The complexity of robot motion planning
The complexity of robot motion planning
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On Translational Motion Planning of a Convex Polyhedron in 3-Space
SIAM Journal on Computing
Handbook of discrete and computational geometry
Generic programming and the STL: using and extending the C++ Standard Template Library
Generic programming and the STL: using and extending the C++ Standard Template Library
Robot Motion Planning
A practical exact motion planning algorithm for polygonal object amidst polygonal obstacles
Proceedings of the Workshop on Geometry and Robotics
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Planning Algorithms
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Complexity of the mover's problem and generalizations
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On soft predicates in subdivision motion planning
Proceedings of the twenty-ninth annual symposium on Computational geometry
Hi-index | 0.00 |
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with sampling-based approaches that are appropriate for higher dimensions. We suggest taking samples that are entire low-dimensional manifolds of the configuration space. These samples capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms then provide powerful primitive operations for complete analysis of the low-dimensional manifolds. We have implemented our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. To this end, we have developed a primitive operation for the analysis of an appropriate set of manifolds using arrangements of curves of rational functions. This modular integration of several carefully engineered components has lead to a significant speedup over the PRM sampling-based algorithm, which represents an approach that is prevalent in practice.