Programmable Self-Assembly Prashanth Bungale October 26, 2004 “Programmable Self-Assembly Using Biologically-Inspired Multiagent Control”, R. Nagpal, ACM Joint Conference on Autonomous Agents and Multi- Agent Systems (AAMAS), Bologna, Italy, July And “Programmable Self-Assembly: Constructing Global Shape Using Biologically- Inspired Local Interactions and Origami Mathematics”, Radhika Nagpal, PhD Thesis, MIT Artificial Intelligence Laboratory Technical Memo , June 2001.

Significantly different approach to the design of self- organizing systems: the desired global shape is specified using an abstract geometry-based language, and the agent program is directly compiled from the global specification. Programmable Self-Assembly: Global Shape Formation

Overview Epithelial Cell Morphogenesis And Drosophila Cell Differentiation Geometry and Origami Mathematics Robust, Programmable Shape Formation Achieving a Global Action using Local Behavior and Interactions Generative Program Instructing in terms of Global Actions

Lessons from Developmental Biology Complex structures from cells with identical DNA Emergent global consequences from strictly local interactions Lessons from Origami Mathematics and Geometry Generative program for scale-independent shape formation using geometry-based language Simple, yet expressive enough to generate wide variety of shapes and patterns

Programmable Cell Sheet

Cell computation model Autonomous Identical program Local communication Local sensing, actuation Limited resources, no global identifiers No global coordinates No global clock

Huzita’s Axioms of Origami

Biologically Inspired Primitives Gradients: Neighborhood Query: Polarity Inversion: Cell-to-cell Contact: Flexible Folding: fold apical or basal surface

Huzita’s Axioms Implemented by Cells

An Example: Origami Cup

An Example: Origami Cup - Unfolded View

Robustness Cell programs are robust –Axioms produce reasonably straight and accurate lines –Scale Independence –Without relying on: regular grids, global coordinates, unique global identifiers, or synchronous operation Robustness achieved by: –Large and dense populations (expected neighbors > 15), depending on average behavior, no centralized control

Interference between gradients from two sources. The concentric bands represent the radially- symmetric uncertainty in distance estimates from a gradient from a sincgle source. The composition of two gradients causes the error to vary spatially. Spatial Variance of Error Accuracy decreases as: Length of crease Distance between sources increases

Analysis of Resource Consumption Resource consumption Cell code conservation

Limitations No compilation has been specified for axioms A5 and A6. Not completely free of centralized control or global coordinates –p1, l1, etc. Not entirely identical cell programs –A combination of pre-programmed internal state and case-based programming (“if c1 (…)”, “if c3 (…)”, etc.) can always make up for specialized programs. Not completely Asynchronous –Global Barrier Synchronization during each fold / crease completion –Calibrated estimate used during distributed crease formation Failure of shape formation sometimes possible due to: –Failure of entire groups of cells forming points or lines, and large regional failures or holes –Failure of barrier synchronization across axioms –Gradient (and thus, region) leakage (caused due to discontinuity of cells) –Absence of cells at intersections (caused due to insufficiently dense cells and wide creases) –Large spatial variance of error –Malicious Cells