Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point to each action and consequently to each situation. We show that in this approach, checking whether there is a reachable situation that satisfies a given formula is undecidable, even if the domain of discourse is restricted to a finite set of objects. We present an alternative approach based on well-established results from timed automata theory by introducing clocks as real-valued fluents with restricted successor state axioms and comparison operators. %that only allow comparisons against fixed rationals. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results on Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

Controlling Golog Programs against MTL Constraints

While Golog is an expressive programming language to control the high-level behavior of a robot, it is often tedious to use on a real robotic system. On an actual robot, the user needs to consider low-level details, such as enabling and disabling hardware components, e.g., a camera to detect objects for grasping. In other words, high-level actions usually pose implicit temporal constraints on the low-level platform, which are typically independent of the concrete program to be executed. In this paper, we propose to make these constraints explicit by modeling them as MTL formulas, which enforce the execution of certain low-level platform operations in addition to the main program. Based on results from timed automata controller synthesis, we describe a method to synthesize a controller that executes both the high-level program and the low-level platform operations concurrently in order to satisfy the MTL specification. This allows the user to focus on the high-level behavior without the need to consider low-level operations. We present an extension to Golog by clocks together with the required theoretical foundations as well as decidability results.