Planning, geometry, and complexity of robot motion
Planning, geometry, and complexity of robot motion
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Handbook of discrete and computational geometry
Robot Motion Planning
Robot Motion: Planning and Control
Robot Motion: Planning and Control
Nonuniform Discretization for Kinodynamic Motion Planning and its Applications
SIAM Journal on Computing
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Shortest path amidst disc obstacles is computable
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On the Probabilistic Foundations of Probabilistic Roadmap Planning
International Journal of Robotics Research
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Planning Algorithms
Motion planning for legged and humanoid robots
Motion planning for legged and humanoid robots
In Praise of Numerical Computation
Efficient Algorithms
A subdivision algorithm in configuration space for findpath with rotation
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Motion planning via manifold samples
ESA'11 Proceedings of the 19th European conference on Algorithms
Towards Exact Numerical Voronoi Diagrams
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We propose to design new algorithms for motion planning problems using the well-known Domain Subdivision paradigm, coupled with "soft" predicates. Unlike the traditional exact predicates in computational geometry, our primitives are only exact in the limit. We introduce the notion of resolution-exact algorithms in motion planning: such an algorithm has an "accuracy" constant K 1, and takes an arbitrary input "resolution" parameter ε0 such that: if there is a path with clearance Kε, it will output a path with clearance ε/K; if there are no paths with clearance ε/K, it reports "no path". Besides the focus on soft predicates, our framework also admits a variety of global search strategies including forms of the A* search and probabilistic search. Our algorithms are theoretically sound, practical, easy to implement, without implementation gaps, and have adaptive complexity. Our deterministic and probabilistic strategies avoid the Halting Problem of current probabilistically complete algorithms. We develop the first provably resolution-exact algorithms for motion-planning problems in SE(2)=R2 x S1. To validate this approach, we implement our algorithms and the experiments demonstrate the efficiency of our approach, even compared to probabilistic algorithms.