  Next-generation autonomous systems must execute complex tasks in uncertain
environments. Active perception, where an autonomous agent selects actions to
increase knowledge about the environment, has gained traction in recent years
for motion planning under uncertainty. One prominent approach is planning in
the belief space. However, most belief-space planning starts with a known
reward function, which can be difficult to specify for complex tasks. On the
other hand, symbolic control methods automatically synthesize controllers to
achieve logical specifications, but often do not deal well with uncertainty. In
this work, we propose a framework for scalable task and motion planning in
uncertain environments that combines the best of belief-space planning and
symbolic control. Specifically, we provide a
counterexample-guided-inductive-synthesis algorithm for probabilistic temporal
logic over reals (PRTL) specifications in the belief space. Our method
automatically generates actions that improve confidence in a belief when
necessary, thus using active perception to satisfy PRTL specifications.
