  In this letter, we consider a distributed submodular maximization problem for
multi-robot systems when attacked by adversaries. One of the major challenges
for multi-robot systems is to increase resilience against failures or attacks.
This is particularly important for distributed systems under attack as there is
no central point of command that can detect, mitigate, and recover from
attacks. Instead, a distributed multi-robot system must coordinate effectively
to overcome adversarial attacks. In this work, our distributed submodular
action selection problem models a broad set of scenarios where each robot in a
multi-robot system has multiple action selections that may fulfill a global
objective, such as exploration or target tracking. To increase resilience in
this context, we propose a fully distributed algorithm to guide each robot's
action selection when the system is attacked. The proposed algorithm guarantees
performance in a worst-case scenario where up to a portion of the robots
malfunction due to attacks. Importantly, the proposed algorithm is also
consistent, as it is shown to converge to the same solution as a centralized
method. Finally, a distributed resilient multi-robot exploration problem is
presented to confirm the performance of the proposed algorithm.
