Fault tolerant motion planning of robotic manipulators based on a nested RRT algorithm

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.

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.

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.

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.

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.

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.

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.

This paper introduces an efficient motion planning method for on-road driving of the autonomous vehicles, which is based on the rapidly exploring random tree (RRT) algorithm. RRT is an incremental sampling-based algorithm and is widely used to solve the planning problem of mobile robots. However, due to the meandering path, the inaccurate terminal state, and the slow exploration, it is often inefficient in many applications such as autonomous vehicles. To address these issues and considering the realistic context of on-road autonomous driving, we propose a fast RRT algorithm that introduces a rule-template set based on the traffic scenes and an aggressive extension strategy of search tree. Both improvements lead to a faster and more accurate RRT toward the goal state compared with the basic RRT algorithm. Meanwhile, a model-based prediction postprocess approach is adopted, by which the generated trajectory can be further smoothed and a feasible control sequence for the vehicle would be obtained. Furthermore, in the environments with dynamic obstacles, an integrated approach of the fast RRT algorithm and the configuration-time space can be used to improve the quality of the planned trajectory and the replanning. A large number of experimental results illustrate that our method is fast and efficient in solving planning queries of on-road autonomous driving and demonstrate its superior performances over previous approaches.

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.

Rapidly-exploring Random Tree (RRT) algorithm has been used for motion planning in numerous and diverse robotic applications. For applications which demands higher motion resolution, the computational cost increases together with the number of motion primitives used to expand the RRT. In this paper we present a method based on optimization by elimination which is applied to the Rapidly-exploring Random Tree algorithm to reduce its computational cost. This method optimizes the efficiency of motion primitives generation. It identifies tree expansion in promising areas by initially generating and analyzing only few motion primitives. Then it increases the number of primitives for motion resolution enhancement in those promising areas. The results achieved by applying this method evidence a substantial decrease in the computational cost.

The current path planning algorithms such as A-star(all stars) algorithm and RRT (Rapidly-exploring Random Trees) algorithm can meet the obstacle avoidance planning of the 6-DOF robot, but the smoothness of the path is not considered. Working in an unreasonable path for a long time will produce a great load on the joints of the 6-DOF robot and seriously affect its life. In this paper, we use reinforcement learning reconcile A-star algorithm and RRT algorithm for smooth path planning of the robot. Experimental results show that compared with A-star algorithm and RRT algorithm, the fusion algorithm has smoother path and more reasonable time.

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.

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.

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.

Robotic manipulators designed for home assistance and new surgical procedures often have significant uncertainty in their actuation due to compliance requirements, cost constraints, and size limits. We introduce a new integrated motion planning and control algorithm for robotic manipulators that makes safety a priority by explicitly considering the probability of unwanted collisions. We first present a fast method for estimating the probability of collision of a motion plan for a robotic manipulator under the assumptions of Gaussian motion and sensing uncertainty. Our approach quickly computes distances to obstacles in the workspace and appropriately transforms this information into the configuration space using a Newton method to estimate the most relevant collision points in configuration space. We then present a sampling-based motion planner based on executing multiple independent rapidly exploring random trees that returns a plan that, under reasonable assumptions, asymptotically converges to a plan that minimizes the estimated collision probability. We demonstrate the speed and safety of our plans in simulation for (1) a 3-D manipulator with 6 DOF, and (2) a concentric tube robot, a tentacle-like robot designed for surgical applications.