Probabilistic roadmaps for path planning in high-dimensional configuration spaces
01 Aug 1996-Vol. 12, Iss: 4, pp 566-580
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).
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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
24 Apr 2000
TL;DR: A simple and efficient randomized algorithm is presented for solving single-query path planning problems in high-dimensional configuration spaces by incrementally building two rapidly-exploring random trees rooted at the start and the goal configurations.
Abstract: A simple and efficient randomized algorithm is presented for solving single-query path planning problems in high-dimensional configuration spaces. The method works by incrementally building two rapidly-exploring random trees (RRTs) rooted at the start and the goal configurations. The trees each explore space around them and also advance towards each other through, the use of a simple greedy heuristic. Although originally designed to plan motions for a human arm (modeled as a 7-DOF kinematic chain) for the automatic graphic animation of collision-free grasping and manipulation tasks, the algorithm has been successfully applied to a variety of path planning problems. Computed examples include generating collision-free motions for rigid objects in 2D and 3D, and collision-free manipulation motions for a 6-DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is also presented.
3,102 citations
Cites methods from "Probabilistic roadmaps for path pla..."
...This limitation, lower-bound hardness results [24], and strong motivation to handle practical planning problems have stimulated the development and success of many path planning methods that use randomization (e.g., [1, 3, 4, 5, 7, 10, 11, 16, 15 , 17, 23, 26])....
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...The probabilistic roadmap approach was the first to address this problem [ 15 ]....
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...Randomized path planning algorithms have usually been designed for one of two contexts: singlequery planning, and multiple-query planning [ 15 ]....
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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 ...
2,993 citations
Cites background or methods from "Probabilistic roadmaps for path pla..."
...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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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•
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
TL;DR: A collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects that transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object.
Abstract: This paper describes a collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects. The algorithm transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object. A trajectory of this reference point which avoids all forbidden regions is free of collisions. Trajectories are found by searching a network which indicates, for each vertex in the transformed obstacles, which other vertices can be reached safely.
2,396 citations
TL;DR: In this article, the authors propose an approach based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object.
Abstract: This paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects. This problem arises in applications that require choosing how to arrange or how to move objects without collisions. The approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object. The configurations forbidden to this object, due to the presence of other objects, can then be characterized as regions in the configuration space, called configuration space obstacles. The paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra.
1,996 citations
01 Oct 1992
TL;DR: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented.
Abstract: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided. >
1,912 citations
"Probabilistic roadmaps for path pla..." refers background in this paper
...Local minima-free potential functions (also called navigation functions) have been defined in [6], [31], [ 46 ]....
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Book•
01 Jul 1990
TL;DR: Algorithms for computing constraints on the position of an object due to the presence of ther objects, which arises in applications that require choosing how to arrange or how to move objects without collisions are presented.
1,641 citations
"Probabilistic roadmaps for path pla..." refers methods in this paper
...First use the algorithm in [ 37 ] to produce the vertices of the obstacles in the link’s C-space....
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...space (C-space [ 37 ]) of the robot is stored as an undirected graph R. The configurations are the nodes of R and the paths computed by the local planner are the edges of R. The learning phase is concluded by some postprocessing of R to improve its connectivity....
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