Efficient reactive controller synthesis for a fragment of linear temporal logic

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Eric M. Wolff, Ufuk Topcu, and Richard M. Murray
Submitted, 2013 International Conference on Robotics and Automation (ICRA)

Motivated by robotic motion planning, we develop a framework for control policy synthesis for both non-deterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, surveillance, and persistent coverage. This fragment is computationally efficient; the complexity of control policy synthesis is a doubly-exponential improvement over standard linear temporal logic for both non-deterministic transition systems and Markov decision processes. This improvement is possible since we compute directly on the original system, as opposed to the automata-based approach commonly used for linear temporal logic. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1).