abstract 17

Bulletin of Computational Applied Mathematics (Bull CompAMa)

17

Loop topological complexity

Younes Derfoufi, My Ismail Mamouni

We introduce here the notion of loop motion planning algorithms and show that it yields to a homotopical invariant: the loop topological complexity, denoted throughout this paper by $\rm{TC}^{\rm{LP}}(-)$, which measures the algorithmic complexity of the motion of a drone as, for example, an unmanned airplane or a guided TV camera. Our main result states that $\rm{TC}(-) = \rm{TC}^{\rm{LP}}(-)$, where $\rm{TC}$ denotes the ordinary topological complexity introduced by M. Farber. Some interesting applications will emerge and will be discussed.

Keywords: motion planning algorithm; topological robotics; topological complexity; loop topological complexity; monoidal topological complexity; Iwase-Sakai conjecture.

Cite this paper:

Derfoufi Y., Mamouni M.I. Loop topological complexity.

Bull. Comput. Appl. Math. (Bull CompAMa),

Vol. 3, No. 2, Jul-Dec, pp.31-36, 2015.