Optimal Receding Horizon Control for Finite Deterministic Systems with Temporal Logic Constraints

In this paper, we develop a provably correct optimal control strategy for a finite deterministic transition system. By assuming that penalties with known probabilities of occurrence and dynamics can be sensed locally at the states of the system, we derive a receding horizon strategy that minimizes the expected average cumulative penalty incurred between two consecutive satisfactions of a desired property. At the same time, we guarantee the satisfaction of correctness specifications expressed as Linear Temporal Logic formulas. We illustrate the approach with a persistent surveillance robotics application.Comment: Technical report accompanying the ACC 2013 pape

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study

Temporal logic motion planning using POMDPs with parity objectives: Case study paper

We consider a case study of the problem of deploying an autonomous air vehicle in a partially observable, dynamic, indoor environment from a specification given as a linear temporal logic (LTL) formula over regions of interest. We model the motion and sensing capabilities of the vehicle as a partially observable Markov decision process (POMDP). We adapt recent results for solving POMDPs with parity objectives to generate a control policy. We also extend the existing framework with a policy minimization technique to obtain a better implementable policy, while preserving its correctness. The proposed techniques are illustrated in an experimental setup involving an autonomous quadrotor performing surveillance in a dynamic environment