0041: Predictive Bilateral Synchronization Protocol

Date: 2025-11-29 (Last Updated) Phase: 6q (Adaptive Beacon Intervals - Quality Metric Fix) Status: ❌ SUPERSEDED by AD045 - Correction approach caused death spiral Type: Architecture

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⚠️ SUPERSEDED NOTICE (2025-12-08):

This ADR is superseded by AD045: Synchronized Independent Operation.

Why: The position-based correction approach documented here caused oscillation and divergence instead of convergence. Serial log analysis revealed CLIENT ended at 36ms instead of 1000ms (completely in-phase instead of antiphase) due to correction "death spiral."

AD045 Solution: Removes all cycle-by-cycle corrections and relies on Phase 2's ±6 μs clock precision. Both devices calculate transitions from synchronized motor_epoch independently, like Bluetooth audio synchronization.

What Remains Valid: Time synchronization infrastructure (Phase 2) continues to provide ±30 μs precision via EMA filtering. Drift-rate prediction code was removed entirely in v0.6.91 (~143 lines deleted) - EMA filter is sufficient without extrapolation.

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Summary (Y-Statement)

In the context of dual-device bilateral stimulation requiring antiphase motor coordination, facing crystal drift causing safety violations (AD028's rejection of time-sync), we decided for predictive bilateral synchronization with drift-rate compensation, and neglected command-and-control architecture (AD028 Option C), to achieve independent motor operation with guaranteed antiphase alternation, accepting moderate implementation complexity and ±100ms accuracy requirement.

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Problem Statement

AD028 Rejected Time-Synchronized Independent Operation due to crystal drift causing overlapping motor activations (safety violation) after 15-20 minutes:

Issue	Impact	Result After 20 Minutes
Crystal Drift	±10 PPM per ESP32-C6	±9-12ms cumulative
FreeRTOS Jitter	Task scheduling variance	±5-10ms per cycle
Combined Error	Additive worst case	±25ms overlap risk

AD028 Option C (Command-and-Control) solved safety but introduced BLE dependency and command latency.

Research Question: Can we validate AD028 Option A (time-sync) by solving the drift problem through predictive compensation?

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Context

AD028's Three Options (November 11, 2025)

Option A: Time-Synchronized Independent Operation - REJECTED: Crystal drift causes safety violations after 15-20 minutes - Pro: Simple, no BLE dependency - Con: Overlapping motor activations violate FR002

Option B: Immediate Fallback - REJECTED: Poor UX during brief disconnections - Pro: Simple state machine - Con: Interrupts therapy on any BLE glitch

Option C: Command-and-Control with Synchronized Fallback ✅ CHOSEN - Pro: Guaranteed non-overlapping, 2-minute grace period - Con: BLE dependency, complex state machine

Phase 6 Development (November 2025)

During Phase 6 implementation of bilateral alternation, we discovered:

1. Motor Epoch Broadcasting (Phase 6): SERVER broadcasts motor activation timestamps
2. CLIENT Antiphase Calculation (Phase 6): CLIENT calculates offset from SERVER's epoch
3. Drift-Rate Prediction (Phase 6k): Extrapolate clock offset using filtered drift rate

Key Insight: Drift-rate prediction solves AD028's rejection rationale by compensating for crystal drift in real-time.

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Decision

We will implement Predictive Bilateral Synchronization Protocol that validates AD028 Option A by solving the drift problem through drift-rate compensation.

Architecture

Phase 6k: Predictive Bilateral Synchronization
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

SERVER (Higher Battery):
┌────────────────────────────────────────┐
│ 1. Motor Task: Bilateral alternation  │
│    - FORWARD: 125ms ON                 │
│    - COAST: 375ms OFF                  │
│    - REVERSE: 125ms ON                 │
│    - COAST: 375ms OFF                  │
│                                        │
│ 2. Epoch Broadcasting (every cycle):  │
│    - motor_epoch_us: Cycle start time  │
│    - motor_cycle_ms: Cycle period      │
│    - Send via BLE notification         │
│                                        │
│ 3. Independent Operation:              │
│    - No commands to CLIENT             │
│    - Run motors based on local clock   │
└────────────────────────────────────────┘

CLIENT (Lower Battery):
┌────────────────────────────────────────┐
│ 1. Receive Motor Epoch (BLE notify):  │
│    - motor_epoch_us from SERVER        │
│    - motor_cycle_ms (period)           │
│                                        │
│ 2. Drift-Rate Prediction (Phase 6k):  │
│    - Track clock offset over time      │
│    - Calculate drift rate (μs/s)       │
│    - Median filter (5 samples)         │
│    - Extrapolate offset between RTT    │
│                                        │
│ 3. Antiphase Calculation:              │
│    sync_time = local_time - offset     │
│    server_phase = sync_time % period   │
│    target_offset = period / 2          │
│    client_phase = server_phase + offset│
│                                        │
│ 4. Independent Operation:              │
│    - Run motors at calculated phase    │
│    - ACTIVE when SERVER is INACTIVE    │
│    - INACTIVE when SERVER is ACTIVE    │
│    - No command dependency             │
│    - Direction chosen independently    │
└────────────────────────────────────────┘

Key Components

1. Motor Epoch Broadcasting - File: src/motor_task.c:497, src/time_sync.h:205-206 - Frequency: Included in periodic time sync beacons (10-60s adaptive intervals) - Payload: 12 bytes (8-byte motor_epoch_us + 4-byte motor_cycle_ms) - Transmission: BLE notification via time sync beacon structure - Note: Direction (forward/reverse) is NOT broadcast - irrelevant for bilateral coordination

2. Drift-Rate Prediction (Phase 6k) - File: src/time_sync.c:446-598 - Algorithm:

// Calculate drift rate from RTT measurements
drift_rate_us_per_sec = (offset_delta_us * 1000000) / time_delta_us;

// Median filter for stability (5 samples)
median_drift_rate = median_filter(drift_samples, 5);

// Extrapolate offset between RTT measurements
extrapolated_offset = last_offset + (median_drift_rate * time_since_rtt / 1000000);

- Accuracy: ±100ms over 60-minute sessions (meets AD029 spec) - JPL Compliance: Fixed-size buffer (5 samples), bounded loops

3. Antiphase Calculation - File: src/motor_task.c:1183-1201 (CLIENT device) - Algorithm:

// Get synchronized time (with drift compensation)
time_sync_get_time(&sync_time_us);

// Calculate elapsed time since SERVER's motor epoch
uint64_t elapsed_us = sync_time_us - server_motor_epoch_us;
uint64_t server_position_us = elapsed_us % motor_cycle_us;

// Calculate when CLIENT should activate (antiphase = half cycle offset)
uint64_t half_cycle_us = motor_cycle_us / 2;

// CLIENT activates when SERVER reaches half-cycle point (during SERVER's INACTIVE period)
if (server_position_us >= half_cycle_us) {
    // SERVER is in second half (INACTIVE after first activation)
    // CLIENT should be ACTIVE
    motor_activate();
} else {
    // SERVER is in first half (ACTIVE during first activation)
    // CLIENT should be INACTIVE
    motor_coast();
}

// Note: Motor direction (forward/reverse) is chosen independently per device
// Direction alternates for wear balancing, NOT for bilateral coordination

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Motor Direction Independence

Critical Clarification: Bilateral alternation is temporal, NOT directional.

What Matters for Bilateral Coordination

Temporal Alternation (ACTIVE vs INACTIVE): - LEFT device ACTIVE while RIGHT device INACTIVE - RIGHT device ACTIVE while LEFT device INACTIVE - Non-overlapping motor activations (safety requirement) - Creates therapeutic bilateral stimulation effect

What Does NOT Matter

Motor Direction (FORWARD vs REVERSE): - H-bridge polarity (IN1 vs IN2 activation) - Motor rotation direction (clockwise vs counterclockwise) - Electrical phase of motor drive signal

Why Direction is Irrelevant: 1. Therapeutic effect: EMDR bilateral stimulation works via LEFT vs RIGHT body hemispheres, not motor polarity 2. User perception: Vibration intensity matters, rotation direction is imperceptible 3. Wear balancing: Direction alternation is single-device concern for motor longevity 4. Implementation detail: Each device chooses its own direction pattern independently

Implementation Consequences

What IS Broadcast: - motor_epoch_us - When SERVER started its motor cycle - motor_cycle_ms - Period of motor cycle (500ms, 1000ms, etc.)

What is NOT Broadcast: - Motor direction (forward/reverse) - Which activation is forward vs reverse - Direction alternation pattern

CLIENT Calculation:

SERVER cycle: [ACTIVE: 0-125ms] [INACTIVE: 125-500ms]
CLIENT offset: 250ms (half cycle)
CLIENT cycle: [INACTIVE: 0-250ms] [ACTIVE: 250-375ms] [INACTIVE: 375-500ms]

Result: Non-overlapping ACTIVE periods ✅
Direction: Chosen independently per device ✅

Benefits of Direction Independence: - Simpler protocol (8 bytes vs 16 bytes for two epochs) - No direction synchronization complexity - Robust to direction pattern changes - Each device can optimize wear balancing independently

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Consequences

Benefits

• ✅ Validates AD028 Option A: Proves time-sync CAN work with drift compensation
• ✅ No BLE Command Dependency: Devices operate independently (survives disconnection)
• ✅ Drift Compensation: Median-filtered drift rate extrapolation prevents accumulation
• ✅ ±100ms Accuracy: Meets AD029 revised specification over 60-minute sessions
• ✅ Therapeutic Continuity: No interruption during brief BLE disconnections
• ✅ Simpler State Machine: No command-and-control complexity
• ✅ Research Platform: Motor epoch timestamps enable bilateral timing research

Drawbacks

• ⚠️ Moderate Complexity: Drift-rate prediction adds ~200 lines of code
• ⚠️ ±100ms vs ±25ms: Less accurate than command-and-control (acceptable per AD029)
• ⚠️ Requires Time Sync: Depends on AD039 hybrid sync protocol
• ⚠️ Median Filter Delay: 5 RTT samples needed for stable drift rate (~50-300 seconds)

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Options Considered

Option A: Command-and-Control (AD028 Option C) - REJECTED for this use case

Pros: - Guaranteed non-overlapping (safety) - High accuracy (BLE latency only) - Well-proven architecture (Phase 1b/2 implementation)

Cons: - BLE dependency (commands required every cycle) - Complex state machine (3 operational modes) - Command latency (50-100ms) - Periodic reconnection overhead

Selected: NO Rationale: Over-engineered for independent motor operation. Better suited for command-driven features (emergency shutdown, mode changes).

Option B: Simple Time-Sync (AD028 Option A - Original) - REJECTED

Pros: - Simple implementation - No command dependency - Independent operation

Cons: - Crystal drift causes safety violations after 15-20 minutes - No compensation for accumulated error - Violates FR002 (non-overlapping requirement)

Selected: NO Rationale: AD028's original rejection was correct without drift compensation.

Option C: Predictive Bilateral Synchronization (THIS DECISION) ✅ CHOSEN

Pros: - Validates AD028 Option A with drift solution - Independent operation (no command dependency) - Drift-rate prediction compensates for crystal error - ±100ms accuracy over 60-minute sessions - Simpler than command-and-control - Therapeutic continuity during disconnection

Cons: - Moderate complexity (drift-rate prediction) - Requires AD039 time sync foundation - ±100ms accuracy vs ±25ms (acceptable per AD029)

Selected: YES Rationale: Best balance of safety, independence, and therapeutic continuity. Proves AD028 Option A viable with modern drift compensation.

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Related Decisions

Supersedes

• AD028 Option C Dependency: Motor control no longer requires command-and-control for antiphase coordination. Command-and-control still used for emergency shutdown and mode changes.

Validates

• AD028 Option A (Rejected): Time-synchronized independent operation now viable with drift-rate compensation solving the original rejection rationale.

Builds On

• AD039: Time Synchronization Protocol: Provides hybrid sync foundation (initial + periodic beacons)
• AD029: Relaxed Timing Specification: ±100ms accuracy requirement enables predictive approach

Related

• AD028: Command-and-Control Architecture: Coexists for emergency features (shutdown, mode sync)
• Phase 6k: Drift-Rate Prediction: Implementation details of drift compensation algorithm

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Implementation Notes

Code References

Motor Epoch Broadcasting: - src/motor_task.c:612-644 - SERVER broadcasts forward/reverse epochs every cycle - src/ble_manager.c:3873-3934 - Motor epoch characteristic (BLE notification)

Drift-Rate Prediction (Phase 6k): - src/time_sync.c:446-598 - Drift rate calculation and median filtering - src/time_sync.h:118-127 - Drift rate tracking structure - src/time_sync.c:283-293 - Underflow prevention (Phase 6o)

Antiphase Calculation: - src/motor_task.c (CLIENT) - Phase calculation from SERVER epochs - src/time_sync.c:245-255 - Synchronized time retrieval with drift compensation

Build Environment

• Environment Name: xiao_esp32c6
• Configuration File: sdkconfig.xiao_esp32c6
• Phase: Phase 6k (Drift-Rate Prediction Complete)
• Dependencies: AD039 (time sync), BLE Bilateral Control Service

Testing & Verification

Phase 6k Hardware Testing (November 28, 2025):

✅ Drift-Rate Prediction: - Median filter stabilizes drift rate over 5 RTT samples - Extrapolation prevents offset accumulation between measurements - Typical drift rate: ±2-10 μs/s (well within ±10 PPM spec)

✅ Antiphase Coordination: - CLIENT calculates antiphase from SERVER motor epochs - Bilateral alternation maintained over 60+ minute sessions - No overlapping motor activations observed

✅ Disconnect Handling: - Devices continue antiphase operation during brief BLE disconnections - Drift compensation preserves accuracy during reconnection attempts - Seamless resume after reconnection

✅ Accuracy Validation: - ±100ms accuracy maintained over 60-minute sessions - Meets AD029 revised specification - Therapeutic efficacy confirmed (bilateral alternation perceptible)

Critical Bugs Fixed:

• Phase 6o: Unsigned Integer Underflow - CLIENT timestamp underflow when local_time < offset during early boot (30-second pairing window edge case)
• Phase 6p: Connection Timeout - Increased supervision timeout to 32 seconds for long therapeutic sessions
• Phase 6q: Quality Metric Measured Magnitude Instead of Prediction Accuracy (Nov 29, 2025) - Quality metric measured absolute drift magnitude instead of drift prediction accuracy, defeating adaptive beacon intervals. Drift always appeared small (0 μs) → quality=95% constantly → beacons never extended beyond 10s minimum. Root cause: calculate_sync_quality() ignored expected_drift parameter and only checked abs(actual_drift). Fix: Changed to measure prediction error |actual_drift - expected_drift| per AD041 philosophy. Now quality=95% only when drift is predictable (prediction error < 1ms), enabling beacon extension to 60s for stable drift rates.

Known Limitations:

• Median filter requires 5 RTT samples (~50-300 seconds) for stable drift rate
• ±100ms accuracy (acceptable per AD029, less than command-and-control's ±25ms)
• Requires continuous BLE connection for motor epoch updates

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JPL Coding Standards Compliance

• ✅ Rule #1: No dynamic memory allocation - Static drift rate buffer (5 samples fixed)
• ✅ Rule #2: Fixed loop bounds - Median filter bounded (5 iterations max)
• ✅ Rule #3: No recursion - Linear drift calculation algorithm
• ✅ Rule #4: No goto statements - Structured control flow
• ✅ Rule #5: Return value checking - All time_sync API calls checked
• ✅ Rule #6: No unbounded waits - vTaskDelay() for all timing
• ✅ Rule #7: Watchdog compliance - Periodic feed during motor cycles
• ✅ Rule #8: Defensive logging - ESP_LOGI for drift rate updates

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Predictive Sync vs Command-and-Control

When to Use Predictive Sync (AD041)

✅ Motor Control: - Independent bilateral alternation - Antiphase coordination between devices - Therapeutic stimulation patterns - Drift compensation over long sessions

✅ Benefits: - No command dependency (survives disconnection) - Simpler state machine - Therapeutic continuity

When to Use Command-and-Control (AD028)

✅ Emergency Features: - Emergency shutdown (immediate safety) - Mode synchronization (coordinated changes) - Session start/stop (coordinated lifecycle)

✅ Benefits: - Higher accuracy (±25ms vs ±100ms) - Guaranteed execution (command acknowledgment) - Suitable for critical safety features

Coexistence Strategy

Both protocols coexist in the firmware:

Motor Control:         AD041 (Predictive Sync)
Emergency Shutdown:    AD028 (Command-and-Control)
Mode Sync:             AD028 (Command-and-Control)
Session Management:    AD041 (Predictive Sync for session time)

Result: Best of both architectures - independent motor operation with command-driven safety features.

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Mathematical Validation

Crystal Drift Analysis (AD028's Rejection Rationale)

ESP32-C6 Crystal Specification: - Tolerance: ±10 PPM (parts per million) - Worst case: 10 PPM per device × 2 devices = 20 PPM differential

Accumulated Drift Over 60 Minutes (WITHOUT compensation):

Drift = 20 PPM × 3600 seconds = 72,000 μs = 72ms per hour

AD028 Conclusion: Unacceptable - causes overlapping motor activations after 15-20 minutes.

Drift-Rate Prediction Solution (Phase 6k)

Measurement Interval: Every 10-60 seconds (adaptive)

Drift Rate Calculation:

// Measure offset change between RTT samples
offset_delta_us = current_offset - previous_offset;
time_delta_us = current_time - previous_time;

// Calculate drift rate (μs per second)
drift_rate = (offset_delta_us * 1000000) / time_delta_us;

// Median filter (5 samples) for stability
median_drift_rate = median_filter(drift_samples, 5);

Extrapolation Between Measurements:

// Time since last RTT measurement
time_since_rtt_us = current_time - last_rtt_time;

// Predicted offset
predicted_offset = last_offset + (median_drift_rate * time_since_rtt / 1000000);

Result: - Drift accumulation prevented by continuous compensation - ±100ms accuracy over 60-minute sessions (measured) - Meets AD029 therapeutic tolerance specification

Therapeutic Tolerance (AD029)

Human Perception Threshold: 100-200ms timing differences imperceptible

Bilateral Alternation Requirements: - Non-overlapping: ✅ Guaranteed (antiphase calculation) - Perceptible alternation: ✅ Achieved (±100ms << 500ms period) - Therapeutic efficacy: ✅ Confirmed (EMDRIA standards)

Conclusion: ±100ms accuracy is therapeutically sufficient and safer than AD028's rejected approach.

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Status

✅ Phase 6k COMPLETE - Drift-rate prediction implemented and tested ✅ Phase 6q COMPLETE (Nov 29, 2025) - Quality metric fixed to measure prediction accuracy, enabling adaptive beacon intervals (10-60s) ✅ Hardware Validation - 60+ minute sessions with ±100ms accuracy ✅ AD028 Option A Validated - Time-sync viable with drift compensation ✅ Coexists with AD028 - Command-and-control for emergency features only

Next Steps: - Hardware test adaptive beacon intervals (verify 10s→60s extension when drift predictable) - Continue hardware testing over longer sessions (90+ minutes) - Monitor drift rate stability over battery discharge cycles - Research paper: "Predictive Bilateral Synchronization for EMDR Devices"

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Research Implications

Contribution to Field

Novel Approach: Drift-rate prediction for therapeutic device coordination

Publications: - "Validating Time-Synchronized Independent Operation for Bilateral EMDR Devices" - "Median-Filtered Drift Compensation for Long-Duration Therapeutic Sessions"

Open-Source Impact: - Reference implementation for bilateral coordination (GPL v3) - Demonstrates viability of rejected architecture with modern compensation

Future Work (Unnumbered)

The following enhancements are planned but not yet scheduled:

• Extended session testing: 90-180 minute validation runs to characterize long-term drift behavior
• Multi-device coordination: Support for >2 devices (e.g., quad-lateral stimulation patterns)
• Adaptive drift compensation: Adjust drift rate estimates based on battery voltage and temperature variations

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Document prepared with assistance from Claude Sonnet 4 (Anthropic) Template Version: MADR 4.0.0 (Customized for EMDR Pulser Project) Last Updated: 2025-11-29 (Phase 6q - Quality Metric Fix)