Graph grammars for self assembling robotic systems

Klavins, Eric; Ghrist, Robert; Lipsky, David B.

doi:10.1109/robot.2004.1302558

Cited by 55 publications

(46 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This technique has at least one machine state for each agent position in the structure, and thus the memory requirement of the agents grows with the area of the structure. Klavins et al (2004) have described robotic self-assembly in terms of graph grammars and conformational switching, resulting in systems with capability and limitations comparable to those of Jones and Matarić (2003).…”

Section: Related Workmentioning

confidence: 99%

Shape Restoration by Active Self-Assembly

Arbuckle

Requicha

2005

Applied Bionics and Biomechanics

View full text Add to dashboard Cite

Shape restoration is defined as the problem of constructing a desired, or goal, solid shape Sg by growing an initial solid Si, which is a subset of the goal but is otherwise unknown. This definition attempts to capture abstractly a situation that often arises in the physical world when a solid object loses its desired shape due to wear and tear, corrosion or other phenomena. For example, if the top of the femur becomes distorted, the hip joint no longer functions properly and may have to be replaced surgically. Growing it in place back to its original shape would be an attractive alternative to replacement. This paper presents a solution to the shape restoration problem by using autonomous assembly agents (robots) that self-assemble to fill the volume between Sg and Si. If the robots have very small dimension (micro or nano), the desired shape is approximated with high accuracy. The assembly agents initially execute a random walk. When two robots meet, they may exchange a small number of messages. The robot behavior is controlled by a finite state machine with a small number of states. Communication contact models chemical communication, which is likely to be the medium of choice for robots at the nanoscale, while small state and small messages are limitations that also are expected of nanorobots. Simulations presented here show that swarms of such robots organize themselves to achieve shape restoration by using distributed algorithms. This is one more example of an interesting geometric problem that can be solved by the Active Self-Assembly paradigm introduced in previous papers by the authors.

show abstract

Section: Related Workmentioning

confidence: 99%

Shape Restoration by Active Self-Assembly

Arbuckle

Requicha

2005

Applied Bionics and Biomechanics

View full text Add to dashboard Cite

show abstract

“…One systematic method of representing locally applicable graph transformations is to use graph grammars (e.g., [16]). A graph grammar, Φ = {r 1 , r 2 , .…”

Section: Preliminariesmentioning

confidence: 99%

Decentralized formation of random regular graphs for robust multi-agent networks

Yazıcıoğlu

Egerstedt

Shamma

2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-Multi-agent networks are often modeled via interaction graphs, where the nodes represent the agents and the edges denote direct interactions between the corresponding agents. Interaction graphs have significant impact on the robustness of networked systems. One family of robust graphs is the random regular graphs. In this paper, we present a locally applicable reconfiguration scheme to build random regular graphs through self-organization. For any connected initial graph, the proposed scheme maintains connectivity and the average degree while minimizing the degree differences and randomizing the links. As such, if the average degree of the initial graph is an integer, then connected regular graphs are realized uniformly at random as time goes to infinity.

show abstract

“…In the interest of both understanding naturally occurring biological systems and creating synthetic systems with additional capabilities, several models of active self-assembly have been proposed recently. These include the graph grammars of Klavins et al [14,15], the nubots model of Woods et al [2,4,23], and the insertion systems of Dabby and Chen [7]. Both graph grammars and nubots are capable of a topologically rich set of assemblies and reconfigurations, but rely on stateful particles forming complex bond arrangements.…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds for Active Self-assembly Using an Insertion Primitive

Malchik

Winslow

2014

Algorithms - ESA 2014

View full text Add to dashboard Cite

We prove two limits on the behavior of a model of self-assembling particles introduced by Dabby and Chen (SODA 2013), called insertion systems, where monomers insert themselves into the middle of a growing linear polymer. First, we prove that the expressive power of these systems is equal to context-free grammars, answering a question posed by Dabby and Chen. Second, we prove that systems of k monomer types can deterministically construct polymers of length n = 2 Θ(k 3/2 ) in O(log 5/3 (n)) expected time, and that this is optimal in both the number of monomer types and expected time.

show abstract

Graph grammars for self assembling robotic systems

Cited by 55 publications

References 12 publications

Shape Restoration by Active Self-Assembly

Shape Restoration by Active Self-Assembly

Decentralized formation of random regular graphs for robust multi-agent networks

Tight Bounds for Active Self-assembly Using an Insertion Primitive

Contact Info

Product

Resources

About