Rapidly-exploring Random Tree Research Articles

RJ-RRT: Improved RRT for Path Planning in Narrow Passages

As a representative of sampling-based planning algorithms, rapidly exploring random tree (RRT), is extensively welcomed in solving robot path planning problems due to its wide application range and easy addition of nonholonomic constraints. However, it is still challenging for RRT to plan the path for configuration space with narrow passages. As a variant algorithm of RRT, rapid random discovery vine (RRV) gives a better solution, but when configuration space contains more obstacles instead of narrow passages, RRV performs slightly worse than RRT. In order to solve these problems, this paper re-examines the role of sampling points in RRT. Firstly, according to the state of the random tree expanding towards the current sampling point, a greedy sampling space reduction strategy is proposed, which decreases the redundant expansion of the random tree in space by dynamically changing the sampling space. Secondly, a new narrow passage judgment method is proposed according to the environment around of sampling point. After the narrow passage is identified, the narrow passage is explored by generating multiple subtrees inside the passage. The subtrees can be merged into the main tree that expands in a larger area by subsequent sampling. These improvements further enhance the value of sampling points. Compared with the existing RRT algorithms, the adaptability for different environments is improved, and the planning time and memory usage are saved.

A collaborative path planning method for mobile cable-driven parallel robots in a constrained environment with considering kinematic stability

Mobile cable-driven parallel robot (MCDPR) is a variant of cable-driven parallel robots (CDPRs) by mounting several mobile bases to replace the conventional fixed frame. The novel modification of adding mobile bases leads MCDPRs being highly flexible and have great potential for complex environments. However, the issue of coupled mobile bases introduces actuated kinematic redundancies which present challenges for path planning. In this paper, we propose a collaborative path planning method for MCDPRs, and it allows the robot to deal with complex internal and external constraints in a high-dimensional state space efficiently. The proposed method quickly generates feasible paths for coupled mobile bases using the adaptive goal-biased rapidly exploring random tree (RRT) method, in which the adaptive sampling method is developed to enhance efficiency. Based on the feasible path of the mobile base, we proposed a grid-based search method to determine the position of the end-effector with considering the stability and kinematic performances. Furthermore, the planned paths are post-processed with the cubic splines to obtain continuous profiles for the robot. Finally, the proposed method is validated through the dynamic simulation software (CoppeliaSim) and experiments based on a MCDPR prototype with an eight-cable-driven parallel robot mounted on four mobile bases.

An RRT-Dijkstra-Based Path Planning Strategy for Autonomous Vehicles

It is challenging to plan paths for autonomous vehicles on half-structured roads because of the vast planning area and complex environmental constraints. This work aims to plan optimized paths with high accuracy and efficiency. A two-step path planning strategy is proposed. The classic planning problem is divided into two simpler planning problems: reduction problems for a vast planning area and solving problems for weighted directed graphs. The original planning area is first reduced using an RRT (Rapidly Exploring Random Tree) based guideline planner. Second, the path planning problem in the smaller planning region is expanded into a weighted directed graph and transformed into a discrete multi-source cost optimization problem, in which a potential energy field based discrete cost assessment function was designed considering obstacles, lanes, vehicle kinematics, and collision avoidance performances, etc. The output path is then obtained by applying a Dijkstra optimizer. Comparative simulations are conducted to assess the effectiveness of the proposed strategy. The results shows that the designed strategy balances efficiency and accuracy with enough planning flexibility and a 22% improvement in real-time performance compared to the classic Lattice planner, without significant loss of accuracy.

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

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

Efficient Path Planning for a Microrobot Passing through Environments with Narrow Passages.

This paper presents an efficient path-planning algorithm for microrobots attempting to pass through environments with narrow passages. Because of the extremely small size of a microrobot, it is suitable for work in this kind of environment. The rapidly exploring random tree (RRT) algorithm, which uses random sampling points, can quickly explore an entire environment and generate a sub-optimal path for a robot to pass through it; however, the RRT algorithm, when used to plan a path for a microrobot passing through an environment with narrow passages, has the problem of being easily limited to local solutions when it confronts with a narrow passage and is unable to find the final path through it. In light of this, the objectives of the considered path planning problem involve detecting the narrow passages, leading the path toward an approaching narrow passage, passing through a narrow passage, and extending the path search more efficiently. A methodology was proposed based on the bidirectional RRT in which image processing is used to mark narrow passages and their entrances and exits so that the bidirectional RRT can be quickly guided to them and combined with the deterministic algorithm to find paths through them. We designed the methodology such that RRT generates the sampling points for path growth. The multiple importance sampling technique is incorporated with bidirectional RRT, named MIS-BiRRT, to make the path grow faster toward the target point and narrow passages while avoiding obstacles. The proposed algorithm also considers multiple candidate paths simultaneously to expand the search range and then retain the best one as a part of the planning path. After validation from simulation, the proposed algorithm was found to generate efficient path planning results for microrobots to pass through narrow passages.

Efficient Informative Path Planning via Normalized Utility in Unknown Environments Exploration.

Exploration is an important aspect of autonomous robotics, whether it is for target searching, rescue missions, or reconnaissance in an unknown environment. In this paper, we propose a solution to efficiently explore the unknown environment by unmanned aerial vehicles (UAV). Innovatively, a topological road map is incrementally built based on Rapidly-exploring Random Tree (RRT) and maintained along with the whole exploration process. The topological structure can provide a set of waypoints for searching an optimal informative path. To evaluate the path, we consider the information measurement based on prior map uncertainty and the distance cost of the path, and formulate a normalized utility to describe information-richness along the path. The informative path is determined in every period by a local planner, and the robot executes the planned path to collect measurements of the unknown environment and restructure a map. The proposed framework and its composed modules are verified in two 3-D environments, which exhibit better performance in improving the exploration efficiency than other methods.

Feedback RRT* algorithm for UAV path planning in a hostile environment

Unmanned aerial vehicle (UAV) path planning in a hostile environment (UPPHE) considers the features and information of defense systems to plan a risk-constrained shortest path for a UAV from the initial position to target. When the characteristics of defense systems cannot be accurately expressed manually, it will be brutal to effectively or efficiently implement the classical planning methods because of the lack of risk information to constrain and guide planning. We present a data-driven approach for UPPHE, the feedback rapidly-exploring random tree star algorithm (FRRT*), with a data-driven risk network and feedback module. FRRT* can use information extracted from situation data to constrain the growth of the random tree and make biased adjustments to improve planning efficiency. Simulation experiments verify the effectiveness of the risk network in guiding planning, and the improved efficiency brought by the feedback module.

APF-IRRT*: An Improved Informed Rapidly-Exploring Random Trees-Star Algorithm by Introducing Artificial Potential Field Method for Mobile Robot Path Planning

An Informed RRT* (IRRT*) algorithm is one of the optimized versions of a Rapidly-exploring Random Trees (RRT) algorithm which finds near-optimal solutions faster than RRT and RRT* algorithms by restricting the search area to an ellipsoidal subset of the state space. However, IRRT* algorithm has the disadvantage of randomness of sampling and a non-real time process, which has a negative impact on the convergence rate and search efficiency in path planning applications. In this paper, we report a hybrid algorithm by combining the Artificial Potential Field Method (APF) with an IRRT* algorithm for mobile robot path planning. By introducing the virtual force field of APF into the search tree expansion stage of the IRRT* algorithm, the guidance of the algorithm increases, which greatly improves the convergence rate and search efficiency of the IRRT* algorithm. The proposed algorithm was validated in simulations and proven to be superior to some other RRT-based algorithms in search time and path length. It also was performed in a real robotic platform, which shows that the proposed algorithm can be well executed in real scenarios.

Homology-Class Guided Rapidly-Exploring Random Tree For Belief Space Planning.

In this work, an efficient homology guided belief space planning method for obstacle-cluttered environments is presented. The proposed planner follows a two-step approach. First, a h-signature guided rapidly-exploring random tree (HRRT) algorithm is proposed to provide nominal trajectories in different homology classes by constructing homology aware sub-trees in a parallel manner. The HRRT planner is extended to a h-signature guided RRT* algorithm, where an inter-homology-class rewire procedure is proposed, increasing the probability of discovering homology classes in narrow space/passages. The iLQG-based belief space planning algorithm is then employed to find locally optimal trajectories minimizing uncertainties in each homology class.

An Enhanced Navigation Algorithm with an Adaptive Controller for Wheeled Mobile Robot Based on Bidirectional RRT

A navigation algorithm providing motion planning for two-wheeled mobile robots is proposed in this paper. The motion planning integrates path planning, velocity planning and controller design. Bidirectional rapidly-exploring random trees algorithms (RRT) with path pruning and smoothing mechanism are firstly used to obtain a collision-free path to the robot destination with directional continuity. Secondly, velocity planning based on trapezoidal velocity profile is used in both linear and angular velocities, but the position error of the endpoint of the curve appears due to the coupling problem of the nonlinear system. To reduce the error, an approximation method is used to gradually modify several parts of time length of the trapezoidal velocity profile, so the continuity of the path can still be maintained. Thirdly, the controller keeping the robot on the planned path and velocity is designed based on the dynamic model of the robot. The parameters of this controller are estimated by the adaptive low, and the gain of controller is dynamic adjusted by fuzzy logic control to avoid the case that the control value is saturated. The controller stability and the convergence of tracking error is guaranteed by Lyapunov theory. Simulation results are presented to illustrate the effectiveness and efficiency.

Local Path Planning of Autonomous Vehicle Based on an Improved Heuristic Bi-RRT Algorithm in Dynamic Obstacle Avoidance Environment.

The existing variants of the rapidly exploring random tree (RRT) cannot be effectively applied in local path planning of the autonomous vehicle and solve the coherence problem of paths between the front and back frames. Thus, an improved heuristic Bi-RRT algorithm is proposed, which is suitable for obstacle avoidance of the vehicle in an unknown dynamic environment. The vehicle constraint considering the driver’s driving habit and the obstacle-free direct connection mode of two random trees are introduced. Multi-sampling biased towards the target state reduces invalid searches, and parent node selection with the comprehensive measurement index accelerates the algorithm’s execution while making the initial path gentle. The adaptive greedy step size, introducing the target direction, expands the node more effectively. Moreover, path reorganization minimizes redundant path points and makes the path’s curvature continuous, and path coherence makes paths between the frames connect smoothly. Simulation analysis clarifies the efficient performance of the proposed algorithm, which can generate the smoothest path within the shortest time compared with the other four algorithms. Furthermore, the experiments on dynamic environments further show that the proposed algorithm can generate a differentiable coherence path, ensuring the ride comfort and stability of the vehicle.

Multiple spacecraft coordination and motion planning for full-coverage inspection of large complex space structures

This paper presents a new multiple spacecraft full-coverage inspection path-planning scheme to closely observe any large complex space structure hovering in space. For this purpose, a decentralized multi-spacecraft methodology is proposed, extending our previous work on the inspection of structures using a single inspector spacecraft for a cooperative collection of small spacecraft. Multi-robot systems are more reliable, flexible, and scalable and can accomplish complex missions, which might be impossible or significantly time-consuming for a single robot. To this end, our previously developed asymptotically optimal sampling-based path planner, called the Rapidly Exploring Random Tree, is combined with a multi-spacecraft coordination methodology. The resulting kinodynamic inspection path planner generates 3-dimensional inspection trajectories for each spacecraft to fully observe any points on the boundary of a complex space structure in close proximity while satisfying the kinematic and dynamic constraints. Spacecraft coordination, communication, and task allocations are developed to reduce the total inspection time, crucial during servicing and proximity operations. Simulation results are presented to demonstrate the ability and effectiveness of our planner.

A Two-Stage Path Planning Algorithm Based on Rapid-Exploring Random Tree for Ships Navigating in Multi-Obstacle Water Areas Considering COLREGs

A two-stage ship path planning method is proposed, based on the Rapid-exploring Random Tree (RRT) algorithm, which is composed of global path planning and local path planning, addressing the important problem of finding an economical and safe path from start to destination for ships under dynamic environment, especially in waters with multiple obstacles and multiple target ships. The global path planning takes into consideration the ship draft and Under Keel Clearance to find navigable water using RRT, and reduces the path length and waypoints based on elliptic sampling and smoothing. In the local path planning, a dynamic collision risk detection model is constructed by introducing the Quaternion Ship Domain under a dynamic environment, and the restrictions of ship manoeuvrability and COLREGs are also involved. The simulation results show that the proposed model can find a satisfactory path within a few iterations, and keep clear of both static obstacles and dynamic ships. The research can be used to make and verify planned ship routes before sailing and to guide officers to make decisions regarding collision avoidance.

A Novel Direct Trajectory Planning Approach Based on Generative Adversarial Networks and Rapidly-Exploring Random Tree

Trajectory planning is essential for self-driving vehicles and has stringent requirements for accuracy and efficiency. The existing trajectory planning methods have limitations in the feasibility of planned trajectories and computational efficiency. This paper proposes a life-long learning framework to achieve effective and high-accuracy direct trajectory planning (DTP) tasks. Based on generative adversarial networks (GANs), this study develops a lightweight GDTP model to map the initial/final states and the control action sequence. Additionally, by embedding the GDTP into the rapidly-exploring random tree (RRT), a GDTP-RRT algorithm is further designed for long-distance and multi-stage planning tasks. Taking the tractor-trailer as an application case, we test the proposed method in multiple scenarios with varying characteristics. The experimental results show that the method can plan highly feasible trajectories in a short time, compared with the most applied algorithm – the cubic curve RRT* (CCRRT*). It is found that the tracking errors of our method are 29.1% and 44.1% lower than the CCRRT* in terms of position and heading angle. This paper provides an effective and stable vehicle trajectory planning method for complex self-driving tasks.

Multi-AGV's Temporal Memory-Based RRT Exploration in Unknown Environment

With the increasing need for multi-robot for exploring the unknown region in a challenging environment, efficient collaborative exploration strategies are needed for achieving such feat. A frontier-based Rapidly-Exploring Random Tree (RRT) exploration can be deployed to explore an unknown environment. However, its' greedy behavior causes multiple robots to explore the region with the highest revenue, which leads to massive overlapping in exploration process. To address this issue, we present a temporal memory-based RRT (TM-RRT) exploration strategy for multi-robot to perform robust exploration in an unknown environment. It computes adaptive duration for each frontier assigned and calculates the frontier's revenue based on the relative position of each robot. In addition, each robot is equipped with a memory consisting of frontier assigned and share among fleets to prevent repeating assignment of same frontier. Through both simulation and actual deployment, we have shown the robustness of TM-RRT exploration strategy by completing the exploration in a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$25.0\,\rm{m}\times \text{54.0}\,\rm{m}$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1350.0}\,\rm{m}^{2}$</tex-math></inline-formula> ) area, while the conventional RRT exploration strategy falls short.

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

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

Obstacle Avoidance for Microrobots in Simulated Vascular Environment Based on Combined Path Planning

In order to increase the feasibility of using microrobots to perform microscale tasks and widen the range of potential applications, the use of autonomous control algorithms such as obstacle avoidance is essential. In this study, aiming at the requirement of microrobots for automatic obstacle avoidance in the simulated blood vessel environment, an automatic obstacle avoidance algorithm based on the combination of improved Rapidly-exploring Random Trees (RRT) algorithm and improved artificial potential field (APF) algorithm is proposed. The improved RRT algorithm is used to plan a global path first, and the redundant nodes on the global path are selected by using conditional constraints and key points, which is prepared to optimize the security and length of the path. Then the global path is segmented according to the key nodes, and each path is optimized with the improved APF algorithm to enhance the real time performance. Comparative simulations and experiments show that the fusion algorithm realizes the optimization of path length, safety, and local minimum problem, and can automatically avoid static and dynamic obstacles in the simulated vascular environment.

The opening workspace control strategy of a novel manipulator-driven emission source microscopy system

Emission source microscopy (ESM) technique can be utilized for localization of electromagnetic interference sources in the electronic systems, but its accuracy is limited by the typical planar scanning mode. In order to increase the accuracy, this paper presents a novel cylinder-aperture ESM measurement system driven by 6-DOF manipulator, and investigated the control strategy to generate the maximum-area aperture and optimized scanning trajectory. Based on the multiple constraints of the cylinder-aperture ESM measurement, we proposes analyzing the impact of the constraints by steps. This can obtain the analytical solution of the manipulator workspace and support solving the maximum aperture area. Besides, a modified RRT*(Rapidly-exploring Random Trees) algorithm is addressed to optimize the manipulator trajectory. The simulation and tests have proven that this algorithm could obviously reduce the joint mutation and cumulative tracking error. In the experimental section, the near-field scanning (NFS) tests, planar-aperture ESM measurement and proposed cylinder-aperture ESM measurement were conducted to measure one benchmark emission source. The results have demonstrated that the cylinder-aperture ESM measurement has the best convergences on the radiation pattern of the emission source.

A multi-objective path planning method for the wave glider in the complex marine environment

Aiming to energy-efficient, short path, and safety, an online dynamic multi-objective path planning method for the wave glider (WG) is proposed to make the WG operate efficiently in the uncertain marine environment. In this paper, a novel kinematic constrained safe rapidly-exploring random tree (KS-RRT*) path planning algorithm is developed, which is subject to the safe area boundaries and kinematics. Biased random sampling method is introduced which the kinematic constraints is used as heuristic function and the KS-RRT* can reduce the extended area of random points. And a path safe (PS) scheme is developed, which can ensure that the WG safely passes through the planned path. In addition, energy cost, path length, and safety metric (SM) of each feasible trajectory are obtained by the KS-RRT*, the technique for order preference by similarity to ideal situation (TOPSIS) is utilized to solve multi-objective path optimization problem, and the final path is smoothed by the B-spline algorithm. The results of simulations show that the proposed KS-RRT* is more suitable for the WG's path planning than traditional path planning algorithm and the proposed multi-objective path optimization method can solve the path planning problem of the WG in complex marine environments.

A novel model predictive artificial potential field based ship motion planning method considering COLREGs for complex encounter scenarios

Ship motion planning is a core issue of autonomous navigation for maritime autonomous surface ships (MASS). This paper proposes a novel model predictive artificial potential field (MPAPF) motion planning method for complex encounter scenarios considering collision avoidance rules. A new ship domain is established, in which a closed interval potential field function is designed to represent the inviolable properties of the ship domain. A Nomoto model with a predefined speed during motion planning is adopted to generate followable paths conforming to the ship kinematics. To solve the local optima problem of traditional artificial potential field (APF) method and guarantee the collision avoidance safety in complex encounter scenarios, a motion planning method based on model predictive strategy and artificial potential field, i.e., MPAPF, is proposed. In this method, the ship motion planning problem is transformed to a non-linear optimization problem with multiple constraints including maneuverability, navigation rules, navigable waterway, etc. Simulation results from 4 case studies show that the proposed MPAPF algorithm can solve the problems above and generate feasible motion paths to avoid ship collision in complex encounter scenarios compared to variants of APF, A-star and rapidly-exploring random trees (RRT).