  Autonomous agents operating in perceptually aliased environments should
ideally be able to solve the data association problem. Yet, planning for future
actions while considering this problem is not trivial. State of the art
approaches therefore use multi-modal hypotheses to represent the states of the
agent and of the environment. However, explicitly considering all possible data
associations, the number of hypotheses grows exponentially with the planning
horizon. As such, the corresponding Belief Space Planning problem quickly
becomes unsolvable. Moreover, under hard computational budget constraints, some
non-negligible hypotheses must eventually be pruned in both planning and
inference. Nevertheless, the two processes are generally treated separately and
the effect of budget constraints in one process over the other was barely
studied. We present a computationally efficient method to solve the nonmyopic
Belief Space Planning problem while reasoning about data association. Moreover,
we rigorously analyze the effects of budget constraints in both inference and
planning.
