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13
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.
Manipulator control with superquadric artificial potential functions: theory and experiments
 IEEE Trans. Syst. Man Cyber
, 1990
"... 1 A repulsive potential added to an attractive well.: : : : : : : : : : : : : : : 5 ..."
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Cited by 37 (6 self)
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1 A repulsive potential added to an attractive well.: : : : : : : : : : : : : : : 5
Polynomial/Rational Approximation of Minkowski Sum Boundary Curves
 Graphical Models and Image Processing
, 1998
"... Given two planar curves, their convolution curve is dened as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, t ..."
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Cited by 21 (3 self)
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Given two planar curves, their convolution curve is dened as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant parts in the convolution curve, one can generate the Minkowski sum boundary. The Minkowski sum can be used in various important geometric computations, especially for collision detection among planar curved objects. Unfortunately, the convolution curve of two rational curves is not rational, in general. Therefore, in practice, one needs to approximate the convolution curves with polynomial/rational curves. Conventional approximation methods of convolution curves typically use piecewise linear approximations, which is not acceptable in many CAD systems due to data proliferation. In this paper, we g...
The Minkowski Sum of 2D Curved Objects
, 1998
"... The Minkowski sum of two planar objects is closely related to the convolution curve of the object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant parts in the convolution curve, one can generate the Minkowski sum boundary. Thi ..."
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Cited by 5 (0 self)
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The Minkowski sum of two planar objects is closely related to the convolution curve of the object boundary curves. That is, the convolution curve is a superset of the Minkowski sum boundary. By eliminating all redundant parts in the convolution curve, one can generate the Minkowski sum boundary. This paper discusses various important issues in the boundary construction of the Minkowski sum. 2 Introduction The Minkowski sum has important applications for collision detection in robot motion planning [2, 8, 13, 18]. Given two planar curved objects O 1 and O 2 , their Minkowski sum is dened as follows: O 1 O 2 = fa + b j a 2 O 1 ; b 2 O 2 g: (1) Given two planar curves C 1 and C 2 , their convolution curve C 1 C 2 is dened by applying the vector sums only to the pairs of curve points that have the same curve tangent direction: C 1 C 2 = fa + b j a 2 C 1 ; b 2 C 2 ; (2) T 1 k T 2 ; hT 1 ; T 2 i > 0 g; where T i is the curve tangent of C i , (i = 1; 2). The Minkowski sum boundar...
A Survey and Experimental Evaluation of Proximity Sensors for Space Robotics
 Proc. IEEE International Conference on Robotics & Automation
, 1994
"... This paper provides an overview of our selection process for proximity sensors for manipulator collision avoidance. Five categories of sensors have been considered for this use in space operations: intensity of re
ection, triangulation, time of ight, capacitive, and inductive. From these categories, ..."
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Cited by 5 (1 self)
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This paper provides an overview of our selection process for proximity sensors for manipulator collision avoidance. Five categories of sensors have been considered for this use in space operations: intensity of re
ection, triangulation, time of ight, capacitive, and inductive. From these categories, the most promising commercial and mature laboratory prototype sensors have been selected and tested. After reviewing the selection process and the experimental results, conclusions are drawn about which sensors are best and why. 1
New approximation methods of planar offset and convolution curves
 In Geometric Modeling: Theory and Practice
, 1997
"... We present new methods to approximate the offset and convolution of planar curves. These methods can be used as fundamental tools in various geometric applications such as NC machining and collision detection of planar curved objects. Using quadratic curve approximation and tangent field matching, ..."
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Cited by 4 (1 self)
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We present new methods to approximate the offset and convolution of planar curves. These methods can be used as fundamental tools in various geometric applications such as NC machining and collision detection of planar curved objects. Using quadratic curve approximation and tangent field matching, the offset and convolution curves can be approximated by polynomial or rational curves within the tolerance of approximation error ɛ>0. We suggest three methods of offset approximation, all of which allow simple error analysis and at the same time provide highprecision approximation. Two methods of convolution approximation are also suggested that approximate convolution curves with polynomial or rational curves.
A Basic Algorithm and Data Structures for SensorBased Path Planning in Unknown Environments
, 2000
"... This work deals with the sensorbased path planning problem. Particularly, we present the case for manipulator arms. We assume that the knowledge of workspace is partially known and that it can be increased by using a laserlike sensor. We propose a representation of the workspace that is well adapt ..."
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Cited by 3 (0 self)
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This work deals with the sensorbased path planning problem. Particularly, we present the case for manipulator arms. We assume that the knowledge of workspace is partially known and that it can be increased by using a laserlike sensor. We propose a representation of the workspace that is well adapted to exploit the information obtained from the sensors and then compute collision detection. A sensorbased version of the Ariadne's Clew Algorithm (ACA) is used to incrementally search for the free space and compute a path to a goal conguration. 1 Introduction This work deals with the problem of sensorbased path planning in unknown environments. Particularly, we present the case for manipulators arms. The problem consists of nding a free trajectory for a robot arm from an initial conguration to a nal conguration in a partially known environment. In order to execute this task, the robot must construct an incremental representation of the workspace by means of some sensor, {a laser b...
Lower Bounds for Shortest Path and Related Problems
 In Proc. 28th Ann. IEEE
, 1987
"... We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of ..."
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Cited by 2 (0 self)
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We present the first lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We first apply the method to the shortest path problem in three dimensions. The problem is to find the shortest path under an L p metric (e.g. a euclidean metric) between two points amid polyhedral obstacles. Although this problem has been extensively studied, there were no previously known lower bounds. We show that there may be exponentially many shortest path classes in singlesource multipledestination problems, and that the singlesource singledestination problem is NPhard. We use a similar proof technique to show that two dimensional dynamic motion planning with bounded velocity is NPhard. Finally we extend the technique to compliant motion planni...
Human Augmentation in Teleoperation of Arm Manipulators in an Environment with Obstacles
, 2000
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Con guration Space as a Means for Augmenting Human Performance in Teleoperation Tasks
"... This paper considers an approach to operatorguided real time motion control of robot arm manipulators that's based on the use of conguration space (Cspace). The goal is to improve operator performance in a complex environment with obstacles. In such tasks, traditional teleoperation techniques ..."
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This paper considers an approach to operatorguided real time motion control of robot arm manipulators that's based on the use of conguration space (Cspace). The goal is to improve operator performance in a complex environment with obstacles. In such tasks, traditional teleoperation techniques, which are all based on control in work space (Wspace), suer from human errors tied to deciencies in human spatial reasoning. The Cspace approach transforms the problem into one humans are much better equipped to handle { moving a point in a maze { and results in a signicant improvement in performance: shorter path, less time to complete the task, and virtually no armobstacle collisions. Versions of the approach are described for two and threedimensional (3D) tasks, and tools are developed to eÆciently interface the human and machine intelligence. Eectiveness of the Cspace approach is demonstrated by a series of experiments, showing an improvement in performance on the order of magnitude in the 2D case and a factor of 2 to 4 in the 3D case, compared to usual work space control. 1