Control in Belief Space with Temporal Logic Specifications

Vasile Cristian Ioan, Leahy Kevin, Cristofalo Eric, Jones Austin, Schwager Mac, and Belta Calin. Control in Belief Space with Temporal Logic Specifications. In IEEE Conference on Decision and Control (CDC), page (accepted), Las Vegas, NV, USA, December 2016. link.

Published date: 
Monday, December 12, 2016

In this paper, we present a sampling-based algorithm to synthesize control policies with temporal and uncertainty constraints. We introduce a specification language called Gaussian Distribution Temporal Logic (GDTL), an extension of Boolean logic that allows us to incorporate temporal evolution and noise mitigation directly into the task specifications, e.g. "Go to region A and reduce the variance of your state estimate below 0.1 $m^2$." Our algorithm generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Furthermore, conventional automata-based methods become tractable. Switching control policies are then computed using a product Markov Decision Process (MDP) between the transition system and the Rabin automaton encoding the task specification. We present algorithms to translate a GDTL formula to a Rabin automaton and to efficiently construct the product MDP by leveraging recent results from incremental computing. Our approach is evaluated in hardware experiments using a camera network and ground robot.