  This paper presents a novel distributed robust optimization scheme for
steering distributions of multi-agent systems under stochastic and
deterministic uncertainty. Robust optimization is a subfield of optimization
which aims in discovering an optimal solution that remains robustly feasible
for all possible realizations of the problem parameters within a given
uncertainty set. Such approaches would naturally constitute an ideal candidate
for multi-robot control, where in addition to stochastic noise, there might be
exogenous deterministic disturbances. Nevertheless, as these methods are
usually associated with significantly high computational demands, their
application to multi-agent robotics has remained limited. The scope of this
work is to propose a scalable robust optimization framework that effectively
addresses both types of uncertainties, while retaining computational efficiency
and scalability. In this direction, we provide tractable approximations for
robust constraints that are relevant in multi-robot settings. Subsequently, we
demonstrate how computations can be distributed through an Alternating
Direction Method of Multipliers (ADMM) approach towards achieving scalability
and communication efficiency. Simulation results highlight the performance of
the proposed algorithm in effectively handling both stochastic and
deterministic uncertainty in multi-robot systems. The scalability of the method
is also emphasized by showcasing tasks with up to 100 agents. The results of
this work indicate the promise of blending robust optimization, distribution
steering and distributed optimization towards achieving scalable, safe and
robust multi-robot control.
