The use of origami principles to create 3-dimensional shapes has the potential to revolutionize active material structures and compliant mechanisms. Active origami structures can be applied to a broad range of areas such as reconfigurable aircraft and deployable space structures as well as instruments for minimally invasive surgery. Our current research is focused on dielectric elastomer (DE) and magneto active elastomer (MAE) materials to create multi-field responsive structures. Such multi-field responsive structures will integrate the DE and MAE materials to enable active structures that fold/unfold in different ways in response to electric and/or magnetic field. They can also unfold either as a result of eliminating the applied field or in response to the application of an opposite field. This concept is demonstrated in a folding cube shape and induced locomotion in the MAE material. Two finite element models are developed for both the DE and MAE materials and validated through physical testing of these materials. The models are then integrated to demonstrate multi-field responses of a bi-fold multi-field responsive structure. The bifold model is designed to fold about one axis in an electric field and a perpendicular axis in a magnetic field. Future modeling efforts and research directions are also discussed based on these preliminary results.

Automatic motion planning has applications ranging from traditional robotics to computer-aided design to computational biology and chemistry. Randomized planners, such as probabilistic roadmap methods (prms), have been highly successful in solving these high degree of freedom problems. However, the traditional prm framework fails to address several practical issues. One of the most important issues is the difficulty of deciding what size roadmap is required to solve a given problem efficiently. prms do not provide an automated way to determine appropriate roadmap size. In this paper, we propose a new prm-based framework called Incremental Map Generation (img) to address this problem. Our strategy is to break the map generation into independent processes. Each process generates an independent roadmap component. img proceeds by adding independent roadmap components to an existing roadmap until some user defined criteria are satisfied. In addition to addressing the roadmap size problem, this framework supports roadmap reproducibility in that any of the roadmap increments can be reproduced by using the same set of seeds. Finally, these independent processes are natural for parallelization.

Origami engineering — the use of origami principles in engineering applications — provides numerous opportunities to revolutionize the way we design, manufacture, assemble, and package products and devices. By combining origami principles with active materials, we can create reconfigurable products and devices that can fold and unfold on demand. In origami, the folded medium is paper, yet many engineering applications require materials with finite thickness to provide the necessary strength and stiffness to achieve the desired functionality. In such applications, it is important to distinguish between bending and folding so that we understand the differences in material behavior when actuated. In this paper, we propose definitions for bending and folding for materials used in engineering applications. The literature is reviewed in detail to provide context and support for the proposed definitions, and examples from our own research with active materials, specifically, magneto-active elastomers (MAE) and dielectric elastomers (DE), are used to illustrate the subtle, yet important, differences between bending and folding in materials with finite thickness.

This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "simple" in the sense that any three curves have no common intersection, any two curves intersect transversally, and each curve is non-singular. A curve is given as the zero set of an analytic function f : R 2 → R 2 , and effective interval forms of f, ∂f ∂x , ∂f ∂y are available. Our solution generalizes the isotopic curve approximation algorithms of Plantinga-Vegter (2004) and Lin-Yap (2009). We use certified numerical primitives based on interval methods. Such algorithms have many favorable properties: they are practical, easy to implement, suffer no implementation gaps, integrate topological with geometric computation, and have adaptive as well as local complexity.

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