Programmable matter by folding

Abstract

Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. This concept requires constituent elements to interact and rearrange intelligently in order to meet the goal. This paper considers achieving programmable sheets that can form themselves in different shapes autonomously by folding. Past approaches to creating transforming machines have been limited by the small feature sizes, the large number of components, and the associated complexity of communication among the units. We seek to mitigate these difficulties through the unique concept of self-folding origami with universal crease patterns. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. To implement this self-folding origami concept, we have developed a scalable end-to-end planning and fabrication process. Given a set of desired objects, the system computes an optimized design for a single sheet and multiple controllers to achieve each of the desired objects. The material, called programmable matter by folding, is an example of a system capable of achieving multiple shapes for multiple functions.

Fig. 1.

32-tile self-folding sheet, capable of achieving two distinct shapes: a “paper airplane” and a “boat.” Joule-heated SMA bending actuator “stapled” into the top (A) and bottom (B) sides of the sheet. Patterned traces cross the silicone flexures and are shown unstretched (C) and after stretching as a flexure bends 180° (D). Silicone flexure bent 180°, with both a single fold (E) and folded again to create a compound fold (four layers thick) (F).

Fig. 2.

The development of the programmable material first uses planning algorithms to plan a single shape, then merges multiple plans for multiple shapes, and finally outputs a design for how to fabricate the components of the sheet.

Fig. 3.

SMA actuator unfolded after annealing (top). The actuator is “stapled” to the sheet in this position, with each of the three legs fitted through a hole in the sheet. Heat is applied at each red arrow to fold the three distal joints (middle). This causes the “heat-activated staple” to clamp the bottom side of the sheet. When the entire actuator is Joule heated, the central joint bends, folding the sheet 180° (bottom).

Fig. 4.

Simulation (left) and experiments (right, with time shown in lower right—mm:ss.s) of a self-folding “boat.”(A). All actuators receiving current (B). Immediately before magnetic closures engage (C). Finished boat on side (D).

Fig. 5.

Flat sheet prior to folding (A). Four-actuator group controlling flaps activated (B). Magnets for the first fold engaged (C). Remaining actuators are activated (D). Final shape (E) and inverted (F).