New York Journal of Mathematics
Volume 24 (2018) 279-292


Jesús González

Simplicial complexity: piecewise linear motion planning in robotics

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Published: March 7, 2018
Keywords: Simplicial complex, barycentric subdivision, contiguous simplicial maps, motion planning.
Subject: 57Q05, 05E45, 55M30, 68T40.

Using the notion of contiguity of simplicial maps, and its relation (via iterated subdivisions) to the notion of homotopy between continuous maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex K, our discretized concept recovers the topological complexity of the realization ∥K∥. Our approach lays the theoretical grounds for designing and implementing algorithms that search for optimal motion planners for autonomous systems in real-life applications.


Partially supported by Conacyt Research Grant 221221.

Author information

Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508, Zacatenco, México City 07000, México