  Consider an agent acting to achieve its temporal goal, but with a "trembling
hand". In this case, the agent may mistakenly instruct, with a certain
(typically small) probability, actions that are not intended due to faults or
imprecision in its action selection mechanism, thereby leading to possible goal
failure. We study the trembling-hand problem in the context of reasoning about
actions and planning for temporally extended goals expressed in Linear Temporal
Logic on finite traces (LTLf), where we want to synthesize a strategy (aka
plan) that maximizes the probability of satisfying the LTLf goal in spite of
the trembling hand. We consider both deterministic and nondeterministic
(adversarial) domains. We propose solution techniques for both cases by relying
respectively on Markov Decision Processes and on Markov Decision Processes with
Set-valued Transitions with LTLf objectives, where the set-valued probabilistic
transitions capture both the nondeterminism from the environment and the
possible action instruction errors from the agent. We formally show the
correctness of our solution techniques and demonstrate their effectiveness
experimentally through a proof-of-concept implementation.
