A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking
01 Jan 2003-pp 403-417
TL;DR: Experimental results show that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multi-robot problems in geometrically complex environments.
Abstract: This paper describes a new probabilistic roadmap (PRM) path planner that is: (1) single-query — instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations as seeds to explore as little space as possible; (2) bidirectional — it explores the robot’s free space by concurrently building a roadmap made of two trees rooted at the query configurations; (3) adaptive — it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision — it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results show that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multi-robot problems in geometrically complex environments.
Citations
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01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
6,340 citations
Cites methods from "A Single-Query Bi-Directional Proba..."
...This method [470, 847] generates samples in a way that attempts to explore new parts of the space....
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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
TL;DR: The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.
Abstract: This paper describes a real-time motion planning algorithm, based on the rapidly-exploring random tree (RRT) approach, applicable to autonomous vehicles operating in an urban environment. Extensions to the standard RRT are predominantly motivated by: 1) the need to generate dynamically feasible plans in real-time; 2) safety requirements; 3) the constraints dictated by the uncertain operating (urban) environment. The primary novelty is in the use of closed-loop prediction in the framework of RRT. The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.
802 citations
Additional excerpts
...The primary difference from previous work [29], [30] is that the lazy check in this paper is about rechecking of the constraints for previously feasible edges, whereas the pre-...
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01 Aug 2004
TL;DR: There is both experimental and theoretical evidence that some forms of grid search are superior to the original PRM, and all of the deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate.
Abstract: We present, implement, and analyze a spectrum of closely-related planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasi-Monte Carlo sampling literature, we have developed deterministic variants of the PRM that use low-discrepancy and low-dispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the optimal-dispersion Sukharev grid, which can be considered as a kind of lattice-based roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original PRM and the recent Lazy PRM. This even includes searching using a grid with subsampled collision checking. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that some forms of grid search are superior to the original PRM.
439 citations
Cites background or methods from "A Single-Query Bi-Directional Proba..."
...…search, such as randomized potential fields (Barraquand and Latombe 1990), multiple heuristics (Kondo 1991),Ariadne’s clew (Mazer et al. 1992; Mazer, Ahuactzin, and Bessière 1998), RRTs (LaValle and Kuffner 2001), or the planner in Hsu, Latombe, and Motwani (1999) and Sánchez and Latombe (2001)....
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...Incremental searching methods, such as Ariadne’s clew (Mazer et al. 1992), bidirectional RRTs (LaValle and Kuffner 2001), or the planners in Hsu, Latombe, and Motwani (1999) and Sánchez and Latombe (2001), can be considered as alternatives toA∗ search in any roadmap approach....
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TL;DR: Experimental results with research prototype rovers demonstrate that the planner allows the entire envelope of vehicle maneuverability in rough terrain, while featuring real-time performance.
Abstract: We present an approach to the problem of differentially constrained mobile robot motion planning in arbitrary cost fields The approach is based on deterministic search in a specially discretized state space We compute a set of elementary motions that connects each discrete state value to a set of its reachable neighbors via feasible motions Thus, this set of motions induces a connected search graph The motions are carefully designed to terminate at discrete states, whose dimensions include relevant state variables (eg, position, heading, curvature, and velocity) The discrete states, and thus the motions, repeat at regular intervals, forming a lattice We ensure that all paths in the graph encode feasible motions via the imposition of continuity constraints on state variables at graph vertices and compliance of the graph edges with a differential equation comprising the vehicle model The resulting state lattice permits fast full configuration space cost evaluation and collision detection Experimental results with research prototype rovers demonstrate that the planner allows us to exploit the entire envelope of vehicle maneuverability in rough terrain, while featuring real-time performance © 2009 Wiley Periodicals, Inc
374 citations
Cites background from "A Single-Query Bi-Directional Proba..."
...Recent works have also discussed “lazy” variants of the roadmap planning methods that avoid collision checking during the roadmap construction phase (e.g., Bohlin, 2001; Bohlin & Kavraki, 2000; Branicky et al., 2001; Sanchez & Latombe, 2001, 2002 )....
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References
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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
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
"A Single-Query Bi-Directional Proba..." refers methods in this paper
..., nonholonomic, stability, dynamic, and visibility constraints) [4, 5]....
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...This planner is similar to those presented in [4, 7]....
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01 Aug 1996
TL;DR: A data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion that can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates are presented.
Abstract: We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR
2,278 citations
"A Single-Query Bi-Directional Proba..." refers background or methods in this paper
..., some checkers pre-compute a hierarchy of bounding volumes for every object in an environment [8, 9, 10]....
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...The pre-computation time of PQP is not included in the running times given below....
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...PQP pre-computes a bounding hierarchy of oriented-bounding boxes for each object....
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...PQP was made available to us by S. Gottschalk, M. Lin, and D. Manocha from the Computer Science Dept. at the University of NorthCarolina in Chapel Hill....
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...For example, we could use PQP for computing distances rather than as a pure collision checker....
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24 Apr 2000
TL;DR: The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner.
Abstract: Describes an approach to probabilistic roadmap planners (PRMs). The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner. Our algorithm builds a roadmap in the configuration space, whose nodes are the user-defined initial and goal configurations and a number of randomly generated nodes. Neighboring nodes are connected by edges representing paths between the nodes. In contrast with PRMs, our planner initially assumes that all nodes and edges in the roadmap are collision-free, and searches the roadmap at hand for a shortest path between the initial and the goal node. The nodes and edges along the path are then checked for collision. If a collision with the obstacles occurs, the corresponding nodes and edges are removed from the roadmap. Our planner either finds a new shortest path, or first updates the roadmap with new nodes and edges, and then searches for a shortest path. The above process is repeated until a collision-free path is returned. Lazy PRM is tailored to efficiently answer single planning queries, but can also be used for multiple queries. Experimental results presented in the paper show that our lazy method is very efficient in practice.
874 citations
"A Single-Query Bi-Directional Proba..." refers background in this paper
...The planner in [13] distributes points uniformly at random in configuration space....
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...We think that lazy collision checking is a promising approach, but that its potential has only been partially exploited in [13]....
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...As noticed in [13], these collision tests cannot be avoided....
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TL;DR: A detailed analysis of the planner's convergence rate shows that, if the state×time space satisfies a geometric property called expansiveness, then a slightly idealized version of the implemented planner is guaranteed to find a trajectory when one exists, with probability quickly converging to 1, as the number of milestones increases.
Abstract: This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot's state × time space by picking control inputs at random and integrating its equations of motion. The result is a probabilistic roadmap of sampled state ×time points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap; instead, for each planning query, it generates a new roadmap to connect an initial and a goal state×time point. The paper presents a detailed analysis of the planner's convergence rate. It shows that, if the state×time space satisfies a geometric property called expansiveness, then a slightly idealized version of our implemented planner is guaranteed to find a trajectory when one exists, with probability quickly converg...
815 citations