Tensegrity topology optimization by force maximization on arbitrary ground structures

This paper presents an optimization approach for design of tensegrity structures based on graph theory. The formulation obtains tensegrities from ground structures, through force maximization using mixed integer linear programming. The method seeks a topology of the tensegrity that is within a given geometry, which provides insight into the tensegrity design from a geometric point of view. Although not explicitly enforced, the tensegrities obtained using this approach tend to be both stable and symmetric. Borrowing ideas from computer graphics, we allow “restriction zones” (i.e., passive regions in which no geometric entity should intersect) to be specified in the underlying ground structure. Such feature allows the design of tensegrities for actual engineering applications, such as robotics, in which the volume of the payload needs to be protected. To demonstrate the effectiveness of our proposed design method, we show that it is effective at extracting both well-known tensegrities and new tensegrities from the ground structure network, some of which are prototyped with the aid of additive manufacturing.