Enhancing tolerance to unexpected jumps in GR(1) games

Abstract

When used as part of a hybrid controller, finite-memory strategies synthesized from linear-time temporal logic (LTL) specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about the underlying model, there may exist unexpected trajectories that manifest as unexpected transitions under control of the strategy. While some disturbances can be captured by augmenting the dynamics model, such approaches may be conservative in that bisimulations may fail to exist for which strategies can be synthesized. In this paper, we consider games of the GR(1) fragment of LTL, and we characterize the tolerance of hybrid controllers to perturbations that appear as unexpected jumps (transitions) to states in the discrete strategy part of the controller. As a first step, we show robustness to certain unexpected transitions that occur in a finite manner, i.e., despite a certain number of unexpected jumps, the sequence of states obtained will still meet a stricter specification and hence the original specification. Additionally, we propose algorithms to improve robustness by increasing tolerance to additional disturbances. A robot gridworld example is presented to demonstrate the application of the developed ideas and also to perform empirical analysis.