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12
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 228 (25 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.
Incremental lowdiscrepancy lattice methods for motion planning
 In Proc. IEEE International Conference on Robotics and Automation
, 2003
"... We present deterministic sequences for use in samplingbased approaches to motion planning. They simultaneously combine the qualities found in many other sequences: i) the incremental and selfavoiding tendencies of pseudorandom sequences, ii) the lattice structure provided by multiresolution grids ..."
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Cited by 34 (11 self)
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We present deterministic sequences for use in samplingbased approaches to motion planning. They simultaneously combine the qualities found in many other sequences: i) the incremental and selfavoiding tendencies of pseudorandom sequences, ii) the lattice structure provided by multiresolution grids, and iii) lowdiscrepancy and lowdispersion measures of uniformity provided by quasirandom sequences. The resulting sequences can be considered as multiresolution grids in which points may be added one at a time, while satisfying the sampling qualities at each iteration. An efficient, recursive algorithm for generating the sequences is presented and implemented. Early experiments show promising performance by using the samples in search algorithms to solve motion planning problems. 1
Nonlinear and Hybrid Control Via RRTs
 In Proc. Intl. Symp. on Mathematical Theory of Networks and Systems
, 2002
"... In this paper, we review rapidlyexploring random trees (RRTs) for motion planning, experiment with them on standard control problems, and extend them to the case of hybrid systems. ..."
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Cited by 17 (2 self)
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In this paper, we review rapidlyexploring random trees (RRTs) for motion planning, experiment with them on standard control problems, and extend them to the case of hybrid systems.
Deterministic Sampling Methods for Spheres and SO(3)
, 2004
"... This paper addresses the problem of generating uniform deterministic samples over the spheres and the threedimensional rotation group, SO(3). The target applications include motion planning, optimization, and verification problems in robotics and in related areas, such as graphics, control theory a ..."
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Cited by 17 (4 self)
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This paper addresses the problem of generating uniform deterministic samples over the spheres and the threedimensional rotation group, SO(3). The target applications include motion planning, optimization, and verification problems in robotics and in related areas, such as graphics, control theory and computational biology. We introduce an infinite sequence of samples that is shown to achieve: 1) lowdispersion, which aids in the development of resolution complete algorithms, 2) lattice structure, which allows easy neighbor identification that is comparable to what is obtained for a grid in R , and 3) incremental quality, which is similar to that obtained by random sampling. The sequence is demonstrated in a samplingbased motion planning algorithm.
Steps toward derandomizing RRTs
 In IEEE/RSJ Int’l Conf. on Intelligent Robots and Systems
, 2003
"... We present two new motion planning algorithms, based on the Rapidly Exploring Random Tree (RRT) family of algorithms. These algorithms represent the first work in the direction of derandomizing RRTs; this is a very challenging problem due to the way randomization is used in RRTs. In RRTs, randomizat ..."
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Cited by 9 (2 self)
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We present two new motion planning algorithms, based on the Rapidly Exploring Random Tree (RRT) family of algorithms. These algorithms represent the first work in the direction of derandomizing RRTs; this is a very challenging problem due to the way randomization is used in RRTs. In RRTs, randomization is used to create Voronoi bias, which causes the search trees to rapidly explore the state space. Our algorithms take steps to increase the Voronoi bias and to retain this property without the use of randomization. Studying these and related algorithms will improve our understanding of how efficient exploration can be accomplished, and will hopefully lead to improved planners. We give experimental results that illustrate how the new algorithms explore the state space and how they compare with existing RRT algorithms. 1
SamplingBased Motion Planning
, 2006
"... There are two main philosophies for addressing the motion planning problem, in Formulation 4.1 from Section 4.3.1. This chapter presents one of the philosophies, samplingbased motion planning, which is outlined in Figure 5.1. The main idea is to avoid the explicit construction of Cobs, as described ..."
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Cited by 4 (1 self)
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There are two main philosophies for addressing the motion planning problem, in Formulation 4.1 from Section 4.3.1. This chapter presents one of the philosophies, samplingbased motion planning, which is outlined in Figure 5.1. The main idea is to avoid the explicit construction of Cobs, as described in Section 4.3, and instead conduct a search that probes the Cspace with a sampling scheme. This probing is enabled by a collision detection module, which the motion planning algorithm considers as a “black box. ” This enables the development of planning algorithms that are independent of the particular geometric models. The collision detection module handles concerns such as whether the models are semialgebraic sets, 3D triangles, nonconvex polyhedra, and so on. This general philosophy has been very successful in recent years for solving problems from robotics, manufacturing, and biological applications that involve thousands and even millions of geometric primitives. Such problems would be practically impossible to solve using techniques that explicitly represent Cobs. Notions of completeness It is useful to define several notions of completeness
Published by Cambridge University Press Overview of Part II: Motion Planning Planning in Continuous Spaces
"... Part II makes the transition from discrete to continuous state spaces. Two alternative titles are appropriate for this part: 1) motion planning, or 2) planning in continuous state spaces. Chapters 3–8 are based on research from the field of motion planning, which has been building since the 1970s; t ..."
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Part II makes the transition from discrete to continuous state spaces. Two alternative titles are appropriate for this part: 1) motion planning, or 2) planning in continuous state spaces. Chapters 3–8 are based on research from the field of motion planning, which has been building since the 1970s; therefore, the name motion planning is widely known to refer to the collection of models and algorithms that will be covered. On the other hand, it is convenient to also think of Part II as planning in continuous spaces because this is the primary distinction with respect to most other forms of planning. In addition, motion planning will frequently refer to motions of a robot in a 2D or 3D world that contains obstacles. The robot could model an actual robot, or any other collection of moving bodies, such as humans or flexible molecules. A motion plan involves determining what motions are appropriate for the robot so that it reaches a goal state without colliding into obstacles. Recall the examples from Section 1.2. Many issues that arose in Chapter 2 appear once again in motion planning.
Part II Motion Planning
"... Part II makes the transition from discrete to continuous state spaces. Two alternative titles are appropriate for this part: 1) motion planning, or 2) planning in continuous state spaces. Chapters 3–8 are based on research from the field of motion planning, which has been building since the 1970s; t ..."
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Part II makes the transition from discrete to continuous state spaces. Two alternative titles are appropriate for this part: 1) motion planning, or 2) planning in continuous state spaces. Chapters 3–8 are based on research from the field of motion planning, which has been building since the 1970s; therefore, the name motion planning is widely known to refer to the collection of models and algorithms that will be covered. On the other hand, it is convenient to also think of Part II as planning in continuous spaces because this is the primary distinction with respect to most other forms of planning. In addition, motion planning will frequently refer to motions of a robot in a 2D or 3D world that contains obstacles. The robot could model an actual robot, or any other collection of moving bodies, such as humans or flexible molecules. A motion plan involves determining what motions are appropriate for the robot so that it reaches a goal state without colliding into obstacles. Recall the examples from Section 1.2. Many issues that arose in Chapter 2 appear once again in motion planning.
Iteratively Locating Voronoi Vertices for Dispersion Estimation
, 2005
"... We present a new samplingbased algorithm for iteratively locating Voronoi vertices of a point set in the unit cube I d = [0, 1] d. The algorithm takes an input sample and executes a series of transformations, each of which projects the sample to a new face of the Voronoi cell in which it is locat ..."
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We present a new samplingbased algorithm for iteratively locating Voronoi vertices of a point set in the unit cube I d = [0, 1] d. The algorithm takes an input sample and executes a series of transformations, each of which projects the sample to a new face of the Voronoi cell in which it is located. After d such transformations, the sample has been transformed into a Voronoi vertex. Locating Voronoi vertices has many potential applications for motion planning, such as estimating dispersion for coverage and verification applications, and providing information useful for Voronoibiased or multipletree planning. We prove theoretical results regarding our algorithm, and give experimental results comparing it to naive sampling for the problem of dispersion estimation.
Sampling and Searching Methods for Practical Motion PLANNING ALGORITHMS
, 2008
"... In its original formulation, the motion planning problem considers the search of a robot path from an initial to a goal configuration. The study of motion planning has advanced significantly in recent years, in large part due to the development of highly successful sampling and searching techniques. ..."
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In its original formulation, the motion planning problem considers the search of a robot path from an initial to a goal configuration. The study of motion planning has advanced significantly in recent years, in large part due to the development of highly successful sampling and searching techniques. Recent advances have influenced samplingbased motion planning algorithms to be used in disparate areas such as humanoid robotics, automotive manufacturing, architecture, computational geography, computer graphics, and computational biology. Many of these methods work well on a large set of problems, however, they have weaknesses and limitations. This thesis expands the basic motion planning techniques to include critical concerns that are not covered by the motion planning algorithms that are in widespread use now. The technical approach is organized around three main thrusts: 1) the development of efficient nearest neighbor searching techniques for spaces arising in motion planning; 2) the development of uniform sampling techniques on these spaces to allow resolution completeness in samplingbased planning algorithms; and 3) the development of guided sampling techniques for efficient exploration on such spaces. We show that most of the modern motion planners incorporate one or more of these components; therefore, addressing these core issues in motion planning does not only lead to a more fundamental understanding of the problem, but also to