Randomized kinodynamic planning
01 May 2001-The International Journal of Robotics Research (SAGE Publications)-Vol. 20, Iss: 5, pp 378-400
TL;DR: In this paper, the authors presented the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design), where the task is to determine control inputs to drive a robot from an unknown position to an unknown target.
Abstract: This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ...
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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
Posted Content•
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
Cites background or methods from "Randomized kinodynamic planning"
...In the context of sampling-based motion planning algorithms, the importance of computing optimal solutions has been pointed out in early seminal papers (LaValle and Kuffner 2001)....
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...1996, 1998) and rapidly-exploring random trees (RRTs) (Kuffner and LaValle 2000; LaValle and Kuffner 2001; LaValle 2006)....
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...Avoiding such a representation is the main underlying idea leading to the development of sampling-based algorithms (Kavraki and Latombe 1994; Kavraki et al. 1996; LaValle and Kuffner 2001)....
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...In particular, RRTs have been shown to work effectively for systems with differential constraints and nonlinear dynamics (LaValle and Kuffner 2001; Frazzoli et al. 2002) as well as purely discrete or hybrid systems (Branicky et al. 2003)....
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...In particular, RRTs have been shown to work effectively for systems with differential constraints and nonlinear dynamics (LaValle and Kuffner 2001; Frazzoli et al. 2002) as well as purely discrete or hybrid systems (Branicky et al....
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Book•
20 May 2005
TL;DR: In this paper, the mathematical underpinnings of robot motion are discussed and a text that makes the low-level details of implementation to high-level algorithmic concepts is presented.
Abstract: A text that makes the mathematical underpinnings of robot motion accessible and relates low-level details of implementation to high-level algorithmic concepts. Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.
1,811 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
13 Jun 2016
TL;DR: In this article, the authors present a survey of the state of the art on planning and control algorithms with particular regard to the urban environment, along with a discussion of their effectiveness.
Abstract: Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.
1,437 citations
References
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Book•
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21 Oct 1957
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Abstract: From the Publisher:
An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls a rich lode of applications and research topics. 1957 edition. 37 figures.
14,187 citations
Book•
01 Jan 1990
TL;DR: This chapter discusses the configuration space of a Rigid Object, the challenges of dealing with uncertainty, and potential field methods for solving these problems.
Abstract: 1 Introduction and Overview.- 2 Configuration Space of a Rigid Object.- 3 Obstacles in Configuration Space.- 4 Roadmap Methods.- 5 Exact Cell Decomposition.- 6 Approximate Cell Decomposition.- 7 Potential Field Methods.- 8 Multiple Moving Objects.- 9 Kinematic Constraints.- 10 Dealing with Uncertainty.- 11 Movable Objects.- Prospects.- Appendix A Basic Mathematics.- Appendix B Computational Complexity.- Appendix C Graph Searching.- Appendix D Sweep-Line Algorithm.- References.
6,186 citations
01 Aug 1996
TL;DR: Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
Abstract: A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
4,977 citations
"Randomized kinodynamic planning" refers background or methods in this paper
...In the probabilistic roadmap approach (Amato and Wu 1996; Kavraki et al. 1996), a graph is constructed in the configuration space by generating random configurations and attempting to connect pairs of nearby configurations with a local planner that will connect pairs of configurations....
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...For the purpose of discussion, we choose two different techniques that have been successful in recent years: randomized potential fields (e.g., Barraquand and Latombe 1991b; Challou et al. 1995) and probabilistic roadmaps (e.g., Amato and Wu 1996; Kavraki et al. 1996)....
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23 May 1998
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Abstract: We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.
4,478 citations