  Safety is crucial for robotic missions within an uncertain environment.
Common safety requirements such as collision avoidance are only
state-dependent, which can be restrictive for complex missions. In this work,
we address a more general formulation as safe-return constraints, which require
the existence of a return-policy to drive the system back to a set of safe
states with high probability. The robot motion is modeled as a Markov Decision
Process (MDP) with probabilistic labels, which can be highly non-ergodic. The
robotic task is specified as Linear Temporal Logic (LTL) formulas over these
labels, such as surveillance and transportation. We first provide theoretical
guarantees on the re-formulation of such safe-return constraints, and a
baseline solution based on computing two complete product automata.
Furthermore, to tackle the computational complexity, we propose a hierarchical
planning algorithm that combines the feature-based symbolic and temporal
abstraction with constrained optimization. It synthesizes simultaneously two
dependent motion policies: the outbound policy minimizes the overall cost of
satisfying the task with a high probability, while the return policy ensures
the safe-return constraints. The problem formulation is versatile regarding the
robot model, task specifications and safety constraints. The proposed
hierarchical algorithm is more efficient and can solve much larger problems
than the baseline solution, with only a slight loss of optimality. Numerical
validations include simulations and hardware experiments of a search-and-rescue
mission and a planetary exploration mission over various system sizes.
