Toward efficient trajectory planning: the path-velocity decomposition
International Journal of Robotics Research
On shortest paths in polyhedral spaces
SIAM Journal on Computing
SIAM Journal on Computing
The complexity of robot motion planning
The complexity of robot motion planning
Motion planning among time dependent obstacles
Acta Informatica
The number of shortest paths on the surface of a polyhedron
SIAM Journal on Computing
Path planning using a tangent graph for mobile robots among polygonal and curved obstacles
International Journal of Robotics Research
Motion planning in the presence of moving obstacles
Journal of the ACM (JACM)
A single-exponential upper bound for finding shortest paths in three dimensions
Journal of the ACM (JACM)
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Finding Shortest Paths on Surfaces Using Level Sets Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maximum thick paths in static and dynamic environments
Proceedings of the twenty-fourth annual symposium on Computational geometry
Maximum thick paths in static and dynamic environments
Computational Geometry: Theory and Applications
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A path-planning problem is considered in the presence of moving polygonal obstacles in three dimensions. A particle is to be moved from a given initial position to a destination position amidst polygonal disjoint barriers moving along known linear trajectories. The particle can move in any direction in space with a single constraint that it cannot move faster than a given speed bound. All obstacles are slowly moving, i.e., their speeds are strictly slower than the maximum speed of the particle. The destination point is also permitted to move along a known trajectory and is assumed to be collision-free at all times. Three properties are stated and proved for a time-minimal path amidst moving polygonal barriers. A few extensions are considered, including piecewise linear motions of the obstacle