  We propose a predictive runtime monitoring framework that forecasts the
distribution of future positions of mobile robots in order to detect and avoid
impending property violations such as collisions with obstacles or other
agents. Our approach uses a restricted class of temporal logic formulas to
represent the likely intentions of the agents along with a combination of
temporal logic-based optimal cost path planning and Bayesian inference to
compute the probability of these intents given the current trajectory of the
robot. First, we construct a large but finite hypothesis space of possible
intents represented as temporal logic formulas whose atomic propositions are
derived from a detailed map of the robot's workspace. Next, our approach uses
real-time observations of the robot's position to update a distribution over
temporal logic formulae that represent its likely intent. This is performed by
using a combination of optimal cost path planning and a Boltzmann noisy
rationality model. In this manner, we construct a Bayesian approach to
evaluating the posterior probability of various hypotheses given the observed
states and actions of the robot. Finally, we predict the future position of the
robot by drawing posterior predictive samples using a Monte-Carlo method. We
evaluate our framework using two different trajectory datasets that contain
multiple scenarios implementing various tasks. The results show that our method
can predict future positions precisely and efficiently, so that the computation
time for generating a prediction is a tiny fraction of the overall time
horizon.
