A well-known weakness of the probabilistic path planners is the so-called narrow passage problem, where a region with a relatively low probability of being sampled must be explored to find a solution path. Many strategies have been proposed to alleviate this problem, most of them based on biasing the sampling distribution. When kinematic constraints appear in the problem, the configuration space typically becomes a non-parametrizable, implicit manifold. Unfortunately, this invalidates most of the existing sampling bias approaches, which rely on an explicit parametrization of the space to explore. In this paper, we propose and evaluate three novel strategies to bias the sampling under the presence of narrow passages in kinematically-constrained systems.
The information of the collisions detected while extending an Rapidly-exploring Random Tree (RRT) can be leveraged to bias the sampling @cite_28 . For instance, using this information the dynamic domain of an RRT node can be defined, i.e, the part of the configuration space where it is worth to extend the tree from that node @cite_17 @cite_14 . As we will see, this approach can be adapted to the kinematically-constrained case defining the dynamic domain in the ambient space rather than in the configuration space.
@cite_28 @cite_14 @cite_17
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Abstract The sampling-based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been proposed that ensures asymptotic optimality. Subsequently its bidirectional version has also been introduced in the literature known as Bidirectional-RRT* (B-RRT*). We introduce a new variant called Intelligent Bidirectional-RRT* (IB-RRT*) which is an improved variant of the optimal RRT* and bidirectional version of RRT* (B-RRT*) algorithms and is specially designed for complex cluttered environments. IB-RRT* utilizes the bidirectional trees approach and introduces intelligent sample insertion heuristic for fast convergence to the optimal path solution using uniform sampling heuristics. The proposed algorithm is evaluated theoretically and experimental results are presented that compares IB-RRT* with RRT* and B-RRT*. Moreover, experimental results demonstrate the superior efficiency of IB-RRT* in comparison with RRT* and B-RRT in complex cluttered environments. Rapidly-exploring Random Trees (RRTs) are effective for a wide range of applications ranging from kinodynamic planning to motion planning under uncertainty. However, RRTs are not as efficient when exploring heterogeneous environments and do not adapt to the space. For example, in difficult areas an expensive RRT growth method might be appropriate, while in open areas inexpensive growth methods should be chosen. In this paper, we present a novel algorithm, Adaptive RRT, that adapts RRT growth to the current exploration area using a two level growth selection mechanism. At the first level, we select groups of expansion methods according to the visibility of the node being expanded. Second, we use a cost-sensitive learning approach to select a sampler from the group of expansion methods chosen. Also, we propose a novel definition of visibility for RRT nodes which can be computed in an online manner and used by Adaptive RRT to select an appropriate expansion method. We present the algorithm and experimental analysis on a broad range of problems showing not only its adaptability, but efficiency gains achieved by adapting exploration methods appropriately. The situation arising in path planning under kinematic constraints, where the valid configurations define a manifold embedded in the joint ambient space, can be seen as a limit case of the well-known narrow corridor problem. With kinematic constraints, the probability of obtaining a valid configuration by sampling in the joint ambient space is not low but null, which complicates the direct application of sampling-based path planners. This paper presents the AtlasRRT algorithm, which is a planner especially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize a manifold and to coordinate the charts, forming an atlas that fully covers it. AtlasRRT simultaneously builds an atlas and a bidirectional rapidly exploring random tree (RRT), using the atlas to sample configurations and to grow the branches of the RRTs, and the RRTs to devise directions of expansion for the atlas. The efficiency of AtlasRRT is evaluated in several benchmarks involving high-dimensional manifolds embedded in large ambient spaces. The results show that the combined use of the atlas and the RRTs produces a more rapid exploration of the configuration space manifolds than existing approaches. The Rapidly Exploring Random Tree Star (RRT*) is an extension of the Rapidly Exploring Random Tree path finding algorithm. RRT* guarantees an optimal, collision free path solution but is limited by slow convergence rates and inefficient memory utilization. This paper presents APGD-RRT*, a variant of RRT* which utilizes Artificial Potential Fields to improve RRT* performance, providing relatively better convergence rates. Simulation results under different environments between the proposed APGD-RRT* and RRT* algorithms demonstrate this marked improvement under various test environments. Rapidly-exploring random trees (RRTs) are pop- ular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sam- pled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on complete- ness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show exper- imentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem. Rapidly-exploring Random Tree star (RRT*) is a recently proposed extension of Rapidly-exploring Random Tree (RRT) algorithm that provides a collision-free, asymptotically optimal path regardless of obstacles geometry in a given environment. However, one of the limitation in the RRT* algorithm is slow convergence to optimal path solution. As a result it consumes high memory as well as time due to the large number of iterations utilised in achieving optimal path solution. To overcome these limitations, we propose the potential function based-RRT* that incorporates the artificial potential field algorithm in RRT*. The proposed algorithm allows a considerable decrease in the number of iterations and thus leads to more efficient memory utilization and an accelerated convergence rate. In order to illustrate the usefulness of the proposed algorithm in terms of space execution and convergence rate, this paper presents rigorous simulation based comparisons between the proposed techniques and RRT* under different environmental conditions. Moreover, both algorithms are also tested and compared under non-holonomic differential constraints. During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a non-optimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT∗, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT∗ algorithms is asymptotically within a constant factor of that required by RRT. Abstract Rapidly-exploring Random Tree star (RRT*) has recently gained immense popularity in the motion planning community as it provides a probabilistically complete and asymptotically optimal solution without requiring the complete information of the obstacle space. In spite of all of its advantages, RRT* converges to optimal solution very slowly. Hence to improve the convergence rate, its bidirectional variants were introduced, the Bi-directional RRT* (B-RRT*) and Intelligent Bi-directional RRT* (IB-RRT*). However, as both variants perform pure exploration, they tend to suffer in highly cluttered environments. In order to overcome these limitations we introduce a new concept of potentially guided bidirectional trees in our proposed Potentially Guided Intelligent Bi-directional RRT* (PIB-RRT*) and Potentially Guided Bi-directional RRT* (PB-RRT*). The proposed algorithms greatly improve the convergence rate and have a more efficient memory utilization. Theoretical and experimental evaluation of the proposed algorithms have been made and compared to the latest state of the art motion planning algorithms under different challenging environmental conditions and have proven their remarkable improvement in efficiency and convergence rate. In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm FMT*. The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a 'lazy' dynamic programming recursion on a predetermined number of probabilistically drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms chiefly RRT and multiple-query algorithms chiefly PRM, and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds-the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order On −1 d+? , where n is the number of sampled points, d is the dimension of the configuration space, and ? is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive. We present ( RRT^ X ), the first asymptotically optimal sampling-based motion planning algorithm for real-time navigation in dynamic environments (containing obstacles that unpredictably appear, disappear, and move). Whenever obstacle changes are observed, e.g., by onboard sensors, a graph rewiring cascade quickly updates the search-graph and repairs its shortest-path -to-goal subtree. Both graph and tree are built directly in the robot’s state space, respect the kinematics of the robot, and continue to improve during navigation. ( RRT^ X ) is also competitive in static environments—where it has the same amortized per iteration runtime as RRT and RRT* ( ( n ) ) and is faster than RRT# ( ( ^2 n ) ). In order to achieve (O ( n ) ) iteration time, each node maintains a set of (O ( n ) ) expected neighbors, and the search graph maintains ( )-consistency for a predefined ( ). Kinodynamic planning algorithms like Rapidly-Exploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, nonconvex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact that the conventional distance metric, Euclidean distance, does not take into account system dynamics and constraints when identifying which node in the existing tree is capable of producing children closest to a given point in state space. We show that an affine quadratic regulator (AQR) design can be used to approximate the exact minimum-time distance pseudometric at a reasonable computational cost. We demonstrate improved exploration of the state spaces of the double integrator and simple pendulum when using this pseudometric within the RRT framework, but this improvement drops off as systems' nonlinearity and complexity increase. Future work includes exploring methods for approximating the exact minimum-time distance pseudometric that can reason about dynamics with higher-order terms. Sampling based planners have become increasingly efficient in solving the problems of classical motion planning and its applications. In particular, techniques based on the rapidly-exploring random trees (RRTs) have generated highly successful single-query planners. Recently, a variant of this planner called dynamic-domain RRT was introduced by (2005). It relies on a new sampling scheme that improves the performance of the RRT approach on many motion planning problems. One of the drawbacks of this method is that it introduces a new parameter that requires careful tuning. In this paper we analyze the influence of this parameter and propose a new variant of the dynamic-domain RRT, which iteratively adapts the sampling domain for the Voronoi region of each node during the search process. This allows automatic tuning of the parameter and significantly increases the robustness of the algorithm. The resulting variant of the algorithm has been tested on several path planning problems. Rapidly-exploring Random Trees (RRTs) are widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swingup task, and on path planning for a nonholonomic car. The RRT* algorithm has efficiently extended Rapidly-exploring Random Trees (RRTs) to endow it with asymptotic optimality. We propose Goal-Rooted Feedback Motion Trees (GR-FMTs) that honor state input constraints and generate collision-free feedback policies. Given analytic solutions for optimal local steering, GR-FMTs obtain and realize safe, dynamically feasible, and asymptotically optimal trajectories toward goals. Second, for controllable linear systems with linear state input constraints, we propose a fast method for local steering, based on polynomial basis functions and segmentation. GR-FMTs with the method obtain and realize trajectories that are collision-free, dynamically feasible under constraints, and asymptotically optimal within a set we define. The formulation includes linear or quadratic programming of small sizes, where constraints are identified by root-finding in low or medium order of polynomials and added progressively. Incremental sampling-based motion planning algorithms such as the Rapidly-exploring Random Trees (RRTs) have been successful in efficiently solving computationally challenging motion planning problems involving complex dynamical systems. A recently proposed algorithm, called the RRT*, also provides asymptotic optimality guarantees, i.e., almost-sure convergence to optimal trajectories (which the RRT algorithm lacked) while maintaining the computational efficiency of the RRT algorithm. In this paper, time-optimal maneuvers for a high-speed off-road vehicle taking tight turns on a loose surface are studied using the RRT* algorithm. Our simulation results show that the aggressive skidding maneuver, usually called the trail-braking maneuver, naturally emerges from the RRT* algorithm as the minimum-time trajectory. Along the way, we extend the RRT* algorithm to handle complex dynamical systems, such as those that are described by nonlinear differential equations and involve high-dimensional state spaces, which may be of independent interest. We also exploit the RRT* as an anytime computation framework for nonlinear optimization problems. The Rapidly-exploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime” algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT* which (like the RRT) finds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT*, committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for real-time implementation. We evaluate the method using a series of Monte Carlo runs in a high-fidelity simulation environment, and compare the operation of the RRT and RRT* methods. We also demonstrate experimental results for an outdoor wheeled A new framework which adopts a rapidly-exploring random tree (RRT) path planner with a Gaussian process (GP) occupancy map is developed for the navigation and exploration of an unknown but cluttered environment. The GP map outputs the probability of occupancy given any selected query point in the continuous space and thus makes it possible to explore the full space when used in conjunction with a continuous path planner. Furthermore, the GP map-generated path is embedded with the probability of collision along the path which lends itself to obstacle avoidance. Finally, the GP map-building algorithm is extended to include an exploration mission considering the differential constraints of a rotary unmanned aerial vehicle and the limitation arising from the environment. Using mutual information as an information-theoretic measure, an informative path which reduces the uncertainty of the environment is generated. Simulation results show that GP map combined with RRT planner can achieve the 3D navigation and e... We present a replanning algorithm for repairing rapidly-exploring random trees when changes are made to the configuration space. Instead of abandoning the current RRT, our algorithm efficiently removes just the newly-invalid parts and maintains the rest. It then grows the resulting tree until a new solution is found. We use this algorithm to create a probabilistic analog to the widely-used D* family of deterministic algorithms, and demonstrate its effectiveness in a multirobot planning domain Breiman (2001a,b) has recently developed an ensemble classification and regression approach that displayed outstanding performance with regard prediction error on a suite of benchmark datasets. As the base constituents of the ensemble are tree-structured predictors, and since each of these is constructed using an injection of randomness, the method is called ‘random forests’. That the exceptional performance is attained with seemingly only a single tuning parameter, to which sensitivity is minimal, makes the methodology all the more remarkable. The individual trees comprising the forest are all grown to maximal depth. While this helps with regard bias, there is the familiar tradeoff with variance. However, these variability concerns were potentially obscured because of an interesting feature of those benchmarking datasets extracted from the UCI machine learning repository for testing: all these datasets are hard to overfit using tree-structured methods. This raises issues about the scope of the repository. With this as motivation, and coupled with experience from boosting methods, we revisit the formulation of random forests and investigate prediction performance on real-world and simulated datasets for which maximally sized trees do overfit. These explorations reveal that gains can be realized by additional tuning to regulate tree size via limiting the number of splits and or the size of nodes for which splitting is allowed. Nonetheless, even in these settings, good performance for random forests can be attained by using larger (than default) primary tuning parameter values. Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories between an initial and terminal configuration in a robot configuration space. Current approaches have however either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently however not yet practical for higher dimensional configuration spaces. We propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories. We propose the Winding Augmented RRT and RRT* (WA-RRT RRT*) algorithms using which homotopy inequivalent trajectories can be found. We evaluate our approach in experiments with configuration spaces of planar linkages with 2–10 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms were able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension.