Growing form-filling tensegrity structures using map L-systems

Abstract

Tensegrities are unique, space-filling structures consisting of disjoint rigid elements (rods) connected by tensile elements (strings), which hold their shape due to a synergistic balance of opposing forces. Due to their complexity there are few effective analytical methods for discovering new, and particularly, large irregularly shaped tensegrity structures. Recent efforts using evolutionary search have been moderately successful, but have relied upon a direct encoding of the structure, and therefore face scalability issues [3]. By contrast we employ to a developmental representation grammatically “grow” tensegrity structures, and as such, issues of scalability, both in terms of representation and of performance, are addressed. Specifically we evolve map L-systems [4] which produce planar graphs [1, 2] corresponding to the structural elements of a tensegrity. Each tensegrity is then reproduced within the Open Dynamics Engine (ODE), and the volume of the convex hull described by the final location of the rigid element endpoints used as fitness. As shown in Figure 1, the map L-system significantly outperforms the direct encoding across all runs. Figure 2 shows a representative evolved tensegrity.