Epistemic planning based on Dynamic Epistemic Logic (DEL) allows agents to reason and plan from the perspective of other agents. The framework of DEL-based epistemic planning thereby has the potential to represent significant aspects of Theory of Mind in autonomous robots, and to provide a foundation for human-robot collaboration in which coordination is achieved implicitly through perspective shifts. In this paper, we build on previous work in epistemic planning with implicit coordination. We introduce a new notion of indistinguishability between epistemic states based on bisimulation, and provide a novel partition refinement algorithm for computing unique representatives of sets of indistinguishable states. We provide an algorithm for computing implicitly coordinated plans using these new constructs, embed it in a perceive-plan-act agent loop, and implement it on a robot. The planning algorithm is benchmarked against an existing epistemic planning algorithm, and the robotic implementation is demonstrated on human-robot collaboration scenarios requiring implicit coordination.

Previous research has claimed dynamic epistemic logic (DEL) to be a suitable formalism for representing essential aspects of a Theory of Mind (ToM) for an autonomous agent. This includes the ability of the formalism to represent the reasoning involved in false-belief tasks of arbitrary order, and hence for autonomous agents based on the formalism to become able to pass such tests. This paper provides evidence for the claims by documenting the implementation of a DEL-based reasoning system on a humanoid robot. Our implementation allows the robot to perform cognitive perspective-taking, in particular to reason about the first- and higher-order beliefs of other agents. We demonstrate how this allows the robot to pass a quite general class of false-belief tasks involving human agents. Additionally, as is briefly illustrated, it allows the robot to proactively provide human agents with relevant information in situations where a system without ToM-abilities would fail. The symbolic grounding problem of turning robotic sensor input into logical action descriptions in DEL is achieved via a perception system based on deep neural networks.