On Stochastic Self-Assembly of Underwater Robots

We present a rule-based approach which incorporates a state machine in a novel manner to carry out self-assembly in underwater environments. The rules formulated along with the state machine govern the manner in which individual robots combine to generate shapes like a straight line, a `T' alphabet and a two sided pyramid. We analyze the factors that affect the time taken to complete self-assembly via simulations. Finally, we adopt a statistical dynamics approach to calculate the combination rates of the robots and show how it yields a Markov process model. We use the Markov model to predict the assembly process and show that it is similar to carrying out the full mechanics-based simulation.