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Planning Algorithms
01 Jan 2006-
About: The article was published on 2006-01-01 and is currently open access. It has received 4417 citations till now. The article focuses on the topics: Kinodynamic planning & Probabilistic roadmap.
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TL;DR: In this paper, the authors studied the asymptotic behavior of the cost of the solution returned by stochastic sampling-based path planning algorithms as the number of samples increases.
Abstract: 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.
3,438 citations
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TL;DR: 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.
Abstract: 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.
2,210 citations
TL;DR: The open motion planning library is a new library for sampling-based motion planning, which contains implementations of many state-of-the-art planning algorithms, and it can be conveniently interfaced with other software components.
Abstract: The open motion planning library (OMPL) is a new library for sampling-based motion planning, which contains implementations of many state-of-the-art planning algorithms. The library is designed in a way that it allows the user to easily solve a variety of complex motion planning problems with minimal input. OMPL facilitates the addition of new motion planning algorithms, and it can be conveniently interfaced with other software components. A simple graphical user interface (GUI) built on top of the library, a number of tutorials, demos, and programming assignments are designed to teach students about sampling-based motion planning. The library is also available for use through Robot Operating System (ROS).
1,472 citations
09 Jun 2011
TL;DR: This paper presents a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace, and derives sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program.
Abstract: In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace In our formulation, each robot acts fully independently, and does not communicate with other robots Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace
1,464 citations
TL;DR: A review of motion planning techniques implemented in the intelligent vehicles literature, with a description of the technique used by research teams, their contributions in motion planning, and a comparison among these techniques is presented.
Abstract: Intelligent vehicles have increased their capabilities for highly and, even fully, automated driving under controlled environments. Scene information is received using onboard sensors and communication network systems, i.e., infrastructure and other vehicles. Considering the available information, different motion planning and control techniques have been implemented to autonomously driving on complex environments. The main goal is focused on executing strategies to improve safety, comfort, and energy optimization. However, research challenges such as navigation in urban dynamic environments with obstacle avoidance capabilities, i.e., vulnerable road users (VRU) and vehicles, and cooperative maneuvers among automated and semi-automated vehicles still need further efforts for a real environment implementation. This paper presents a review of motion planning techniques implemented in the intelligent vehicles literature. A description of the technique used by research teams, their contributions in motion planning, and a comparison among these techniques is also presented. Relevant works in the overtaking and obstacle avoidance maneuvers are presented, allowing the understanding of the gaps and challenges to be addressed in the next years. Finally, an overview of future research direction and applications is given.
1,162 citations