Linear motion planning with controlled collisions and pure planar braids

Jesús González; José Luis León-Medina; Christopher Roque-Márquez

doi:10.4310/hha.2021.v23.n1.a15

Linear motion planning with controlled collisions and pure planar braids

Homology Homotopy and Applications ◽

10.4310/hha.2021.v23.n1.a15 ◽

2021 ◽

Vol 23 (1) ◽

pp. 275-296

Author(s):

Jesús González ◽

José Luis León-Medina ◽

Christopher Roque-Márquez

Keyword(s):

Motion Planning ◽

Linear Motion

Download Full-text

A Randomized Greedy Algorithm for Piecewise Linear Motion Planning

Mathematics ◽

10.3390/math9192358 ◽

2021 ◽

Vol 9 (19) ◽

pp. 2358

Author(s):

Carlos Ortiz ◽

Adriana Lara ◽

Jesús González ◽

Ayse Borat

Keyword(s):

Motion Planning ◽

Piecewise Linear ◽

Randomized Algorithm ◽

Robot Motion ◽

Topological Complexity ◽

Robot Motion Planning ◽

Automated Guided Vehicle ◽

Linear Motion ◽

Lusternik Schnirelmann ◽

Robust To Noise

We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle R, and outputs an explicit system of piecewise linear motion planners for R. The algorithm is designed in such a way that the cardinality of the output is probabilistically close (with parameters chosen by the user) to the minimal possible cardinality.This yields the first automated solution for robust-to-noise robot motion planning in terms of simplicial complexity (SC) techniques, a discretization of Farber’s topological complexity TC. Besides its relevance toward technological applications, our work reveals that, unlike other discrete approaches to TC, the SC model can recast Farber’s invariant without having to introduce costly subdivisions. We develop and implement our algorithm by actually discretizing Macías-Virgós and Mosquera-Lois’ notion of homotopic distance, thus encompassing computer estimations of other sectional category invariants as well, such as the Lusternik-Schnirelmann category of polyhedra.

Download Full-text