, we use the main framework of the deep Q-network to approximate the Q-value function by training a deep neural network. During the training phase, the whale optimization algorithm is introduced for path exploration to generate a richer action decision experience. Finally, experiments show that the proposed algorithm can enable the UAV to autonomously plan a collision-free feasible path in an uncertain environment. And compared with classic reinforcement learning algorithms, the proposed algorithm has a better performance in learning efficiency, path planning success rate, and path length.

A knowledge-based task planning approach for robot multi-task manipulation

Task planning is a crucial component in facilitating robot multi-task manipulations. Language-based task planning methods offer practicality in receiving commands from humans in real-life scenarios and require only low-cost labeled data. However, existing methods often rely on sequence models for planning, which primarily focus on mapping language to sequences of sub-tasks while neglecting the knowledge about tasks and objects. To overcome these limitations, we propose a knowledge-based task planning approach called Recurrent Graph Convolutional Network (RGCN). It is devised with a novel structure that combined GCN (Kipf and Welling in International Conference on Learning Representations (ICLR), 2017) and LSTM (Hochreiter and chmidhuber in Neural Comput 9 (8): 1735-1780, 1997. https://doi.org/10.1162/neco.1997.9.8.1735) which enables it to leverage knowledge graph data and historical predictions. The experimental results demonstrate that our approach achieves the impressive task planning success rate of 95.7%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${95.7\\%}$$\\end{document}, surpassing the best baseline method significantly, which achieves 78.7%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${78.7\\%}$$\\end{document}. Furthermore, we evaluate the performance of multi-task manipulation across a specific set of 20 tasks within a simulated environment. Notably, RGCN combined with pre-trained primitive tasks exhibits the highest success rate compared with state-of-art multi-task learning methods. Our method is proven to be significant for language-conditioned task planning and is qualified for instructing robots for multi-task manipulation.

An Improved Distributed Sampling PPO Algorithm Based on Beta Policy for Continuous Global Path Planning Scheme

Traditional path planning is mainly utilized for path planning in discrete action space, which results in incomplete ship navigation power propulsion strategies during the path search process. Moreover, reinforcement learning experiences low success rates due to its unbalanced sample collection and unreasonable design of reward function. In this paper, an environment framework is designed, which is constructed using the Box2D physics engine and employs a reward function, with the distance between the agent and arrival point as the main, and the potential field superimposed by boundary control, obstacles, and arrival point as the supplement. We also employ the state-of-the-art PPO (Proximal Policy Optimization) algorithm as a baseline for global path planning to address the issue of incomplete ship navigation power propulsion strategy. Additionally, a Beta policy-based distributed sample collection PPO algorithm is proposed to overcome the problem of unbalanced sample collection in path planning by dividing sub-regions to achieve distributed sample collection. The experimental results show the following: (1) The distributed sample collection training policy exhibits stronger robustness in the PPO algorithm; (2) The introduced Beta policy for action sampling results in a higher path planning success rate and reward accumulation than the Gaussian policy at the same training time; (3) When planning a path of the same length, the proposed Beta policy-based distributed sample collection PPO algorithm generates a smoother path than traditional path planning algorithms, such as A*, IDA*, and Dijkstra.

DDNSAS: Deep reinforcement learning based deep Q-learning network for smart agriculture system

As the global population continues to grow and environmental conditions become increasingly unpredictable, meeting the demands for food becomes increasingly difficult. To overcome these challenges, smart agriculture has emerged as the key technology. Deep Learning model with Internet of Things (IoT), unmanned aerial vehicle (UAV), and edge–fog–cloud architecture enabled smart agriculture as a key component for next agriculture revolution. In this work, we present two stage end-to-end DRL based smart agricultural system. In stage one, we proposed ACO enabled DQN (MACO-DQN) model to offload task including fire detection, pest detection, crop growth monitoring, irrigation scheduling, soil monitoring, climate monitoring, field monitoring etc. MACO-DQN model offload the task to either edge, fog or cloud networking devices based on latency, energy consumption and computing power. Once the task offloaded to computing devices (edge, fog or cloud), task of prediction and monitoring various agriculture activities is performed at stage two. In stage two, we proposed DRL based DQN (RL-DQN) model for prediction and monitoring agricultural task activities. Finally, we demonstrate experimental findings of our proposed model that represent a marked enhancement in terms of convergence speed, planning success rate, and path accuracy. To evaluate its performance, the method presented in this paper was compared to traditional deep Q-networks-based intensive learning method under consistent experimental conditions. Overall, 98.5% precision, 99.1% recall, 98.1% F-measure, and 98.5% accuracy is obtained when using our proposed methodology and based on the performance results the model outperforms other existing methodologies.

PRM-D* Method for Mobile Robot Path Planning

Various navigation tasks involving dynamic scenarios require mobile robots to meet the requirements of a high planning success rate, fast planning, dynamic obstacle avoidance, and shortest path. PRM (probabilistic roadmap method), as one of the classical path planning methods, is characterized by simple principles, probabilistic completeness, fast planning speed, and the formation of asymptotically optimal paths, but has poor performance in dynamic obstacle avoidance. In this study, we use the idea of hierarchical planning to improve the dynamic obstacle avoidance performance of PRM by introducing D* into the network construction and planning process of PRM. To demonstrate the feasibility of the proposed method, we conducted simulation experiments using the proposed PRM-D* (probabilistic roadmap method and D*) method for maps of different complexity and compared the results with those obtained by classical methods such as SPARS2 (improving sparse roadmap spanners). The experiments demonstrate that our method is non-optimal in terms of path length but second only to graph search methods; it outperforms other methods in static planning, with an average planning time of less than 1 s, and in terms of the dynamic planning speed, our method is two orders of magnitude faster than the SPARS2 method, with a single dynamic planning time of less than 0.02 s. Finally, we deployed the proposed PRM-D* algorithm on a real vehicle for experimental validation. The experimental results show that the proposed method was able to perform the navigation task in a real-world scenario.

A novel reinforcement learning based tuna swarm optimization algorithm for autonomous underwater vehicle path planning

Path planning technology is an important guarantee for the safe navigation of autonomous underwater vehicle (AUV) in water, and it is also an important indicator of the intelligence of autonomous underwater vehicle. Aiming at the path planning problem of AUV in complex environments, this article presents a reinforcement learning-based tuna swarm optimization algorithm called the QLTSO. In this algorithm, individuals are independent of each other, and the choice of each individual strategy is decided by reinforcement learning. Four strategies are set for each individual in the algorithm: spiral foraging, parabolic foraging, optimization adjustment and ESOS strategy. Finally, the cubic B-spline curve is used to smooth the path so that the autonomous underwater vehicle can better track the path. To verify the superiority of the QLTSO algorithm, the algorithm is compared with other advanced optimization algorithms. The simulation results show that the QLTSO algorithm can plan safe and effective AUV navigation paths in a variety of two-dimensional and three-dimensional complex environments with better convergence and robustness, and the planning success rate is up to 100%, which is an effective AUV path planning algorithm.

Prioritized Safe Interval Path Planning for Multi-Agent Pathfinding With Continuous Time on 2D Roadmaps

We address a challenging multi-agent pathfinding (MAPF) problem for hundreds of agents moving on a 2D roadmap with continuous time. Despite its known potential for producing better solutions compared to typical grid and discrete-time cases, few approaches have been established to solve this problem due to the intractability of collision checks on a large scale. In this work, we propose Prioritized Safe-Interval Path Planning with Continuous-Time Conflicts (PSIPP/CTC) that extends a scalable prioritized planning algorithm to work on the 2D roadmap and continuous-time setup by alleviating intensive collision checks. Our approach involves a novel concept named Continuous-Time Conflict (CTC), which describes a pair among vertices and edges associated with continuous-time intervals within which collisions can happen between agents. We pre-compute CTCs using geometric neighbor-search and sweeping techniques and annotate roadmaps with the CTCs just once before planning starts. Doing so allows us to efficiently enumerate collision-free time intervals for all vertices and edges and find each agent's path with continuous time in prioritized planning. Extensive experimental evaluations demonstrate that PSIPP/CTC significantly outperforms existing methods in terms of planning success rate and runtime while maintaining an acceptable solution quality. As a proof of concept, we also confirmed the effectiveness of the proposed approach on a physics simulation with differential wheeled robots.

Rapid citrus harvesting motion planning with pre-harvesting point and quad-tree

Aiming at the problems of low success rate and long planning time of harvesting robots in unstructured and complex environments, a harvesting motion planning algorithm based on pre-harvesting guide points (Pre-harvesting Guide Informed—RRT*, PGI-RRT*) is proposed. This algorithm is on the basis of progressively optimal informed RRT * algorithm. The third point between the starting point and the target point is selected as the pre-harvesting guide point. The four random trees are generated between the initial point, the target point and the guide point at the same time to quickly obtain the initial path. In the PGI-RRT* algorithm, P probability sampling is used to replace random sampling to improve the blindness of sampling. New nodes are generated by the dynamic step size. To do so can improve the speed and flexibility of the PGI-RRT* algorithm to explore the unknown space, and improve the convergence speed of the optimal path. 2D simulation experiments show that, compared with Informed-RRT*, the PGI-RRT* algorithm can reduce the time to find the initial path by about 75–86 %, and improve the success rate by 18–32 %. 3D simulation experiments and experiments in laboratory and field environments show that the PGI-RRT* algorithm proposed in this paper can significantly reduce the planning time and improve the planning success rate. Compared to the 9 algorithms added to the pre-harvesting guide points for double path planning in the OMPL, the PGI-RRT* algorithm can reduce the path planning time by 40–60 %, and improve the success rate of path planning to 95 %, and shorten the execution time of the manipulator by about 8 s.

Kinematic-Based Multi-Objective Design Optimization of a Grapevine Pruning Robotic Manipulator

Annual cane pruning of grape vineyards is a time-consuming and labor-intensive job, but no mechanized or automatic way has been developed to do it yet. Robotic pruning can be a perfect alternative to human labor. This article proposes a systematic seven-stage procedure to design a kinematically optimized manipulator, named ‘Prubot’, to manage vineyards’ cane pruning. The manipulator structure was chosen, resulting in a 7R (Revolute) manipulator with a spherical shoulder and wrist. To obtain the design constraints, the manipulator task space was modeled. The robot’s second and third link lengths were determined by optimizing the global translational version of the measure of manipulability and the measure of isotropy of the manipulator arm section. Finally, simulations confirmed the appropriateness of the manipulator workspace. Furthermore, sampling-based path planning simulations were carried out to evaluate the manipulator’s kinematic performance. Results illustrated the impressive kinematic performance of the robot in terms of path planning success rate (≅100%). The simulations also suggest that among the eight single-query sampling-based path planning algorithms used in the simulations, Lazy RRT and KPIECE are the best (≤5 s & ~100%) and worst ≥5 s &≤25% path planning algorithms for such a robot in terms of computation time and success rate, respectively. The procedure proposed in this paper offers a foundation for the kinematic and task-based design of a cane pruning manipulator. It could be promisingly used for designing similar agricultural manipulators.

Augmented Value Iteration Networks with Artificial Potential Fields for Path Planning

Value iterative networks (VINs), as a differentiable path planning method, taking environmental images as input, can solve path planning problems in new and unseen environments with powerful generalization capabilities. But the planning success rate decreases rapidly as the planning space scales. We propose the potential field augmented VIN by replacing the environmental map with the potential map as input and implementing this process in the form of dilated convolutions, giving more a priori information to the subsequent planning computation while hardly increasing the computational cost. Experiments on 2D grid-world show that the improved method has higher path planning success rates and smaller difference of predicted paths from shortest paths, as well as smaller performance degradation with increasing map size.

Research on Key Technologies of Smart City Building Interior Decoration Construction based on In-Depth Learning

The intelligentization of building interior decoration construction is of great significance to the construction of smart city, and robot automation has brought an opportunity for this. Robot self-decoration is the development trend in the future. One of the key issues involved, is the self-planning of mobile path. In this regard, the research adopts the proximal policy optimization algorithms (PPO) to improve the self-planning path ability of the decoration robot. For the information of lidar and robot status, the Full Connect Neural Network (FCNN) is used to process it. In addition, the reward function and the corresponding Credit Assignment Problem (CAP) model are designed, to accelerate the learning process of path planning. Aiming at the dynamic uncertainty in the actual environment, the adaptive loss function is used to build an auxiliary model to predict the environmental change. The simulation results show that the research and design strategy significantly improves the learning efficiency and path planning success rate of the decoration robot, and shows good adaptability to the dynamic environment, which has important reference significance for the practical application of the decoration robot.

Path planning of the fruit tree pruning manipulator based on improved RRT-Connect algorithm

Aiming to realize the obstacle avoidance of the fruit tree pruning manipulator in unstructured complex natural environment, an improved bidirectional fast extended random tree (RRT-Connect) algorithm was presented in this study. The manipulator and obstacles were properly simplified based on their geometrical characteristics to build collision detection models taking account of the obstacles, ground, and manipulator itself and to carry out the obstacle avoidance path planning. Goal-biased strategy and adaptive step size adjustment principle were introduced to accelerate the path search speed. Bidirectional pruning optimal strategy and cubic non-uniform B-spline interpolation method were adopted to optimize the path generated by RRT-Connect. The simulation path planning experiment was carried out in the simulation system of the fruit tree pruning manipulator and the practical obstacle avoidance path planning experiment was carried out on the real fruit tree pruning manipulator path planning experiment platform. The results showed that the path planning time and the path length of the improved RRT-Connect algorithm reduced by about 55% and 60% respectively compared with the basic RRT-Connect algorithm. The path planning success rate of the improved RRT-Connect algorithm was 100%, and the planned path was smooth, continual and executable, which could effectively guide the manipulator to avoid obstacles and lead the end effector of the manipulator to the goal point. The proposed improved algorithm not only has certain application value for obstacle avoidance of the fruit tree pruning manipulator in fruit tree pruning environment, but also has theoretical reference value for path planning of other types of robots. Keywords: manipulator, path planning, RRT-Connect, jujube pruning, obstacle avoidance, non-uniform B-spline DOI: 10.25165/j.ijabe.20221502.6249 Citation: Chen Y Y, Fu Y X, Zhang B, Fu W, Shen C J. Path planning of the fruit tree pruning manipulator based on improved RRT-Connect algorithm. Int J Agric & Biol Eng, 2022; 15(2): 177–188.

CL-MAPF: Multi-Agent Path Finding for Car-Like robots with kinematic and spatiotemporal constraints

Multi-Agent Path Finding has been widely studied in the past few years due to its broad application in the field of robotics and AI. However, previous solvers rely on several simplifying assumptions. This limits their applicability in numerous real-world domains that adopt nonholonomic car-like agents rather than holonomic ones. In this paper, we give a mathematical formalization of the Multi-Agent Path Finding for Car-Like robots (CL-MAPF) problem. We propose a novel hierarchical search-based solver called Car-Like Conflict-Based Search to address this problem. It applies a body conflict tree to address collisions considering the shapes of the agents. We introduce a new algorithm called Spatiotemporal Hybrid-State A* as the single-agent planner to generate agents’ paths satisfying both kinematic and spatiotemporal constraints. We also present a sequential planning version of our method, sacrificing a small amount of solution quality to achieve a significant reduction in runtime. We compare our method with two baseline algorithms on a dedicated benchmark and validate it in real-world scenarios. The experiment results show that the planning success rate of both baseline algorithms is below 50% for all six scenarios, while our algorithm maintains that of over 98%. It also gives clear evidence that our algorithm scales well to 100 agents in 300 m × 300 m scenario and is able to produce solutions that can be directly applied to Ackermann-steering robots in the real world. The benchmark and source code are released in https://github.com/APRIL-ZJU/CL-CBS. The video of the experiments can be found on YouTube.

Convolutionally evaluated gradient first search path planning algorithm without prior global maps

Most of the existing path planning algorithms require a prior global map. Although there have been some algorithms proposed for unknown environments, they can only deal with those which just have several hidden obstacles in a roughly known global map. In order to improve the efficiency of robot’s path planning without prior global maps, this paper proposes a Convolutionally Evaluated Gradient First Search (CE-GFS) path planning algorithm. It allows the robot to collect environmental information and complete path planning simultaneously. Firstly, the Gradient First Search (GFS) algorithm is proposed based on the gradient score parameter, with which the conventional cost function is replaced. The GFS can adapt to any moving direction through the environmental information surrounding the mobile robot and computing the gradient score parameter. Secondly, CE-GFS path planning algorithm is proposed based on GFS and convolutional evaluation method. The CE-GFS helps the robots to evaluate the efficiency of the global path and get global perception ability, so that they are prevented from going astray, which can significantly improve the efficiency of path planning. Finally, several simulation tests and field tests have been carried out. The test results show that convolutional evaluation improves the efficiency of CE-GFS by 86.94% on average compared with GFS at the price of 0.18% decrease in path planning success rate. Moreover, the time cost of the proposed CE-GFS algorithm is 42.18% less than that of FAR-Planner in some special cases.