ONDAS — Oscillating Normalized Dynamic Adaptive Stabilization

The Core Principle

A fixed-wing or conventional aircraft generates control forces continuously — a control surface deflection or RPM change produces a steady-state moment. An ornithopter does not. Every gram of thrust, every Newton of torque, is phase-bound within the wingbeat cycle. The same force impulse applied at different points in the stroke produces fundamentally different results.

ONDAS acknowledges this reality and modulates stabilization effort synchronously with the flapping cycle.

Cadence — The Timing Brain

Cadence is the most critical ONDAS filter because it determines when correction happens within each wingbeat.

Cadence shifts the modulation window to align with the phase where the aerodynamic lever arm is longest. Wrong cadence = fighting wing physics. Correct cadence = every milliwatt becomes control authority.

Parameters

Ferocity P — Immediate Asymmetric Thrust

Ferocity P increases the waveform squareness (trapezoidal shaping: dwell at ±1, cosine ramp between) proportionally to the current PID error.

• More thrust on one side → immediate moment
• The braked wing at stroke-end experiences induced drag — this is the counter-moment
• Effect: direct, proportional, immediate

Ferocity D — Anticipatory Drag Exploitation

Ferocity D completes the picture. Where P provides thrust asymmetry, D leverages the drag of the contralateral wing as a brake.

• Reads error rate of change and anticipates
• Can deliberately exploit the drag of a slowed wing for yaw/pitch moments
• P+D together create a differential moment pair — thrust on side A, drag on side B — more efficient than thrust-only

Three Ways Cadence/Ferocity D Increases Ferocity

1. Direct — D boosts P during rapid error change

In gusts or aggressive maneuvers, error_rate is large. D multiplies this and adds to base ferocity. The wing becomes sharper (more trapezoidal) because P+D together demand more squareness than P alone. Result: maximum authority precisely when critical.

2. Indirect — Cadence shifts the leverage point

Cadence modulates when in the cycle ferocity acts. Moving the window into a more aerodynamically sensitive phase (e.g., downstroke center vs. upstroke end) means the same ferocity value produces more effect — effectively amplification without numerical change.

3. Combinatorial — D × Cadence during stall recovery

In a stall: high sink rate → D detects the rate → increases ferocity. Simultaneously, cadence shifts modulation into the downstroke phase where the wing has maximum bite. The interplay: D provides the force, cadence the right moment. Without cadence, D-force arrives at the wrong phase and dissipates uselessly.

Additional ONDAS Parameters

The New Generation: Statistical Envelope and Order Tracker

The eight layers above are the oscillator domain — they modulate the wingbeat. Around them, two measurement modules now form the statistical envelope that schedules the layers and adapts them online:

flowchart LR
    e["Attitude error"] --> M["ondas_metrics<br/>λ_e(s) · q90 · weak-L²<br/>phase envelope"]
    e --> T["ondas_tracker<br/>Vold–Kalman, follows ω(t)"]
    T -->|"b"| G["Consensus gate<br/>r vs. lock-in sinθ"]
    G -->|"α ∈ [−1,+1]"| R["Resonance replace-blend"]
    M -->|"q90"| W["Anti-windup I-clamp"]
    M -.->|"q90 (roadmap)"| D["D-cutoff adaptation"]

• ondas_metrics (B) — a 32-bin survival-function histogram of |error| per axis (λ_e(s), log-spaced, exponential leak τ ≈ 1 s) providing q90, the weak-L² tail norm and the tail mass; plus a 16-bin Poincaré phase envelope sampled at stroke reversals with a golden-angle rotation — the synchronous residual, logged to Blackbox.
• ondas_tracker (A) — a Vold–Kalman order tracker: a 2nd-order resonator (ζ = 0.06, Q ≈ 8.3) whose coefficients follow the instantaneous wingbeat frequency per sample, so it keeps extracting the flap-synchronous error component under throttle sweeps where fixed filters detune. Feed is pre-resonance (open loop — it never sees its own contribution).
• Consensus gate — the tracker may take over the resonance boost only when it and the independent lock-in reference agree: correlation r = EMA(b·sinθ)/√(EMA(sin²θ)·EMA(b²)) with a soft-knee over r = 0.3, slow in / fast out. At α = 0 the legacy resonance path is restored exactly.
• Substrate — the flapping amplitude uses a Marcinkiewicz-consistent geometric soft-knee (no authority kink), and the I-branch is anti-windup censored at κ·q90 so BALANCE and SAUDADE never absorb gust spikes as learned trim.

Full mathematics, simulated testing and build verification: see the development article below.

Analogy

Cadence is the conductor. Ferocity P and D are the instruments.

Without a conductor, they play — but not together. With one, noise becomes music.

See Also

• ONDAS Development — Mathematical Methods and Simulated Testing — the envelope/tracker generation
• ONDAS Tuning Guide — practical tuning procedure
• MSP Protocol — wire format for ONDAS parameters
• Flight Profiles — profile-aware ONDAS configuration