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The cost of bounded curvature
- Computing Geometry
, 2013
"... We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations σ, σ′, let `(σ, σ′) be the shortest bounded-curvature path from σ to σ′. For d> 0, let ..."
Abstract
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Cited by 2 (0 self)
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We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations σ, σ′, let `(σ, σ′) be the shortest bounded-curvature path from σ to σ′. For d> 0, let
Convex Tours of Bounded Curvature
- In Proc. 2nd Annu. European Sympos. Algorithms
, 1999
"... We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with n vertices. We present an O(m + ..."
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Cited by 2 (1 self)
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We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with n vertices. We present an O
Riemannian Consensus for Manifolds With Bounded Curvature
"... Abstract—Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in Euclidean space. In this work we propose Riemannian consensus, a natu ..."
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Cited by 7 (1 self)
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with bounded curvature and we analyze the differences with respect to the Euclidean case. We test the proposed algorithms on synthetic data sampled from the space of rotations, the sphere and the Grassmann manifold. Index Terms — Grassmann manifold, Riemannian manifold. I.
A Boundary of the Set of the Riemannian Manifolds with Bounded Curvatures and
, 1988
"... In [12], Gromov introduced a metric (Hausdorff distance) on the class of all metric spaces. There, he proved the precompactness of the set consisting of the isometry classes of Riemannian manifolds with bounded curvatures and diameters. In this paper we shall study the structure of the closure of th ..."
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Cited by 36 (2 self)
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In [12], Gromov introduced a metric (Hausdorff distance) on the class of all metric spaces. There, he proved the precompactness of the set consisting of the isometry classes of Riemannian manifolds with bounded curvatures and diameters. In this paper we shall study the structure of the closure of this
The Classification of Homotopy Classes of Bounded Curvature of Paths
"... Abstract. A bounded curvature path is a continuously differentiable piece-wise C2 path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this work we study the homotopy classes of bounded curvature paths for generic points in the tangent bundle of the Eu ..."
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Cited by 2 (2 self)
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Abstract. A bounded curvature path is a continuously differentiable piece-wise C2 path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this work we study the homotopy classes of bounded curvature paths for generic points in the tangent bundle
Computing Curvature Bounds for Bounded Curvature Subdivision
- Computer-Aided Geometric Design
, 2001
"... For a stationary, ane invariant, symmetric, linear and local subdivision scheme that is C 2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing an interval ..."
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Cited by 6 (2 self)
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For a stationary, ane invariant, symmetric, linear and local subdivision scheme that is C 2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing
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