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228
Robot Motion Planning: A Distributed Representation Approach
, 1991
"... We propose a new approach to robot path planning that consists of building and searching a graph connecting the local minima of a potential function defined over the robot’s configuration space. A planner based on this approach has been implemented. This planner is considerably faster than previous ..."
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Cited by 402 (26 self)
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We propose a new approach to robot path planning that consists of building and searching a graph connecting the local minima of a potential function defined over the robot’s configuration space. A planner based on this approach has been implemented. This planner is considerably faster than previous path planners and solves problems for robots with many more degrees of freedom (DOFs). The power of the planner derives both from the "good " properties of the potential function and from the efficiency of the techniques used to escape the local minima of this function. The most powerful of these techniques is a Monte Carlo technique that escapes local minima by executing Brownian motions. The overall approach is made possible by the systematic use of distributed representations (bitmaps) for the robot’s work space and configuration space. We have experimented with the planner using several computersimulated robots, including rigid objects with 3 DOFs (in 2D work space) and 6 DOFs (in 3D work space) and manipulator arms with 8, 10, and 31 DOFs (in 2D and 3D work spaces). Some of the most significant experiments are reported in this article.
The NPcompleteness column: an ongoing guide
 JOURNAL OF ALGORITHMS
, 1987
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freem ..."
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Cited by 239 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freeman & Co., New York, 1979 (hereinafter referred to as "[G&J]"; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Pathplanning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape
 ALGORITHMICA
, 1987
"... The problem of path planning for an automaton moving in a twodimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is impos ..."
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Cited by 190 (3 self)
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The problem of path planning for an automaton moving in a twodimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's "'tactile sensor. " This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worstcase lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worstcase upper bounds on the length of generated paths are produced.
On the Relationship Between Classical Grid Search and Probabilistic Roadmaps
"... We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that use ..."
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Cited by 134 (10 self)
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We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that use lowdiscrepancy and lowdispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the optimaldispersion Sukharev grid, which can be considered as a kind of latticebased 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.
Efficient Collision Detection for Animation and Robotics
, 1993
"... We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two ..."
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Cited by 125 (17 self)
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We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...
The bridge test for sampling narrow passages with probabilistic roadmap planners
 IN PROC. IEEE INT. CONF. ON ROBOTICS & AUTOMATION
, 2003
"... Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but narrow passages in a robot’s configuration space create significant difficulty for PRM planners. This paper presents a hybrid sampling strategy in the PRM framework for finding pat ..."
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Cited by 120 (6 self)
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Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but narrow passages in a robot’s configuration space create significant difficulty for PRM planners. This paper presents a hybrid sampling strategy in the PRM framework for finding paths through narrow passages. A key ingredient of the new strategy is the bridge test, which boosts the sampling density inside narrow passages. The bridge test relies on simple tests of local geometry and can be implemented efficiently in highdimensional configuration spaces. The strengths of the bridge test and uniform sampling complement each other naturally and are combined to generate the final hybrid sampling strategy. Our planner was tested on point robots and articulated robots in planar workspaces. Preliminary experiments show that the hybrid sampling strategy enables relatively small roadmaps to reliably capture the connectivity of configuration spaces with difficult narrow passages.
Towards Exact Geometric Computation
, 1994
"... Exact computation is assumed in most algorithms in computational geometry. In practice, implementors perform computation in some fixedprecision model, usually the machine floatingpoint arithmetic. Such implementations have many wellknown problems, here informally called "robustness issues&quo ..."
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Cited by 96 (6 self)
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Exact computation is assumed in most algorithms in computational geometry. In practice, implementors perform computation in some fixedprecision model, usually the machine floatingpoint arithmetic. Such implementations have many wellknown problems, here informally called "robustness issues". To reconcile theory and practice, authors have suggested that theoretical algorithms ought to be redesigned to become robust under fixedprecision arithmetic. We suggest that in many cases, implementors should make robustness a nonissue by computing exactly. The advantages of exact computation are too many to ignore. Many of the presumed difficulties of exact computation are partly surmountable and partly inherent with the robustness goal. This paper formulates the theoretical framework for exact computation based on algebraic numbers. We then examine the practical support needed to make the exact approach a viable alternative. It turns out that the exact computation paradigm encomp...
A Combinatorial Approach to Planar Noncolliding Robot Arm Motion Planning
 In Proc. 41st FOCS
, 2000
"... We propose a combinatorial approach to plan noncolliding motions for a planar robot arm. The approach works even with certain types of movable polygonal obstacles and flexible polygonal fences. This yields a very efficient deterministic algorithm for a category of robot arm motion planning problems ..."
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Cited by 95 (15 self)
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We propose a combinatorial approach to plan noncolliding motions for a planar robot arm. The approach works even with certain types of movable polygonal obstacles and flexible polygonal fences. This yields a very efficient deterministic algorithm for a category of robot arm motion planning problems with many degrees of freedom, for which the known general roadmap techniques have exponential complexity. The main result is an efficient algorithm for convexifying a simple (open or closed) polygonal path with rigid nonintersecting motions in the plane. It works by computing in O(n&sup2;) time a monotone mechanism with one degree of freedom, whose motion is controlled by the rotation of a single edge around one of its endpoints. As it moves, all the interdistances between pairs of points not joined by a bar are nondecreasing, thus guaranteeing noncollision. At most O(n&sup2;) such motions suffice to reach a convex configuration of the original linkage. At each step, recomputing the next motion from ...