Variant step size RRT: An efficient path planner for UAV in complex environments

This paper proposes a hybrid Unmanned Aerial Vehicle (UAV) path planning method that combines the Rapidly-exploring Random Tree (RRT) algorithm with Proximal Policy Optimization (PPO). The proposed method aims to enhance the efficiency and adaptability of UAV path planning in complex and dynamic environments. The RRT algorithm excels at quickly generating a feasible path from a start point to a goal point. However, the quality of its paths is often suboptimal, and it lacks adaptability in dynamic settings. In contrast, PPO, a deep reinforcement learning algorithm, optimizes paths through iterative policy updates, enabling the UAV to adapt to environmental changes. Our approach first employs RRT to generate an initial path, which is subsequently refined by PPO to improve smoothness and adaptability. Experimental results demonstrate that the RRT-PPO hybrid method performs favorably in terms of path length, computational time, and obstacle avoidance capability, effectively improving the task completion efficiency of UAVs in complex environments.

An object pick-and-place system with a camera, a six-degree-of-freedom (DOF) robot manipulator, and a two-finger gripper is implemented based on the robot operating system (ROS) in this paper. A collision-free path planning method is one of the most fundamental problems that has to be solved before the robot manipulator can autonomously pick-and-place objects in complex environments. In the implementation of the real-time pick-and-place system, the success rate and computing time of path planning by a six-DOF robot manipulator are two essential key factors. Therefore, an improved rapidly-exploring random tree (RRT) algorithm, named changing strategy RRT (CS-RRT), is proposed. Based on the method of gradually changing the sampling area based on RRT (CSA-RRT), two mechanisms are used in the proposed CS-RRT to improve the success rate and computing time. The proposed CS-RRT algorithm adopts a sampling-radius limitation mechanism, which enables the random tree to approach the goal area more efficiently each time the environment is explored. It can avoid spending a lot of time looking for valid points when it is close to the goal point, thus reducing the computing time of the improved RRT algorithm. In addition, the CS-RRT algorithm adopts a node counting mechanism, which enables the algorithm to switch to an appropriate sampling method in complex environments. It can avoid the search path being trapped in some constrained areas due to excessive exploration in the direction of the goal point, thus improving the adaptability of the proposed algorithm to various environments and increasing the success rate. Finally, an environment with four object pick-and-place tasks is established, and four simulation results are given to illustrate that the proposed CS-RRT-based collision-free path planning method has the best performance compared with the other two RRT algorithms. A practical experiment is also provided to verify that the robot manipulator can indeed complete the specified four object pick-and-place tasks successfully and effectively.

PurposeThe purpose of this paper is to present a new nested rapidly‐exploring random tree (RRT) algorithm for fault tolerant motion planning of robotic manipulators.Design/methodology/approachAnother RRT algorithm is nested within the general RRT algorithm. This second nested level is used to check whether the new sampled node in the first nested level is fault tolerant. If a solution can be found in the second nested RRT, the reduced manipulator after failures at the new sampled node can still fulfill the remaining task and this new sampled node is added into the nodes of RRT in the first level. Thus, the nodes in the first level RRT algorithm are all fault tolerant postures. The final trajectory joined by these nodes is also obviously fault tolerant. Besides fault tolerance, this new nested RRT algorithm also can fulfill some secondary tasks such as improvement of dexterity and obstacle avoidance. Sufficient simulations and experiments of this new algorithm on fault tolerant motion planning of robotic manipulators are implemented.FindingsIt is found that the new nested RRT algorithm can fulfill fault tolerance and some other secondary tasks at the same time. Compared to other existing fault tolerant algorithms, this new algorithm is more efficient.Originality/valueThe paper presents a new nested RRT algorithm for fault tolerant motion planning.

Double manipulator path planning is the basis for overhead line live working robot to complete the task. The previous dual manipulator motion path planning method has some problems, such as low success rate, low convergence speed, unstable guidance, and easy to lead to path discontinuity in complex environment. Therefore, this paper proposes a decoupling motion planning method for two manipulators of live working robot based on hybrid RRT (Rapidly-Exploring Random Trees) algorithm. The hybrid RRT algorithm combines target offset RRT algorithm, bidirectional RRT algorithm and dynamic expansion RRT algorithm. MATLAB robot toolbox is used to simulate the motion path planning of 6-DOF double manipulator of overhead line live working robot. The results show that the method proposed in this paper can realize the loose coupling and efficient collision free motion planning of double manipulator of live working robot.

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

The online cooperative path planning problem is discussed for multi-quadrotor maneuvering in an unknown dynamic environment. Based on the related basic concepts, typical three-dimensional obstacle models, such as spherical and cubic, and their collision checking criteria are presented in this article. An improved rapidly exploring random tree (RRT) algorithm with goal bias and greed property is proposed based on the heuristic search strategy to overcome the shortcomings of the classical RRT algorithm. Not only are the kinematic constraints of the quadrotor established but the time and space coordination strategy matching with the improved RRT algorithm is also presented in this article. Furthermore, a novel online collision avoidance strategy according to the partial information of the surrounding environment is proposed. On the basis of the above work, a distributed online path planning strategy is proposed to obtain the feasible path for each quadrotor. Numerical simulation results show that the improved RRT algorithm has better search efficiency than the classical RRT algorithm. And the satisfactory path planning and path tracking results prove that the above model and related planning strategies are reasonable and effective.

Path planning is an important problem in the field of unmanned aerial vehicles (UAVs). However, it is inefficient for many rapidly-exploring random tree (RRT) based methods to rapidly find a feasible solution in a complex environment. To solve the path planning problem for the UVA in a complex environment, an improved dynamic step size RRT algorithm combined with a new path length control strategy is proposed. Firstly, the algorithm adopts a biased-goal sampling strategy to guide the growth of the tree, and an expansion direction constraint strategy is adopted to limit the expansion direction of the tree. Secondly, an improved dynamic step size strategy is proposed to speed up the path searching process. Thirdly, a path length constraint strategy is designed, which is used to constrain the path length during the searching process for a solution. Finally, simulation results demonstrate that the proposed method achieves improvement in both computational time and the path quality.

Many path planning algorithms have been introduced so far, but most are costly, in path cost and in processing time, in large-scale uncluttered 3D environments such as underground mining stopes explored by an unmanned aerial vehicle (UAV). Rapidly-exploring Random Tree (RRT) algorithms are popular because of their probabilistic completeness and rapidity in finding a feasible path in single-query problems. Many of the algorithms (e.g. Informed RRT*, RRT#) developed to improve RRT need considerable time to converge in large environments. Shortcutting an RRT is an old idea that has been proven to outperform RRT variants. This paper introduces a new method, RRT-Rope, that aims at finding a near-optimal solution in a drastically shorter amount of time. The proposed approach benefits from fast computation of a feasible path with an altered version of RRT-connect, and post-processes it quickly with a deterministic shortcutting technique, taking advantage of intermediate nodes added to each branch of the tree. This paper presents simulations and statistics carried out to show the efficiency of RRT-Rope, which gives better results in terms of path cost and computation time than other popular RRT variations and shortening techniques in all our simulation environments, and is up to 70% faster than the next best algorithm in a representative stope.

Aiming at the problems of long planning time and path feasibility existing in genetic algorithm (GA) for path planning, an improved method integrating GA with Rapidly-exploring Random Tree (RRT) algorithm is proposed. By generating initial path populations using the RRT algorithm, eliminating redundant paths with a deletion operator, and introducing an elite selection strategy to optimize the selection operation, the continuity of paths and the convergence speed of the algorithm are effectively improved. Additionally, a path point backtracking method is utilized to further optimize path length and turning points. Experimental results show that the improved algorithm outperforms the traditional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A^{*}$</tex> algorithm and other improved GA in terms of path length, number of inflection points, and iteration times. The path length is shortened by an average of 8%, and the iteration times are reduced to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$53 \%-85 \%$</tex> of those of the comparative algorithms, verifying its high efficiency and robustness in complex environments.

This paper presents the motion planning of unicycle-like robot using single Rapidly-exploring Random Tree (RRT) algorithm, combining with Branch and Bound (BB) method. RRT can construct the searching tree efficiently between initial configuration and goal configuration. Based on the constructed searching tree, the optimal path can be extracted with BB algorithm rapidly. Obstacles avoidance is realized by checking whether the contour points of robot locate in the space of obstacles. The simulation result in a complex environment with unicycle-like robot proves the validity of proposed algorithms.

In this paper, an improved APF-GFARRT* (artificial potential field-guided fuzzy adaptive rapidly exploring random trees) algorithm based on APF (artificial potential field) guided sampling and fuzzy adaptive expansion is proposed to solve the problems of weak orientation and low search success rate when randomly expanding nodes using the RRT (rapidly exploring random trees) algorithm for disinfecting robots in the dense environment of disinfection operation. Considering the inherent randomness of tree growth in the RRT* algorithm, a combination of APF with RRT* is introduced to enhance the purposefulness of the sampling process. In addition, in the context of RRT* facing dense and restricted environments such as narrow passages, adaptive step-size adjustment is implemented using fuzzy control. It accelerates the algorithm’s convergence and improves search efficiency in a specific area. The proposed algorithm is validated and analyzed in a specialized environment designed in MATLAB, and comparisons are made with existing path planning algorithms, including RRT, RRT*, and APF-RRT*. Experimental results show the excellent exploration speed of the improved algorithm, reducing the average initial path search time by about 46.52% compared to the other three algorithms. In addition, the improved algorithm exhibits faster convergence, significantly reducing the average iteration count and the average final path cost by about 10.01%. The algorithm’s enhanced adaptability in unique environments is particularly noteworthy, increasing the chances of successfully finding paths and generating more rational and smoother paths than other algorithms. Experimental results validate the proposed algorithm as a practical and feasible solution for similar problems.

Sampling-based search algorithms such as Rapidly-Exploring Random Trees (RRT) have been utilized for mobile robot path planning and motion planning in high dimensional continuous spaces. This paper presents a path planning method for a planetary exploration rover in rough terrain. The proposed method exploits the framework of a sampling-based search, the optimal RRT (RRT*) algorithm. The terrain geometry used for planning is composed of point cloud data close to continuous space captured by a light detection and ranging (LIDAR) sensor. During the path planning phase, the proposed RRT*algorithm directly samples a point (node) from the LIDAR point cloud data. The path planner then considers the rough terrain traversability of the rover during the tree expansion process of RRT*. This process improves conventional RRT*in that the generated path is safe and feasible for the rover in rough terrain. In this paper, simulation study on the proposed path planning algorithm in various real terrain data confirms its usefulness.

Sampling-based algorithms such as the Rapidly-exploring Random Tree (RRT) have been recently proposed as an effective approach to computationally hard motion planning problem. However, while the RRT algorithm is known to be able to find a feasible solution quickly, there are no guarantees on the quality of such solution, e.g., with respect to a given cost functional. To address this limitation, the authors recently proposed a new algorithm, called RRT*, which ensures asymptotic optimality, i.e., almost sure convergence of the solution returned by the algorithm to an optimal solution, while maintaining the same properties of the standard RRT algorithm, both in terms of computation of feasible solutions, and of computational complexity. In this paper, the RRT* algorithm is extended to deal with differential constraints. A sufficient condition for asymptotic optimality is provided. It is shown that the RRT* algorithm equipped with any local steering procedure that satisfies this condition converges to an optimal solution almost surely. In particular, simple local steering procedures are provided for a Dubins' vehicle as well as a double integrator. Simulation examples are also provided for these systems comparing the RRT and the RRT* algorithms.

Recent advances in path-planning algorithms have transformed robotics. The Rapidly exploring Random Tree (RRT) algorithm underpins autonomous robot navigation. This paper systematically examines the uses and development of RRT algorithms in single and multiple robots to demonstrate their importance in modern robotics studies. To do this, we have reviewed 70 works on RRT algorithms in single and multiple robot path planning from 2015 to 2023. RRT algorithm evolution, including crucial turning points and innovative techniques, have been examined. A detailed comparison of the RRT Algorithm versions reveals their merits, limitations, and development potential. The review’s identification of developing regions and future research initiatives will enable roboticists to use RRT algorithms. This thorough review is essential to the robotics community, inspiring new ideas, helping problem-solving, and expediting single- and multi-robot system development. This highlights the necessity of RRT algorithms for autonomous and collaborative robotics advancement.

Aiming at the problems of strong randomness, unsmooth path and local optimum in the path planning of the Rapidly-exploring Random Trees (RRT) algorithm. The paper designs an improved RRT algorithm with variable step size and goal orientation (VO-RRT), which introduces variable step size, oriented expansion node, optimized initial path and smoothed path four parts. Through several experiments in 2D and 3D space to prove that the VO-RRT algorithm has enhanced obstacle avoidance ability and improved path smoothness in different obstacle spaces. The path nodes generated by the VO-RRT algorithm in 3D space are tested in URsim simulation software and manipulator body to verify the executability of the optimized path.