2,664 research outputs found
Enhancing the Transition-based RRT to deal with complex cost spaces
The Transition-based RRT (T-RRT) algorithm enables to solve motion planning problems involving configuration spaces over which cost functions are defined, or cost spaces for short. T-RRT has been successfully applied to diverse problems in robotics and structural biology. In this paper, we aim at enhancing T-RRT to solve ever more difficult problems involving larger and more complex cost spaces. We compare several variants of T-RRT by evaluating them on various motion planning problems involving different types of cost functions and different levels of geometrical complexity. First, we explain why applying as such classical extensions of RRT to T-RRT is not helpful, both in a mono-directional and in a bidirectional context. Then, we propose an efficient Bidirectional T-RRT, based on a bidirectional scheme tailored to cost spaces. Finally, we illustrate the new possibilities offered by the Bidirectional T-RRT on an industrial inspection problem
Asymptotically Optimal Sampling-Based Motion Planning Methods
Motion planning is a fundamental problem in autonomous robotics that requires
finding a path to a specified goal that avoids obstacles and takes into account
a robot's limitations and constraints. It is often desirable for this path to
also optimize a cost function, such as path length.
Formal path-quality guarantees for continuously valued search spaces are an
active area of research interest. Recent results have proven that some
sampling-based planning methods probabilistically converge toward the optimal
solution as computational effort approaches infinity. This survey summarizes
the assumptions behind these popular asymptotically optimal techniques and
provides an introduction to the significant ongoing research on this topic.Comment: Posted with permission from the Annual Review of Control, Robotics,
and Autonomous Systems, Volume 4. Copyright 2021 by Annual Reviews,
https://www.annualreviews.org/. 25 pages. 2 figure
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
Researc
CVT-based 2D motion planning with maximal clearance
Maximal clearance is an important property that is highly desirable in multi-agent motion planning. However, it is also inherently difficult to attain. We propose a novel approach to achieve maximal clearance by exploiting the ability of evenly distributing a set of points by a centroidal Voronoi tessellation (CVT). We adapt the CVT framework to multi-agent motion planning by adding an extra time dimension and optimize the trajectories of the agents in the augmented domain. As an optimization framework, our method can work naturally on complex regions. We demonstrate the effectiveness of our algorithm in achieving maximal clearance in motion planning with some examples.published_or_final_versionThe 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, 9-13 May 2011. In Proceedings of the IEEE-ICRA, 2011, p. 2281-228
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