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16
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 337 (21 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Path Planning Using Lazy PRM
 In IEEE Int. Conf. Robot. & Autom
, 2000
"... This paper describes a new 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 configu ..."
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Cited by 247 (18 self)
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This paper describes a new 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 userdefined 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 collisionfree, 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 collisionfree path is returned.
QuasiRandomized Path Planning
 In Proc. IEEE Int’l Conf. on Robotics and Automation
, 2001
"... We propose the use of quasirandom sampling techniques for path planning in highdimensional conguration spaces. Following similar trends from related numerical computation elds, we show several advantages oered by these techniques in comparison to random sampling. Our ideas are evaluated in the con ..."
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Cited by 78 (8 self)
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We propose the use of quasirandom sampling techniques for path planning in highdimensional conguration spaces. Following similar trends from related numerical computation elds, we show several advantages oered by these techniques in comparison to random sampling. Our ideas are evaluated in the context of the probabilistic roadmap (PRM) framework. Two quasirandom variants of PRMbased planners are proposed: 1) a classical PRM with quasirandom sampling, and 2) a quasirandom LazyPRM. Both have been implemented, and are shown through experiments to oer some performance advantages in comparison to their randomized counterparts. 1 Introduction Over two decades of path planning research have led to two primary trends. In the 1980s, deterministic approaches provided both elegant, complete algorithms for solving the problem, and also useful approximate or incomplete algorithms. The curse of dimensionality due to highdimensional conguration spaces motivated researchers from the 199...
RRTConnect: An efficient approach to singlequery path planning
 Proc. IEEE Int’l Conf. on Robotics and Automation
, 2000
"... A simple and efficient randomized algorithm is presented for solving singlequery path planning problems in highdimensional configuration spaces. The method works by incrementally building two Rapidlyexploring Random Trees (RRTs) rooted at the start and the goal configurations. The trees each expl ..."
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Cited by 37 (0 self)
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A simple and efficient randomized algorithm is presented for solving singlequery path planning problems in highdimensional configuration spaces. The method works by incrementally building two Rapidlyexploring 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 7DOF kinematic chain) for the automatic graphic animation of collisionfree grasping and manipulation tasks, the algorithm has been successfully applied to a variety of path planning problems. Computed examples include generating collisionfree motions for rigid objects in 2D and 3D, and collisionfree manipulation motions for a 6DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is also presented.
Exact Collision Checking Of Robot Paths
, 2002
"... This paper describes a new efficient collision checker to test single straightline segments in cspace, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multirobot systems. Such planners ..."
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Cited by 34 (6 self)
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This paper describes a new efficient collision checker to test single straightline segments in cspace, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multirobot systems. Such planners spend most of their time checking local paths between randomly sampled configurations for collision. While commonly used approaches test intermediate configurations on a segment at a prespecified resolution, the checker presented in this paper is exact, i.e., it cannot fail to find an existing collision, even when some robot links and obstacles are very thin. Its efficiency relies on its core algorithm, which dynamically adjusts the required resolution by relating the distances between objects in the workspace to the maximum lengths of the paths traced out by points on these objects. The checker's efficiency is further increased by several additional techniques presented in this paper, which adequately approximate distances between objects and lengths of travelled paths in workspace, and order collision tests to reveal collisions as early as possible. The new checker has been extensively tested, first on segments randomly generated in cspace, next as part of an existing PRM planner, and finally as part of a path smoother/optimizer. These experiments show that the checker is faster than a resolutionbased approach (with suitable resolution), with the enormous advantage that it never returns an incorrect answer. The checker also admits a number of straightforward extensions. For example, it can monitor a minimum workspace distance between each robot link and other objects (e.g., obstacles, links of other robots).
An Adaptive Framework for `Single Shot' Motion Planning
 In Proceedings of the IEEE International Conference on Robotics and Automation
, 1999
"... This paper proposes an adaptive framework for single shot motion planning, i.e., planning without preprocessing. This framework can be used in any situation, and in particular, is suitable for crowded environments in which the robot's free Cspace has narrow corridors such as maintainability st ..."
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Cited by 23 (2 self)
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This paper proposes an adaptive framework for single shot motion planning, i.e., planning without preprocessing. This framework can be used in any situation, and in particular, is suitable for crowded environments in which the robot's free Cspace has narrow corridors such as maintainability studies in complex 3D CAD models. Our strategy is to adaptively select a planner whose strengths match the current situation, and then, online, switch to a different planner when circumstances change. This requires techniques to evaluate the characteristics of the current query, and a set of planners which are characterized so that we can match the query with the best planner for it. Our experimental results in complex 3D environments show that our strategy solves queries that none of the planners could solve on their own.
Deterministic vs. Probabilistic Roadmaps
, 2002
"... Within the popular probabilistic roadmap (PRM) framework for motion planning, we challenge the use of randomization. By applying quasirandom sampling techniques, we illustrate both experimental and theoretical advantages of using deterministic samples. Two quasirandom variants of PRMbased planner ..."
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Cited by 9 (2 self)
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Within the popular probabilistic roadmap (PRM) framework for motion planning, we challenge the use of randomization. By applying quasirandom sampling techniques, we illustrate both experimental and theoretical advantages of using deterministic samples. Two quasirandom variants of PRMbased planners are proposed: 1) a classical PRM with quasirandom sampling, and 2) a quasirandom latticebased Lazy roadmap. Both have been implemented, and are shown through experiments to oer some performance advantages in comparison to their randomized counterparts. Furthermore, our theoretical analysis shows that our approach leads to deterministic resolution completeness. We obtain the best possible asymptotic convergence rate, which is shown to be superior to that obtained by random sampling.
Optimization Techniques for Probabilistic Roadmaps
, 2000
"... Recently, a new class of randomized path planning methods, known as Probabilistic Roadmap Methods (PRMs) have shown great potential for solving complicated highdimensional problems. PRMs use randomization (usually during preprocessing) to construct a graph (a roadmap) of representative paths in the ..."
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Cited by 7 (1 self)
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Recently, a new class of randomized path planning methods, known as Probabilistic Roadmap Methods (PRMs) have shown great potential for solving complicated highdimensional problems. PRMs use randomization (usually during preprocessing) to construct a graph (a roadmap) of representative paths in the robot's con guration space. Vertices correspond to collisionfree con gurations of the robot. An edge exists between two vertices if a path between the two corresponding con gurations can be found by a local planning method. PRMs solve many high degree of freedom (dof) motion planning problems. Unfortunately, for some problems running times may still be unacceptably large and solutions suboptimal. We provide speed and quality optimization strategies applicable in cluttered 3dimensional workspaces....
Using Randomization to Find and Optimize Feasible Trajectories for Nonlinear Systems
 Proc. Annual Allerton Conference on Communications, Control, Computing
, 2000
"... Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our ..."
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Cited by 6 (0 self)
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Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our current planning results for two challenging sets of nonlinear systems: 1) the determination of automobile trajectories through obstacle courses; 2) the design of reentry trajectories for a reusable launch vehicle model based on the NASA X33 prototype. We also briefly describe some early results on using randomization to optimize trajectories in the presence of state space constraints. 1
Robust Combination of Local Controllers
 Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI01
, 2001
"... Finding solutions to high dimensional Markov Decision Processes (MDPs) is a difficult problem, especially in the presence of uncertainty or if the actions and time measurements are continuous. Frequently this difficulty can be alleviated by the availability of problemspecific knowledge. For example ..."
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Cited by 5 (0 self)
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Finding solutions to high dimensional Markov Decision Processes (MDPs) is a difficult problem, especially in the presence of uncertainty or if the actions and time measurements are continuous. Frequently this difficulty can be alleviated by the availability of problemspecific knowledge. For example, it may be relatively easy to design controllers that are good locally, though having no global guarantees. We propose a nonparametric method to combine these local controllersto obtain globally good solutions. We apply this formulation to two types of problems: motion planning (stochastic shortest path problems) and discountedcost MDPs. For motion planning, we argue that only considering the expected cost of a pathmay be overly simplistic in the presence of uncertainty. We propose an alternative: finding the minimum cost path, subject to the constraint that the robot must reach the goal with high probability. For this problem, we prove that a polynomial number of samples is sufficient to obtain a high probability path. For discounted MDPs, we consider various problem formulations that explicitly deal with model uncertainty. We provide empirical evidence of the usefulness of these approaches using the control of a robot arm.