Controller Synthesis for Golog Programs over Finite Domains with Metric Temporal Constraints
This work addresses the challenge of adapting abstract robot programs to real-world hardware constraints, providing a decidable synthesis procedure for roboticists.
The paper tackles the problem of synthesizing controllers for Golog programs on robots by incorporating metric temporal constraints, reducing it to MTL synthesis and proving that the synthesized controller preserves the original program's effects while satisfying all constraints.
Executing a Golog program on an actual robot typically requires additional steps to account for hardware or software details of the robot platform, which can be formulated as constraints on the program. Such constraints are often temporal, refer to metric time, and require modifications to the abstract Golog program. We describe how to formulate such constraints based on a modal variant of the Situation Calculus. These constraints connect the abstract program with the platform models, which we describe using timed automata. We show that for programs over finite domains and with fully known initial state, the problem of synthesizing a controller that satisfies the constraints while preserving the effects of the original program can be reduced to MTL synthesis. We do this by constructing a timed automaton from the abstract program and synthesizing an MTL controller from this automaton, the platform models, and the constraints. We prove that the synthesized controller results in execution traces which are the same as those of the original program, possibly interleaved with platform-dependent actions, that they satisfy all constraints, and that they have the same effects as the traces of the original program. By doing so, we obtain a decidable procedure to synthesize a controller that satisfies the specification while preserving the original program.