LTL control in uncertain environments with probabilistic satisfaction guarantees*
Chu (Dennis) Ding, Xu
Smith, Stephen L.
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Citation (published version)Xu Chu (Dennis) Ding, Stephen L. Smith, Calin Belta, Daniela Rus. 2011. "LTL Control in Uncertain Environments with Probabilistic Satisfaction Guarantees*." IFAC Proceedings Volumes, v. 44, issue 1, pp. 3515 - 3520.
We present a method to generate a robot control strategy that maximizes the probability to accomplish a task. The task is given as a Linear Temporal Logic (LTL) formula over a set of properties that can be satisfied at the regions of a partitioned environment. We assume that the probabilities with which the properties are satisfied at the regions are known, and the robot can determine the truth value of a proposition only at the current region. Motivated by several results on partitioned-based abstractions, we assume that the motion is performed on a graph. To account for noisy sensors and actuators, we assume that a control action enables several transitions with known probabilities. We show that this problem can be reduced to the problem of generating a control policy for a Markov Decision Process (MDP) such that the probability of satisfying an LTL formula over its states is maximized. We provide a complete solution for the latter problem that builds on existing results from probabilistic model checking. We include an illustrative case study.