Theoretical foundations of high-speed robot team deployment

In this paper we study the multi-robot deployment problem under hard temporal constraints. After proposing a model for this task, we consider the simplest deployment algorithm and we analyze the relationship between three fundamental parameters, the temporal deadline, the probability of success, and the number of robots. Because an exact analysis of even the simplest algorithm is computationally intractable, we derive an approximate bound leading to performance curves useful to answer design questions (how many robots are needed to get a certain performance guarantee?) or analysis questions (what is the probability of success given a certain deadline and number of robots?) Simulations show that the bounds are sharp and provide a useful tool to predict team deployment performance and tradeoffs.