124 research outputs found

    Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic

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    Rapidly-exploring random trees (RRTs) are popular 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 sampled 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 completeness 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 experimentally 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.Comment: 8 pages, 11 figures. Videos available at https://www.youtube.com/watch?v=d7dX5MvDYTc and https://www.youtube.com/watch?v=nsl-5MZfwu

    Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

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    In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in R2\mathbb{R}^2 and R8\mathbb{R}^8 and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at http://www.youtube.com/watch?v=TQIoCC48gp

    RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning

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    Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the shortest path between any two points, which would normally be a straight line path in the configuration space. Subsequently, we increase the power of sRMPD by using it as a "connect" subroutine call in a higher-level sampling-based algorithm mRMPD that is inspired by multi-RRT. As a consequence, mRMPD spawns a larger number of space exploring trees in regions of the configuration space that are characterized by a higher density of obstacles. The overall effect is a hybrid tree growing strategy with a trade-off between random exploration as made possible by multi-RRT based logic and immediate exploitation of opportunities to connect two states as made possible by sRMPD. The mRMPD planner can be biased with regard to this trade-off for solving different kinds of planning problems efficiently. Based on the test cases we have run, our experiments show that mRMPD can reduce planning time by up to 80% compared to basic RRT

    Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

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    Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16 Figure

    On the performance of sampling-based optimal motion planners

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    Sampling based algorithms provide efficient methods of solving robot motion planning problem. The advantage of these approaches is the ease of their implementation and their computational efficiency. These algorithms are probabilistically complete i.e. they will find a solution if one exists, given a suitable run time. The drawback of sampling based planners is that there is no guarantee of the quality of their solutions. In fact, it was proven that their probability of reaching an optimal solution approaches zero. A breakthrough in sampling planning was the proposal of optimal based sampling planners. Current optimal planners are characterized with asymptotic optimality i.e. they reach an optimal solutions as time approaches infinity. Motivated by the slow convergence of optimal planners, post-processing and heuristic approach have been suggested. Due to the nature of the sampling based planners, their implementation requires tuning and selection of a large number of parameters that are often overlooked. This paper presents the performance study of an optimal planner under different parameters and heuristics. We also propose a modification in the algorithm to improve the convergence rate towards an optimal solution
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