Opportunistic Qualitative Planning in Stochastic Systems with Preferences over Temporal Logic Objectives

Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this work, we study preference-based planning in a stochastic system modeled as a Markov decision process, subject to a possible incomplete preference over temporally extended goals. Our contributions are three folds: First, we introduce a preference language to specify preferences over temporally extended goals. Second, we define a novel automata-theoretic model to represent the preorder induced by given preference relation. The automata representation of preferences enables us to develop a preference-based planning algorithm for stochastic systems. Finally, we show how to synthesize opportunistic strategies that achieves an outcome that improves upon the current satisfiable outcome, with positive probability or with probability one, in a stochastic system. We illustrate our solution approaches using a robot motion planning example.