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