TY - JOUR
T1 - Models and motion planning
AU - De Berg, Mark
AU - Katz, Matthew J.
AU - Overmars, Mark H.
AU - van Der Stappen, A. Frank
AU - Vleugels, Jules
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (M. de Berg), [email protected] (M.J. Katz), [email protected] (M.H. Overmars), [email protected] (A.F. van der Stappen), [email protected] (J. Vleugels). 1 Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - We study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is Θ(n f/2 + n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a threedimensional uncluttered environment is Θ(n2f/3 + n). All these bounds fit nicely between the Θ(n) bound for the maximum free-space complexity for low-density environments and the Θ(nf) bound for unrestricted environments. Surprisingly-because contrary to the situation in the plane-the maximum free-space complexity is Θ(nf) for a three-dimensional environment with small simple-cover complexity.
AB - We study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is Θ(n f/2 + n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a threedimensional uncluttered environment is Θ(n2f/3 + n). All these bounds fit nicely between the Θ(n) bound for the maximum free-space complexity for low-density environments and the Θ(nf) bound for unrestricted environments. Surprisingly-because contrary to the situation in the plane-the maximum free-space complexity is Θ(nf) for a three-dimensional environment with small simple-cover complexity.
KW - Free space complexity
KW - Input models
KW - Motion planning
UR - https://www.scopus.com/pages/publications/31244433187
U2 - 10.1016/S0925-7721(01)00022-0
DO - 10.1016/S0925-7721(01)00022-0
M3 - Article
AN - SCOPUS:31244433187
SN - 0925-7721
VL - 23
SP - 53
EP - 68
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 1
ER -