Online Horizon Selection in Receding Horizon Temporal Logic Planning

Temporal logics have proven effective for correct-by-construction synthesis of controllers for a wide range of applications. Receding horizon frameworks mitigate the computational intractability of reactive synthesis for temporal logic, but have thus far been limited by pursuing a single sequence of short horizon problems to the current goal. We propose a receding horizon algorithm for reactive synthesis that automatically determines a path to the currently pursued goal at runtime, in response to a nondeterministic environment. This is achieved by allowing each short horizon to have multiple local goals, and determining which local goal to pursue based on the current global goal, currently perceived environment and a pre-computed invariant dependent on each global goal. We demonstrate the utility of this additional flexibility in grant-response tasks, using a search-and-rescue example. Moreover, we show that these goal-dependent invariants mitigate the conservativeness of the receding horizon approach

Robust Control of Uncertain Markov Decision Processes with Temporal Logic Specifications

We present a method for designing robust controllers for dynamical systems with linear temporal logic specifications. We abstract the original system by a finite Markov Decision Process (MDP) that has transition probabilities in a specified uncertainty set. A robust control policy for the MDP is generated that maximizes the worst-case probability of satisfying the specification over all transition probabilities in the uncertainty set. To do this, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming allows us to solve for a $\epsilon$-suboptimal robust control policy with time complexity $O(\log 1/\epsilon)$ times that for the non-robust case. We then implement this control policy on the original dynamical system