Stochastic Control for Self-Assembly of XBots

Abstract

We propose a stochastic, decentralized algorithm for the self-assembly of a group of modular robots into a geometric shape. The method is inspired by chemical kinetics simulations, particularly, the Gillespie algorithm [1, 2] that is widely used in biochemistry, and is specifically designed for modules with dynamic constraints, such as the XBot [3]. The most important feature of our algorithm is that all modules are identical and all decision making is local. Individual modules decide how to move based only on information available to them and their neighbors and the geometric, kinematic and dynamic constraints. Each module knows the details of the goal configuration, keeps track of its own location, and communicates position information locally with adjacent modules only when modules in their vicinity have reconfigured. We show that this stochastic method leads to trajectories with convergence comparable to those obtained from a brute-force exploration of the state space. However, the computational power (speed and memory) requirements are independent of the number of modules, while the brute-force approach scales quadratically with the number of modules. We present the schematic of the modules, preliminary experimental results to illustrate the basic moves, and simulation results to demonstrate the efficacy of the algorithm.