  This paper proposes a model-based framework to automatically and efficiently
design understandable and verifiable behaviors for swarms of robots. The
framework is based on the automatic extraction of two distinct models: 1) a
neural network model trained to estimate the relationship between the robots'
sensor readings and the global performance of the swarm, and 2) a probabilistic
state transition model that explicitly models the local state transitions
(i.e., transitions in observations from the perspective of a single robot in
the swarm) given a policy. The models can be trained from a data set of
simulated runs featuring random policies. The first model is used to
automatically extract a set of local states that are expected to maximize the
global performance. These local states are referred to as desired local states.
The second model is used to optimize a stochastic policy so as to increase the
probability that the robots in the swarm observe one of the desired local
states. Following these steps, the framework proposed in this paper can
efficiently lead to effective controllers. This is tested on four case studies,
featuring aggregation and foraging tasks. Importantly, thanks to the models,
the framework allows us to understand and inspect a swarm's behavior. To this
end, we propose verification checks to identify some potential issues that may
prevent the swarm from achieving the desired global objective. In addition, we
explore how the framework can be used in combination with a "standard"
evolutionary robotics strategy (i.e., where performance is measured via
simulation), or with online learning.
