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.