  This paper proposes Distributed Model Predictive Covariance Steering (DMPCS),
a novel method for safe multi-robot control under uncertainty. The scope of our
approach is to blend covariance steering theory, distributed optimization and
model predictive control (MPC) into a single methodology that is safe, scalable
and decentralized. Initially, we pose a problem formulation that uses the
Wasserstein distance to steer the state distributions of a multi-robot team to
desired targets, and probabilistic constraints to ensure safety. We then
transform this problem into a finite-dimensional optimization one by utilizing
a disturbance feedback policy parametrization for covariance steering and a
tractable approximation of the safety constraints. To solve the latter problem,
we derive a decentralized consensus-based algorithm using the Alternating
Direction Method of Multipliers (ADMM). This method is then extended to a
receding horizon form, which yields the proposed DMPCS algorithm. Simulation
experiments on large-scale problems with up to hundreds of robots successfully
demonstrate the effectiveness and scalability of DMPCS. Its superior capability
in achieving safety is also highlighted through a comparison against a standard
stochastic MPC approach. A video with all simulation experiments is available
in https://youtu.be/Hks-0BRozxA.
