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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.
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 19 (2 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...
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 2 (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...