Realizability Is Not Enough: Encoding, Liveness, and Auditing of Synthesized Robot Supervisors

Abstract:High-level robotic supervisors coordinate capabilities whose reported outcomes determine the robot's next action. Reactive synthesis can generate such supervisors with formal guarantees, but deployment requires more than proving a Generalized Reactivity (1) (GR(1)) specification realizable. Designers must encode failure-prone capabilities, choose liveness assumptions that match retry intent, audit strategies, and translate them into robot software. We present an open-source pipeline for Robot Operating System (ROS) 2 Flexible Behavior Engine (FlexBE) supervisors that generates capability-based GR(1) specifications, analyzes assumptions before synthesis, audits strategies, reduces states with a behavior-preservation proof, and emits executable state machines. Across four case studies (six comparisons), including hardware on two quadcopter platforms, we compare enumerated and one-hot encodings and two liveness formulations. Under the tested backend, enumerated encoding usually synthesizes faster, although fewer propositions do not reliably predict smaller controllers or lower symbolic cost. System-Goal without pending memory is the only liveness treatment confirmed to yield executable controllers under both encodings across the reported grid; Fair-Outcome can permit realizable cycles without designer-intended completion. For this backend and model, we recommend enumerated encoding with System-Goal and auditing every realized strategy, since proposition count and realizability do not measure deployability. The auditor is sound and complete for four structural defect classes (protocol violations, deadlocks, bounded-failure violations, goal-unreachable traps) but is not a general liveness verifier, and the reduction preserves capability-level behavior. Together, these stages narrow the gap between formal realizability and controllers that pass protocol and structural-progress checks.

88 pages, 14 figures. Includes detailed technical appendices and experimental results for four application domains

Robotics (cs.RO); Logic in Computer Science (cs.LO)

I.2.9; D.2.4; F.3.1

arXiv:2609.30460 [cs.RO]

(or arXiv:2609.30460v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.30460 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.