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21
On the probabilistic foundations of probabilistic roadmap planning
 In Proc. Int. Symp. on Robotics Research
, 2005
"... Probabilistic roadmap (PRM) planners [5, 16] solve apparently difficult motion planning problems where the robot’s configuration space C has dimensionality six or more, and the geometry of the robot and the obstacles is described by hundreds of thousands of triangles. While an algebraic planner woul ..."
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Cited by 61 (11 self)
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Probabilistic roadmap (PRM) planners [5, 16] solve apparently difficult motion planning problems where the robot’s configuration space C has dimensionality six or more, and the geometry of the robot and the obstacles is described by hundreds of thousands of triangles. While an algebraic planner would be overwhelmed by the high cost of computing an exact representation of the free space F, defined as the collisionfree subset of C, a PRM planner builds only an extremely simplified representation of F, called a probabilistic roadmap. This roadmap is a graph, whose nodes are configurations sampled from F with a suitable probability measure and whose edges are simple collisionfree paths, e.g., straightline segments, between the sampled configurations. PRM planners work surprisingly well in practice, but why? Previous work has partially addressed this question by identifying and formalizing properties of F that guarantee good performance for a PRM planner using the uniform sampling measure (e.g.,
Advanced Programming Techniques Applied to Cgal’s Arrangement Package
, 2007
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Multistep motion planning for freeclimbing robots
 in WAFR
, 2004
"... Abstract. This paper studies nongaited, multistep motion planning, to enable limbed robots to freeclimb vertical rock. The application of a multistep planner to a real freeclimbing robot is described. This planner processes each of the many underlying onestep motion queries using an incrementa ..."
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Cited by 36 (8 self)
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Abstract. This paper studies nongaited, multistep motion planning, to enable limbed robots to freeclimb vertical rock. The application of a multistep planner to a real freeclimbing robot is described. This planner processes each of the many underlying onestep motion queries using an incremental, samplebased technique. However, experimental results point toward a better approach, incorporating the ability to detect when onestep motions are infeasible (i.e., to prove disconnection). Current work on a general method for doing this, based on recent advances in computational real algebra, is also presented. 1
Highlevel filtering for arrangements of conic arcs
 In Proc. ESA 2002
, 2002
"... Abstract. Many computational geometry algorithms involve the construction and maintenance of planar arrangements of conic arcs. Implementing a general, robust arrangement package for conic arcs handles most practical cases of planar arrangements covered in literature. A possible approach for impleme ..."
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Cited by 36 (9 self)
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Abstract. Many computational geometry algorithms involve the construction and maintenance of planar arrangements of conic arcs. Implementing a general, robust arrangement package for conic arcs handles most practical cases of planar arrangements covered in literature. A possible approach for implementing robust geometric algorithms is to use exact algebraic number types — yet this may lead to a very slow, inefficient program. In this paper we suggest a simple technique for filtering the computations involved in the arrangement construction: when constructing an arrangement vertex, we keep track of the steps that lead to its construction and the equations we need to solve to obtain its coordinates. This construction history can be used for answering predicates very efficiently, compared to a naïve implementation with an exact number type. Furthermore, using this representation most arrangement vertices may be computed approximately at first and can be refined later on in cases of ambiguity. Since such cases are relatively rare, the resulting implementation is both efficient and robust. 1
Code flexibility and program efficiency by genericity: Improving cgal’s arrangements
 In Proc. 12th Annu. Euro. Sympos. Alg
, 2004
"... Abstract. Arrangements of planar curves are fundamental structures in computational geometry. We describe the recent developments in the arrangement package of Cgal, the Computational Geometry Algorithms Library, making it easier to use, to extend and to adapt to a variety of applications. This impr ..."
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Cited by 17 (13 self)
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Abstract. Arrangements of planar curves are fundamental structures in computational geometry. We describe the recent developments in the arrangement package of Cgal, the Computational Geometry Algorithms Library, making it easier to use, to extend and to adapt to a variety of applications. This improved flexibility of the code does not come at the expense of efficiency as we mainly use genericprogramming techniques, which make dexterous use of the compilation process. To the contrary, we expedited key operations as we demonstrate by experiments. 1
Integrating task and PRM motion planning: Dealing with many infeasible motion planning queries
"... To accomplish a task an autonomous robot must break this task into “primitive ” subtasks and order them to satisfy precedence constraints. Each subtask requires performing a motion. The existence of a feasible trajectory is an additional precondition for the subtask, but a very expensive one to test ..."
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Cited by 13 (0 self)
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To accomplish a task an autonomous robot must break this task into “primitive ” subtasks and order them to satisfy precedence constraints. Each subtask requires performing a motion. The existence of a feasible trajectory is an additional precondition for the subtask, but a very expensive one to test. Probabilistic RoadMaps (PRM) are an effective approach to plan feasible trajectories when these exist. However, PRM planners are unable to detect that no solution exists. On the other hand, a task/motion planner must often consider many subtasks, a fraction of which, only, admit feasible trajectories. This paper proposes a general algorithm (I‐TMP) that specifically addresses this issue. This algorithm interweaves task and motion planning, and allows distributing computational effort where it is most useful. It is probabilistically complete in the following sense: if I‐TMP can generate a sequence of subtasks that admits a feasible trajectory, such a trajectory will eventually be found with high probability. An application of I‐TMP to multilimbed robots navigating on rough terrain is presented. I.
Hybrid motion planning using Minkowski sums
 IN PROC. ROBOTICS: SCI. SYS.
, 2008
"... Probabilistic and deterministic planners are two major approximatebased frameworks for solving motion planning problems. Both approaches have their own advantages and disadvantages. In this work, we provide an investigation to the following question: Is there a planner that can take the advantages ..."
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Cited by 12 (5 self)
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Probabilistic and deterministic planners are two major approximatebased frameworks for solving motion planning problems. Both approaches have their own advantages and disadvantages. In this work, we provide an investigation to the following question: Is there a planner that can take the advantages from both probabilistic and deterministic planners? Our strategy to achieve this goal is to use the pointbased Minkowski sum of the robot and the obstacles in workspace. Our experimental results show that our new method, called Msum planner, which uses the geometric properties of Minkowski sum to solve motion planning problems, provides advantages over the existing probabilistic or deterministic planners. In particular, Msum planner is significantly more efficient than the Probabilistic Roadmap Methods (PRMs) and its variants for problems that can be solved by reusing configurations.
A Hybrid Approach for Complete Motion Planning
"... Abstract — We present an efficient algorithm for complete motion planning that combines approximate cell decomposition (ACD) with probabilistic roadmaps (PRM). Our approach uses ACD to subdivide the configuration space into cells and computes localized roadmaps by generating samples within these cel ..."
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Cited by 11 (0 self)
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Abstract — We present an efficient algorithm for complete motion planning that combines approximate cell decomposition (ACD) with probabilistic roadmaps (PRM). Our approach uses ACD to subdivide the configuration space into cells and computes localized roadmaps by generating samples within these cells. We augment the connectivity graph for adjacent cells in ACD with pseudofree edges that are computed based on localized roadmaps. These roadmaps are used to capture the connectivity of free space and guide the adaptive subdivision algorithm. At the same time, we use cell decomposition to check for path nonexistence and generate samples in narrow passages. Overall, our hybrid algorithm combines the efficiency of PRM methods with the completeness of ACDbased algorithms. We have implemented our algorithm on 3DOF and 4DOF robots. We demonstrate its performance on planning scenarios with narrow passages or no collisionfree paths. In practice, we observe up to 10 times improvement in performance over prior complete motion planning algorithms. I.