  Multi-robot belief space planning (MR-BSP) is essential for reliable and safe
autonomy. While planning, each robot maintains a belief over the state of the
environment and reasons how the belief would evolve in the future for different
candidate actions. Yet, existing MR-BSP works have a common assumption that the
beliefs of different robots are consistent at planning time. Such an assumption
is often highly unrealistic, as it requires prohibitively extensive and
frequent communication capabilities. In practice, each robot may have a
different belief about the state of the environment. Crucially, when the
beliefs of different robots are inconsistent, state-of-the-art MR-BSP
approaches could result in a lack of coordination between the robots, and in
general, could yield dangerous, unsafe and sub-optimal decisions. In this
paper, we tackle this crucial gap. We develop a novel decentralized algorithm
that is guaranteed to find a consistent joint action. For a given robot, our
algorithm reasons for action preferences about 1) its local information, 2)
what it perceives about the reasoning of the other robot, and 3) what it
perceives about the reasoning of itself perceived by the other robot. This
algorithm finds a consistent joint action whenever these steps yield the same
best joint action obtained by reasoning about action preferences; otherwise, it
self-triggers communication between the robots. Experimental results show
efficacy of our algorithm in comparison with two baseline algorithms.
