File size: 6,798 Bytes
32502a8 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 | """Music-timed, 50 Hz Electric Slide choreography for a Microduck flock.
The motion is deliberately kinematic for the first visual prototype: root poses
and servo poses are sampled directly in MuJoCo. That makes the 25-duck show
repeatable while keeping a clean seam for replacing the sampler with an ONNX
policy later.
"""
from __future__ import annotations
from dataclasses import dataclass
import math
BPM = 111.0
BEAT_SECONDS = 60.0 / BPM
COUNTS_PER_WALL = 18
WALLS = 4
SHOW_BEATS = COUNTS_PER_WALL * WALLS
SHOW_SECONDS = SHOW_BEATS * BEAT_SECONDS
CONTROL_HZ = 50
# Official STAND keyframe, in official actuator/joint order.
STAND_POSE = (
0.0,
-0.08726646259971647,
-0.457924,
-0.004940,
0.452984,
0.3490658503988659,
0.3490658503988659,
0.0,
0.0,
0.0,
0.08726646259971647,
0.457924,
0.004940,
-0.452984,
)
# Per-count root translation in the duck's local frame (forward, left) and yaw.
# Right is negative local y. Four 18-count walls trace a closed square.
ROOT_STEPS = (
(0.00, -0.10, 0.0), # grapevine right: side
(0.00, -0.04, 0.0), # cross behind
(0.00, -0.10, 0.0), # side
(0.00, 0.00, 0.0), # touch
(0.00, 0.10, 0.0), # grapevine left: side
(0.00, 0.04, 0.0), # cross behind
(0.00, 0.10, 0.0), # side
(0.00, 0.00, 0.0), # touch
(-0.08, 0.00, 0.0), # walk back
(-0.08, 0.00, 0.0),
(-0.08, 0.00, 0.0),
(0.00, 0.00, 0.0), # touch
(0.08, 0.00, 0.0), # rock forward
(0.00, 0.00, 0.0), # toe touch + scoop
(-0.08, 0.00, 0.0), # rock back
(0.00, 0.00, 0.0), # toe touch + lean
(0.05, 0.00, 0.0), # step into turn
(0.00, 0.00, math.pi / 2.0), # scuff + quarter turn left
)
@dataclass(frozen=True)
class DuckPose:
position: tuple[float, float, float]
quaternion: tuple[float, float, float, float]
joints: tuple[float, ...]
def formation_positions(grid: int = 5, spacing: float = 0.52) -> list[tuple[float, float]]:
"""Return a centered, row-major square formation."""
center = (grid - 1) / 2.0
return [
((col - center) * spacing, (center - row) * spacing)
for row in range(grid)
for col in range(grid)
]
def _smoothstep(value: float) -> float:
value = max(0.0, min(1.0, value))
return value * value * (3.0 - 2.0 * value)
def _rotate(x: float, y: float, yaw: float) -> tuple[float, float]:
cosine, sine = math.cos(yaw), math.sin(yaw)
return cosine * x - sine * y, sine * x + cosine * y
def root_motion(beat: float) -> tuple[float, float, float]:
"""Integrate the 18-count pattern through the supplied beat (0..72)."""
beat = max(0.0, min(float(SHOW_BEATS), beat))
whole = int(math.floor(beat))
fraction = _smoothstep(beat - whole)
x = y = yaw = 0.0
for index in range(whole):
dx, dy, dyaw = ROOT_STEPS[index % COUNTS_PER_WALL]
world_dx, world_dy = _rotate(dx, dy, yaw)
x += world_dx
y += world_dy
yaw += dyaw
if whole < SHOW_BEATS:
dx, dy, dyaw = ROOT_STEPS[whole % COUNTS_PER_WALL]
world_dx, world_dy = _rotate(dx, dy, yaw)
x += world_dx * fraction
y += world_dy * fraction
yaw += dyaw * fraction
return x, y, yaw
def _quaternion(yaw: float, pitch: float, roll: float) -> tuple[float, float, float, float]:
"""MuJoCo wxyz quaternion from ZYX yaw, pitch, and roll."""
cy, sy = math.cos(yaw / 2), math.sin(yaw / 2)
cp, sp = math.cos(pitch / 2), math.sin(pitch / 2)
cr, sr = math.cos(roll / 2), math.sin(roll / 2)
return (
cr * cp * cy + sr * sp * sy,
sr * cp * cy - cr * sp * sy,
cr * sp * cy + sr * cp * sy,
cr * cp * sy - sr * sp * cy,
)
def sample_pose(time_seconds: float, duck_index: int, base_xy: tuple[float, float]) -> DuckPose:
"""Sample one duck at show time, including subtle flock-specific attitude."""
beat = (time_seconds / BEAT_SECONDS) % SHOW_BEATS
count = int(beat) % COUNTS_PER_WALL
phase = beat - math.floor(beat)
step_pulse = math.sin(math.pi * phase)
groove = math.sin(2.0 * math.pi * (beat / 2.0 + (duck_index % 5) * 0.035))
row = duck_index // 5
col = duck_index % 5
accent = (row - 2) * 0.018 + (col - 2) * 0.012
travel_x, travel_y, yaw = root_motion(beat)
z = 0.12 + 0.006 * abs(groove)
pitch = 0.025 * groove
roll = -0.035 * groove + accent
pose = list(STAND_POSE)
# Continuous knee compression gives the loose, grounded look in the clip.
compression = 0.035 + 0.055 * abs(groove)
pose[3] += compression
pose[13] -= compression
pose[2] += compression * 0.45
pose[12] -= compression * 0.45
# Alternating weight shift and foot pickup for traveling counts.
if count in (0, 2, 4, 6, 8, 10):
lead_left = count in (4, 6, 10)
lift = 0.16 * step_pulse
if lead_left:
pose[2] += lift
pose[3] += lift * 0.70
pose[4] -= lift * 0.45
roll += 0.055 * step_pulse
else:
pose[11] -= lift
pose[12] -= lift * 0.70
pose[13] += lift * 0.45
roll -= 0.055 * step_pulse
# Touches are visible: a toe point, a beak nod, and a tiny hold.
if count in (3, 7, 11):
pose[6] -= 0.13 * step_pulse
pose[7] += 0.14 * groove
z -= 0.008 * step_pulse
# The reference clip's character section: low scoop forward, lean back,
# then let the head lead the new wall.
if count in (12, 13):
scoop = step_pulse if count == 13 else _smoothstep(phase)
z -= 0.022 * scoop
pitch += 0.11 * scoop
pose[5] += 0.24 * scoop
pose[6] -= 0.22 * scoop
pose[7] += (0.18 + accent) * scoop
pose[8] -= 0.14 * groove
elif count in (14, 15):
lean = step_pulse if count == 15 else _smoothstep(phase)
pitch -= 0.09 * lean
pose[5] -= 0.18 * lean
pose[6] += 0.15 * lean
pose[8] += 0.18 * groove
elif count in (16, 17):
turn_lead = step_pulse if count == 16 else math.sin(math.pi * phase)
pose[7] += 0.38 * turn_lead
pose[8] += 0.13 * groove
z += 0.012 * step_pulse
# Keep the flock coordinated while the head-roll accent ripples by row.
pose[8] += 0.075 * math.sin(2 * math.pi * (beat / 4.0 + row * 0.08))
return DuckPose(
position=(base_xy[0] + travel_x, base_xy[1] + travel_y, z),
quaternion=_quaternion(yaw, pitch, roll),
joints=tuple(pose),
)
def sample_flock(time_seconds: float, grid: int = 5, spacing: float = 0.52) -> list[DuckPose]:
positions = formation_positions(grid, spacing)
return [sample_pose(time_seconds, index, xy) for index, xy in enumerate(positions)]
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