  In multi-robot multi-target tracking, robots coordinate to monitor groups of
targets moving about an environment. We approach planning for such scenarios by
formulating a receding-horizon, multi-robot sensing problem with a mutual
information objective. Such problems are NP-Hard in general. Yet, our objective
is submodular which enables certain greedy planners to guarantee
constant-factor suboptimality. However, these greedy planners require robots to
plan their actions in sequence, one robot at a time, so planning time is at
least proportional to the number of robots. Solving these problems becomes
intractable for large teams, even for distributed implementations. Our prior
work proposed a distributed planner (RSP) which reduces this number of
sequential steps to a constant, even for large numbers of robots, by allowing
robots to plan in parallel while ignoring some of each others' decisions.
Although that analysis is not applicable to target tracking, we prove a similar
guarantee, that RSP planning approaches performance guarantees for fully
sequential planners, by employing a novel bound which takes advantage of the
independence of target motions to quantify effective redundancy between robots'
observations and actions. Further, we present analysis that explicitly accounts
for features of practical implementations including approximations to the
objective and anytime planning. Simulation results -- available via open source
release -- for target tracking with ranging sensors demonstrate that our
planners consistently approach the performance of sequential planning (in terms
of position uncertainty) given only 2--8 planning steps and for as many as 96
robots with a 24x reduction in the number of sequential steps in planning.
Thus, this work makes planning for multi-robot target tracking tractable at
much larger scales than before, for practical planners and general tracking
problems.
