Enhancing tolerance to unexpected jumps in GR(1) games

Abstract

zWhen used as part of a hybrid controller, nite-memory strategies synthesized from linear-time temporal logic (LTL) speci cations 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 rst step, we show robustness to certain unexpected transitions that occur in a nite manner, i.e., despite a certain number of unexpected jumps, the sequence of states obtained will still meet a stricter speci cation and hence the original speci cation. 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. CCS CONCEPTS•Computing methodologies →Arti cial intelligence; •So ware and its engineering →Formal methods;

Control and Discovery of Environment Behaviour

“…The community studying motion and high-level mission planning (e.g., [25], [26]) has recently addressed the problem of recovery from inaccurate description of the environment [27], [28], [29], [30], [31], [32], partial models of the environment [33] and model inference [34], [35]. In the first group of works, synthesis procedures are adapted to tolerate modelling assumption violations.…”

“…The work presented in [27], considers uncertainties in open finite transition systems due to unmodeled transitions. In the same vein, [28] proposes a way to synthesise robust controllers that will be able to win even if certain unexpected transitions that occur a finite number of times. Similarly, [29] solves the problem of synthesising error resilient systems from specifications in temporal logic.…”

Contracts of Reactivity

“…For instance, [17] exploits "locality" to compute modal µ-calculus fixpoints [3] that enable patching system strategies in the presence of updated information about the game graph. Similarly, [10] discusses a way to recover from a finite number of unexpected actuation or sensing errors with pre-computed safe strategies that attempt to bring the system back to the nominal control trajectory. In addition to making specific assumptions on the environment, these methods also rely on the fact that such recovery strategies are always feasible for the original set of objectives.…”

Resilient abstraction-based controller design

“…Another approach to robust reactive synthesis considers particular specifications of the form A → G; in every environment that fulfills the assumption A the controller needs to enforce the property G. In this context robustness is for example understood w.r.t. assumption violations [4], [8], [10], hidden or missing inputs [3] or unexpected jumps in the game graph [6]. While the abstraction generated within our resilient ABCD method can be understood as a particular safety assumption A for the given synthesis problem interpreted as G, the assumption violations we consider are already explicitly modeled by automatically generated disturbance edges.…”