Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Art gallery theorems and algorithms
Art gallery theorems and algorithms
The complexity of robot motion planning
The complexity of robot motion planning
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On translational motion planning in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Motion planning amidst fat obstacles (extended abstract)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A probabilistic learning approach to motion planning
WAFR Proceedings of the workshop on Algorithmic foundations of robotics
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
A random sampling scheme for path planning
International Journal of Robotics Research
Handbook of discrete and computational geometry
OBPRM: an obstacle-based PRM for 3D workspaces
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Software review: d-cubed's dimensional constraint manager
Journal of Computing and Information Science in Engineering
Robot Motion Planning
Retraction: A new approach to motion-planning
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Motion Planning with Six Degrees of Freedom
Motion Planning with Six Degrees of Freedom
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Accurate sampling-based algorithms for surface extraction and motion planning
Accurate sampling-based algorithms for surface extraction and motion planning
A GPU-based voxelization approach to 3D Minkowski sum computation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
A sweep and translate algorithm for computing voxelized 3D Minkowski sums on the GPU
Computer-Aided Design
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We present a new sampling-based algorithm for complete motion planning. Our algorithm relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point, called the guard, can see every point in the star-shaped region. The resulting set of guards capture the intra-region connectivity--the connectivity between points belonging to the same star-shaped region. We capture the inter-region connectivity by computing connectors that link guards of adjacent regions. The guards and connectors are combined to obtain the star-shaped roadmap. We present an efficient algorithm to compute the roadmap in a deterministic manner without explicit computation of the free space. We show that the star-shaped roadmap captures the connectivity of the free space, thereby enabling us to perform complete motion planning. Our approach is relatively simple to implement. We apply our approach to perform motion planning of robots with translational and rotational degrees of freedom (dof). We highlight its performance in challenging scenarios with narrow passages or when there is no collision-free path for robots with low degrees of freedom.