plurigrid QuackBot Duckoid
Trit: +1 (PLUS - generative/constructive) Color: #1FC4E0 (Cyan) URI: skill://quackbot-duckoid#1FC4E0
Overview
A mechanic wobbling duckoid robot that:
- 🦆 Quacks with piezo-synthesized duck calls
- 🎵 Composes nonstandard musical scales (Bohlen-Pierce, just intonation, xenharmonic)
- 🌀 Wobbles via 2-DOF gimbal base with IMU feedback
- 💰 Costs ~$68 total BOM
Physical Design
┌───────┐
╱ O O ╲ ← LED eyes ($0.50)
│ ══════ │ ← Servo beak ($2)
│ )))) │ ← Piezo speaker ($1)
╲________╱
│
┌────────┴────────┐
╱ ╲
│ ┌─────────┐ │
│ │ ESP32-S3│ │ ← MCU ($8)
Wing ──▶│ │ +IMU │ │◀── Wing
($2ea) │ └─────────┘ │ ($2ea)
│ ┌───────┐ │
│ │ LiPo │ │ ← Battery ($12)
╲ └───────┘ ╱
└────────┬────────┘
│
╔════════╧════════╗
║ WOBBLE BASE ║
║ ┌───┐ ┌───┐ ║ ← 2x MG996R ($10)
║ │ S │───│ S │ ║
║ └───┘ └───┘ ║
╚════════╤════════╝
◯────┴────◯ ← Rubber feet ($2)
Bill of Materials (BOM)
| Component | Qty | Unit Cost | Total |
|---|---|---|---|
| Head | $15 | ||
| SG90 Micro Servo (beak) | 1 | $2 | $2 |
| Piezo Buzzer/Speaker | 1 | $1 | $1 |
| 5mm LED (eyes) | 2 | $0.25 | $0.50 |
| MPU6050 IMU | 1 | $3 | $3 |
| 3D Print (head shell) | 1 | $8.50 | $8.50 |
| Body | $25 | ||
| ESP32-S3 DevKit | 1 | $8 | $8 |
| PAM8403 Amplifier | 1 | $1 | $1 |
| 2S LiPo 1000mAh | 1 | $12 | $12 |
| PCA9685 PWM Driver | 1 | $4 | $4 |
| Wobble Base | $20 | ||
| MG996R Servo | 2 | $5 | $10 |
| 3D Print (gimbal) | 1 | $5 | $5 |
| Rubber Feet | 2 | $1 | $2 |
| Brass Counterweight | 1 | $3 | $3 |
| Wings | $8 | ||
| SG90 Micro Servo | 2 | $2 | $4 |
| 3D Print (wings) | 2 | $2 | $4 |
| TOTAL | $68 |
Nonstandard Musical Scales
QuackBot composes using xenharmonic scales that are not 12-TET:
Bohlen-Pierce Scale (13 steps per tritave)
Ratio: 1 25/21 9/7 7/5 5/3 9/5 15/7 7/3 25/9 3 ...
Step: 0 1 2 3 4 5 6 7 8 9 ...
Cents: 0 133.2 266.9 400.1 533.8 666.9 800.1 933.1 1066.9 1200
Just Intonation (Ptolemaic)
JUST_RATIOS = {
'C': 1/1, # Unison
'D': 9/8, # Major second
'E': 5/4, # Major third
'F': 4/3, # Perfect fourth
'G': 3/2, # Perfect fifth
'A': 5/3, # Major sixth
'B': 15/8, # Major seventh
}
Wendy Carlos Alpha/Beta/Gamma
CARLOS_ALPHA = 78.0 # cents per step (15.385 steps/octave)
CARLOS_BETA = 63.8 # cents per step (18.809 steps/octave)
CARLOS_GAMMA = 35.1 # cents per step (34.188 steps/octave)
Quack-Native Scale (custom)
A duck-optimized scale based on duck vocalization formants:
QUACK_SCALE = [
1.0, # Root quack
1.059, # Minor second quack
1.189, # Minor third quack
1.335, # Fourth quack
1.498, # Fifth quack
1.682, # Sixth quack
1.888, # Seventh quack
]
# Formant frequencies: F1=1200Hz, F2=2400Hz, F3=3600Hz
Wobble Dynamics
The 2-DOF gimbal creates a chaotic wobble pattern using coupled oscillators:
import numpy as np
class WobbleDynamics:
"""Kuramoto-style coupled oscillator for duck wobble."""
def __init__(self, natural_freq=2.0, coupling=0.5):
self.omega = natural_freq # rad/s
self.K = coupling
self.theta = [0.0, np.pi/4] # pitch, roll phases
def step(self, dt: float, imu_feedback: tuple) -> tuple:
"""Compute next wobble angles."""
pitch_accel, roll_accel = imu_feedback
# Kuramoto coupling
phase_diff = self.theta[1] - self.theta[0]
# Update phases with coupling and feedback
self.theta[0] += dt * (
self.omega +
self.K * np.sin(phase_diff) +
0.1 * pitch_accel
)
self.theta[1] += dt * (
self.omega * 1.1 + # Slight detuning
self.K * np.sin(-phase_diff) +
0.1 * roll_accel
)
# Convert to servo angles (±30°)
pitch_angle = 30 * np.sin(self.theta[0])
roll_angle = 30 * np.sin(self.theta[1])
return pitch_angle, roll_angle
class QuackSynthesizer:
"""Duck vocalization synthesizer."""
FORMANTS = [1200, 2400, 3600] # Hz
def quack(self, duration_ms: int = 200, pitch_shift: float = 1.0):
"""Generate a quack waveform."""
sr = 16000
t = np.linspace(0, duration_ms/1000, int(sr * duration_ms/1000))
# Fundamental with pitch shift
f0 = 220 * pitch_shift
# Sum formants
signal = np.zeros_like(t)
for i, formant in enumerate(self.FORMANTS):
amp = 1.0 / (i + 1) # Decreasing amplitude
signal += amp * np.sin(2 * np.pi * formant * pitch_shift * t)
# Apply envelope (sharp attack, quick decay)
envelope = np.exp(-t * 20) * (1 - np.exp(-t * 100))
return (signal * envelope * 32767).astype(np.int16)
def compose_nonstandard(self, scale: list, pattern: list) -> list:
"""Compose using nonstandard scale."""
quacks = []
for note_idx, duration in pattern:
pitch = scale[note_idx % len(scale)]
quacks.append(self.quack(duration, pitch))
return quacks
MJCF Model
<mujoco model="quackbot">
<compiler angle="radian" meshdir="meshes"/>
<default>
<joint damping="0.1" armature="0.01"/>
<geom friction="0.8 0.02 0.01"/>
</default>
<asset>
<mesh name="body" file="duck_body.stl"/>
<mesh name="head" file="duck_head.stl"/>
<mesh name="beak" file="duck_beak.stl"/>
<mesh name="wing" file="duck_wing.stl"/>
</asset>
<worldbody>
<!-- Wobble Base -->
<body name="base" pos="0 0 0.05">
<geom type="cylinder" size="0.08 0.02" rgba="0.2 0.2 0.2 1"/>
<!-- Pitch Joint -->
<body name="pitch_link" pos="0 0 0.03">
<joint name="pitch" type="hinge" axis="0 1 0" range="-0.5 0.5"/>
<!-- Roll Joint -->
<body name="roll_link" pos="0 0 0.02">
<joint name="roll" type="hinge" axis="1 0 0" range="-0.5 0.5"/>
<!-- Duck Body -->
<body name="body" pos="0 0 0.08">
<geom type="mesh" mesh="body" rgba="1 0.9 0 1"/>
<inertial pos="0 0 0" mass="0.3" diaginertia="0.001 0.001 0.001"/>
<!-- Head -->
<body name="head" pos="0 0.06 0.05">
<geom type="mesh" mesh="head" rgba="1 0.9 0 1"/>
<!-- Beak -->
<body name="beak" pos="0 0.03 0">
<joint name="beak" type="hinge" axis="1 0 0" range="0 0.3"/>
<geom type="mesh" mesh="beak" rgba="1 0.5 0 1"/>
</body>
</body>
<!-- Left Wing -->
<body name="wing_l" pos="-0.06 0 0.02">
<joint name="wing_l" type="hinge" axis="0 1 0" range="-0.5 0.5"/>
<geom type="mesh" mesh="wing" rgba="1 0.9 0 1"/>
</body>
<!-- Right Wing -->
<body name="wing_r" pos="0.06 0 0.02">
<joint name="wing_r" type="hinge" axis="0 1 0" range="-0.5 0.5"/>
<geom type="mesh" mesh="wing" rgba="1 0.9 0 1" euler="0 0 3.14"/>
</body>
</body>
</body>
</body>
</body>
</worldbody>
<actuator>
<position name="pitch_servo" joint="pitch" kp="50"/>
<position name="roll_servo" joint="roll" kp="50"/>
<position name="beak_servo" joint="beak" kp="20"/>
<position name="wing_l_servo" joint="wing_l" kp="10"/>
<position name="wing_r_servo" joint="wing_r" kp="10"/>
</actuator>
</mujoco>
ESP32 Firmware Skeleton
#include <ESP32Servo.h>
#include <driver/i2s.h>
#include <MPU6050.h>
// Servos
Servo pitchServo, rollServo, beakServo, wingLServo, wingRServo;
// IMU
MPU6050 imu;
// Wobble state
float theta[2] = {0, M_PI/4};
const float omega = 2.0;
const float K = 0.5;
void setup() {
// Attach servos
pitchServo.attach(13);
rollServo.attach(12);
beakServo.attach(14);
wingLServo.attach(27);
wingRServo.attach(26);
// Init IMU
Wire.begin();
imu.initialize();
// Init I2S for audio
i2s_config_t i2s_config = {
.mode = I2S_MODE_MASTER | I2S_MODE_TX,
.sample_rate = 16000,
.bits_per_sample = I2S_BITS_PER_SAMPLE_16BIT,
.channel_format = I2S_CHANNEL_FMT_ONLY_LEFT,
.communication_format = I2S_COMM_FORMAT_I2S,
.dma_buf_count = 8,
.dma_buf_len = 64,
};
i2s_driver_install(I2S_NUM_0, &i2s_config, 0, NULL);
}
void loop() {
// Read IMU
int16_t ax, ay, az, gx, gy, gz;
imu.getMotion6(&ax, &ay, &az, &gx, &gy, &gz);
// Wobble dynamics (Kuramoto)
float dt = 0.02;
float phase_diff = theta[1] - theta[0];
theta[0] += dt * (omega + K * sin(phase_diff) + 0.0001 * ax);
theta[1] += dt * (omega * 1.1 + K * sin(-phase_diff) + 0.0001 * ay);
// Servo angles
int pitch = 90 + 30 * sin(theta[0]);
int roll = 90 + 30 * sin(theta[1]);
pitchServo.write(pitch);
rollServo.write(roll);
// Occasional quack
if (random(100) < 2) {
quack();
}
// Wing flap (sync with wobble)
wingLServo.write(90 + 20 * sin(theta[0] * 2));
wingRServo.write(90 - 20 * sin(theta[0] * 2));
delay(20);
}
void quack() {
// Generate quack waveform
int16_t buffer[800];
for (int i = 0; i < 800; i++) {
float t = i / 16000.0;
float env = exp(-t * 20) * (1 - exp(-t * 100));
float sig = sin(2 * M_PI * 1200 * t) +
0.5 * sin(2 * M_PI * 2400 * t) +
0.25 * sin(2 * M_PI * 3600 * t);
buffer[i] = (int16_t)(sig * env * 16000);
}
// Beak animation
beakServo.write(120);
size_t bytes_written;
i2s_write(I2S_NUM_0, buffer, sizeof(buffer), &bytes_written, portMAX_DELAY);
beakServo.write(90);
}
GF(3) Triads
quackbot-duckoid (+1) ⊗ wobble-dynamics (0) ⊗ nonstandard-scales (+1) = needs -1
quackbot-duckoid (+1) ⊗ topos-of-music (-1) ⊗ wobble-dynamics (0) = 0 ✓
quackbot-duckoid (+1) ⊗ ksim-rl (-1) ⊗ mujoco-scenes (0) = 0 ✓
Related Skills
topos-of-music(-1): Mazzola's mathematical music theorywobble-dynamics(0): Kuramoto oscillators for motionnonstandard-scales(+1): Xenharmonic scale generationksim-rl(-1): RL training for behaviorscatsharp-sonification(0): GF(3) color → sound mapping
Cost Optimization Strategies
- Use SG90 over MG996R where torque permits (saves $6)
- ESP32-C3 instead of S3 if BLE sufficient (saves $3)
- Passive piezo instead of active speaker (saves $0.50)
- Shared 3D print batch for multiple units (saves 30%)
Minimum viable BOM: $52
References
@article{bohlen1978,
title={13 Tonstufen in der Duodezime},
author={Bohlen, Heinz},
journal={Acustica},
year={1978}
}
@book{carlos1987,
title={Tuning: At the Crossroads},
author={Carlos, Wendy},
year={1987}
}
@article{kuramoto1975,
title={Self-entrainment of a population of coupled oscillators},
author={Kuramoto, Yoshiki},
journal={Lecture Notes in Physics},
year={1975}
}