Path planning for graded concrete element fabrication

Abstract

The technology of functionally graded concrete (FGC) is a new methodology in the field of concrete construction, striving for mass savings by adjusting the elements interior design. A promising approach herein is meso-gradation, where concrete hollow spheres are placed inside the formwork before casting the element; this allows up to 50% mass savings without a loss in load-bearing capacity, whilst also ensuring recyclability compared to e.g. bubble decks. In order to prevent damage/displacement of the spheres during automated fabrication, the extruded concrete flow must avoid the spheres, whilst neatly covering the elements area in order to prevent cavities. Both requirements formulate a complex path planning problem that must be solved in order to achieve automated fabrication. In this paper, we propose a method for solving this problem, which is based on theoretical findings on Hamiltonian triangulations. Our approach is based on the idea that the elements area is triangulated, such that all sphere centers are corners of triangles. For each triangle, a smooth path can be planned straightforwardly on a consideration of the geometry, such that the global path is made of a sequence of local ones. This necessitates finding a triangulation that is hamiltonian, i.e. a sequence where all triangles are visited exactly once. To this end, we first present a new class of triangulations and proof their hamiltonicity, followed by an algorithm that generates such triangulations on certain FGC element geometries. This is followed by the local path planning problem, whose special structure with start/end tangential and curvature constraints facilitates the use of a polar coordinate approach.