3,663 research outputs found

    Asymptotically near-optimal RRT for fast, high-quality, motion planning

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    We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little running-time overhead when compared to RRT

    An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

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    We study a path-planning problem amid a set O\mathcal{O} of obstacles in R2\mathbb{R}^2, in which we wish to compute a short path between two points while also maintaining a high clearance from O\mathcal{O}; the clearance of a point is its distance from a nearest obstacle in O\mathcal{O}. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let nn be the total number of obstacle vertices and let ε(0,1]\varepsilon \in (0,1]. Our algorithm computes in time O(n2ε2lognε)O(\frac{n^2}{\varepsilon ^2} \log \frac{n}{\varepsilon}) a path of total cost at most (1+ε)(1+\varepsilon) times the cost of the optimal path.Comment: A preliminary version of this work appear in the Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithm

    Efficient motion planning for problems lacking optimal substructure

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    We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in O((nBn)log(nBn)+nBm)O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right) time, where~nn and mm are the number of vertices and edges of the graph, respectively, and nBn_B is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm

    The Ariadne's Clew Algorithm

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    We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic environments - ones where obstacles may move. The Ariadne's clew algorithm comprises two sub-algorithms, called Search and Explore, applied in an interleaved manner. Explore builds a representation of the accessible space while Search looks for the target. Both are posed as optimization problems. We describe a real implementation of the algorithm to plan paths for a six degrees of freedom arm in a dynamic environment where another six degrees of freedom arm is used as a moving obstacle. Experimental results show that a path is found in about one second without any pre-processing

    06421 Abstracts Collection -- Robot Navigation

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    From 15.10.06 to 20.10.06, the Dagstuhl Seminar 06421 ``Robot Navigation\u27\u27generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    CAT-RRT: Motion Planning that Admits Contact One Link at a Time

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    Current motion planning approaches rely on binary collision checking to evaluate the validity of a state and thereby dictate where the robot is allowed to move. This approach leaves little room for robots to engage in contact with an object, as is often necessary when operating in densely cluttered spaces. In this work, we propose an alternative method that considers contact states as high-cost states that the robot should avoid but can traverse if necessary to complete a task. More specifically, we introduce Contact Admissible Transition-based Rapidly exploring Random Trees (CAT-RRT), a planner that uses a novel per-link cost heuristic to find a path by traversing high-cost obstacle regions. Through extensive testing, we find that state-of-the-art optimization planners tend to over-explore low-cost states, which leads to slow and inefficient convergence to contact regions. Conversely, CAT-RRT searches both low and high-cost regions simultaneously with an adaptive thresholding mechanism carried out at each robot link. This leads to paths with a balance between efficiency, path length, and contact cost
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