Precise Truss Assembly using Commodity Parts and Low Precision Welding

We describe an Intelligent Precision Jigging Robot (IPJR), which allows high precision assembly of commodity parts with low-precision bonding. We present preliminary experiments in 2D that are motivated by the problem of assembling a space telescope optical bench on orbit using inexpensive, stock hardware and low-precision welding. An IPJR is a robot that acts as the precise "jigging", holding parts of a local assembly site in place while an external low precision assembly agent cuts and welds members. The prototype presented in this paper allows an assembly agent (in this case, a human using only low precision tools), to assemble a 2D truss made of wooden dowels to a precision on the order of millimeters over a span on the order of meters. We report the challenges of designing the IPJR hardware and software, analyze the error in assembly, document the test results over several experiments including a large-scale ring structure, and describe future work to implement the IPJR in 3D and with micron precision

On the mathematics of self-assembly

Self-assembly is the ubiquitous process by which simple objects come together under simple rules to form more complex objects. Self-assembly occurs in nature to produce structures of extraordinary complexity. In the future, it may be possible to harness the power of self-assembly to manufacture useful devices in enormous quantities at little cost. In order to do so, it would be valuable to have a deep understanding of self-assembly, at both theoretical and practical levels. I first describe experimental work with DNA self-assembly. DNA is an ideal substance to use in experimental self-assembly: It has well-understood structure; it has readily-available tools to synthesize, manipulate, and visualize it; and it has "programmable" interactions with other molecules of DNA. I describe two self-assembling DNA complexes that can further self-assemble into regular lattices. Mathematical models of self-assembly have been created to aid in the analysis of the power and limits of self-assembly. I explore decidability questions in a mathematical model of self-assembly known as the tile assembly model. I prove the undecidability of distinguishing self-assembling systems in which infinite structures can be assembled from systems in which only finite structures can be assembled. Many self-assembly processes are rooted in chemistry. The event-systems model generalizes the classical theory of chemical thermodynamics and places the kinetic theory of chemical reactions on a firm mathematical foundation. I prove that many of the expectations acquired through empirical study are warranted. Finally, I use the event-systems model to explore questions in pure mathematics. The atomic hypothesis in chemistry (the theory that every substance is composed of a unique set of atoms) is analogous to the fundamental theorem of arithmetic in mathematics (the theory that every natural number is the product of a unique set of primes). I exploit this analogy by creating event-systems in which the basic components are natural numbers that can ”react" through multiplication. Important thermodynamic properties such as temperature and pressure have purely mathematical implications in these systems. In particular, the pressure at equilibrium is the Riemann zeta function's value of the temperature of the system

Path finding in the tile assembly model

Swarm robotics, active self-assembly, and amorphous computing are fields that focus on designing systems of large numbers of small, simple components that can cooperate to complete complex tasks. Many of these systems are inspired by biological systems, and all attempt to use the simplest components and environments possible, while still being capable of achieving their goals. The canonical problems for such biologically-inspired systems are shape assembly and path finding. We will demonstrate path finding in the well-studied tile assembly model, a model of molecular self-assembly that is strictly simpler than other biologically inspired models. As in related work, our systems function in the presence of obstacles and can be made fault-tolerant. The path-finding systems use Θ(1) distinct components and find minimal-length paths in time linear in the length of the path.

CS599: Structure and Dynamics of Networked Information (Spring 2005) 02/02/2005: α-communities

Last time, we looked at a notion of community where we required high overall edge density among groups of nodes. This made no requirement on individual nodes. In particular, the definition favors the inclusion of high-degree nodes (in WWW terms: popular sites, e.g., yahoo.com, google.com, cnn.com). One may argue that communities should consist of nodes which predominantly belong to that community, i.e., have most of their links within the community. Definition 1 Let α ∈ [0, 1] and G be a graph (e.g., the web graph). A set S ⊆ G is called an α-community in G iff dS(v) ≥ α for all nodes v ∈ S, where dS(v) is the degree of v in S. If we omit the exact value of α, we assume α = 1 [1]. This definition captures an individual’s belonging to 2 the group. If every page in a set of pages S has most of its links to other pages in S, then S is a 1 2-community. The larger α, the more “tightly knit ” the community is. So the best communities are the ones with large α. However, this leads to the problem that the whole graph is the “best ” community, because all of its edges are within the selected set (itself), making it a 1-community. The entire graph is not a very interesting community. We are more interested in discovering significantly smaller communities which nevertheless have many edges inside. As an extension, we may also wish to forc

Machine Detectable Object Camouflage

Outdoor equipment (e.g., cellular telephony towers) is often camouflaged to hide it from human view which can make it difficult for field technicians to locate such equipment. This disclosure describes techniques that make such camouflaged objects easily detectable by machines equipped with appropriate sensors while remaining hidden from the human view. For example, a cellular telephony tower can be painted with material that includes a laser scintillation material. Such material can be easily detected by a LIDAR scan. Other techniques can include: use of two shades of paint that are clearly distinguishable by machine photoreceptors but appear as the same color to a human; painting with near-color match fiducial markings to enable easy detection by cameras; use of infrared reflective (IR) materials for easy passive identification; carpet patterns that include modifications that encode information; etc. Camouflage can be used on any type of object and a corresponding suitable technique to make it machine detectable can be employed

On the decidability of self-assembly of infinite ribbons

Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. A systematic study of self-assembly as a mathematical process has been initiated. The individual components are modelled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific “glue”, and two adjacent tiles will stick iff they have matching glues on their abutting edges. Tiles that stick to each other may form various two-dimensional “structures ” such as squares, rectangles, or may cover the entire plane. In this paper we focus on a special type of structure, called ribbon: A non-self-crossing sequence of tiles on the plane, in which successive tiles are adjacent along an edge, and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. The proof is based on a construction, due to Robinson, of a special set of tiles that allow only aperiodic tilings of the plane. This construction is used to create a special set of directed tiles (tiles with arrows painted on the top) with the “strong plane-filling property”- a variation of the “plane-filling property ” previously defined by J. Kari. A construction of “sandwich ” tiles is then used in conjunction with this special tile set, to reduce the well-known undecidable Tiling Problem to the problem of the existence of an infinite directed zipper (a special kind of ribbon). A “motif ” construction is then introduced that allows one tile system to simulate another by using geometry to represent glues. Using motifs, the infinite directed zipper problem is reduced to the infinite ribbon problem, proving the latter undecidable. The result settles an open problem formerly known as th