Phase-preserving barrier projection of rhythmic references for safety-critical quadrotor flight

Recurring quadrotor missions such as orbit inspection and perimeter sweeping require references that repeat in phase while respecting obstacles and geofence limits. Sending an unsafe periodic reference directly to a downstream safety filter makes the plant-level filter correct the same unsafe command every cycle. This paper formulates a phase-preserving reference projection: at each sample, the nominal oscillator velocity is projected onto the admissible directions of an eroded safe set, while a separate internal clock advances at its prescribed rate. The projected reference is then tracked by an actuator-constrained plant safety filter with a residual-acceleration margin covering wind, mass mismatch, and inner-loop realization error. The analysis proves invariance of the eroded reference set in continuous time, quantifies the effect of both relaxation variables, gives a robust high-order plant safety result, and states a tracking-tube condition connecting the two layers. Full rigid-body simulations use a geometric attitude loop and a 0.01 s main sampling period. In the nominal obstacle scenario, the proposed controller maintains 0.269 m minimum clearance, preserves the full 10.44 rad phase advance, and reduces integrated plant-level intervention by \(45.1\%\) , from 21.855 m/s for plant-only robust filtering to 11.995 m/s. Predictive, governor, and reachability/tube-inspired baselines, a wind sweep, and inertia-mismatch cases are also reported. These numerical results apply to the tested operating envelope; they are not hardware-flight or global intersample-safety claims.