Identifying and exploiting tolerance to unexpected jumps in synthesized strategies for GR(1) specifications

Abstract— When used as part of a hybrid controller, finitememory strategies synthesized from LTL specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about this 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 characterize the tolerance of such hybrid controllers synthesized for generalized reactivity(1) specificationsto disturbances 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 obtain empirical computational and memory cost estimates.