Sampling-based Stochastic Optimal Control with Metric Interval Temporal Logic Specifications

This paper describes a method to find optimal policies for stochastic dynamic systems that maximise the probability of satisfying real-time properties. The method consists of two phases. In the first phase, a coarse abstraction of the original system is created. In each region of the abstraction, a sampling-based algorithm is utilised to compute local policies that allow the system to move between regions. Then, in the second phase, the selection of a policy in each region is obtained by solving a reachability problem on the Cartesian product between the abstraction and a timed automaton representing a real-time specification given as a metric interval temporal logic formula. In contrast to current methods that require a fine abstraction, the proposed method achieves computational tractability by modelling the coarse abstraction of the system as a bounded-parameter Markov decision process (BMDP). Moreover, once the BMDP is created, this can be reused for new specifications assuming the same stochastic system and workspace. The method is demonstrated with an autonomous driving example.