Hardware lab 09 · Inertial sensing

Motion sensors disagree. Fusion makes them useful.

Rotate and shake a virtual controller while watching its accelerometer, gyroscope, register bytes, three orientation estimates, calibration bias, and drift.

fast gyro integration × α + slow gravity correction × (1 − α) → stable roll and pitch · yaw remains gyro-only

Live six-axis bench

SAMPLE: 0 · 0.00 s
|ACCEL|: 1.034 g
|ANGULAR RATE|: 0.0 °/s
ACCEL TRUST: 90%
GESTURE: STEADY

Motion and sensor conditions

Hold a direction to command angular velocity. Release it and the controller stops, but an uncalibrated gyro estimate keeps drifting from electrical bias.

Commanded turn rate75 °/sSample rate60 HzAccelerometer noise σ0.01 gGyroscope noise σ0.3 °/sComplementary α0.98

Injected gyroscope zero-rate bias

X / roll bias1.15 °/sY / pitch bias-0.72 °/sZ / yaw bias0.86 °/s

ROLL

PITCH

YAW

Keyboard: arrows control roll/pitch · Q/E control yaw.

Stabilization experiment

Use the fused estimate to hold roll and pitch within 3° of level. A shake temporarily makes gravity an unreliable reference.

STABILIZED

Estimator	Roll	Pitch	Yaw	R/P error
True pose	0.0°	0.0°	0.0°	reference
Accel only	-0.6°	-0.3°	not observable	0.6°
Gyro only	-0.6°	-0.3°	0.0°	0.6°
Complementary	-0.6°	-0.3°	0.0°	0.6° to level

Bias calibration

A still calibration averages 192 gyro samples and subtracts the measured zero-rate offset. Calibration is rejected if the controller is moving.

STATUSUNCALIBRATED

SAMPLES0

ACTUAL BIAS X/Y/Z1.15 · -0.72 · 0.86

ESTIMATED BIAS X/Y/Z0.00 · 0.00 · 0.00

Raw signal scope

Six channels before fusion

Axis	Raw accel	Gravity model	Raw gyro	Bias-corrected
X	0.0055 g	0.0000 g	1.034 °/s	1.034 °/s
Y	-0.0101 g	0.0000 g	-1.171 °/s	-1.171 °/s
Z	1.0341 g	1.0000 g	1.503 °/s	1.503 °/s

Accelerometer axes: X right · Y forward · Z up. Gyro axes: X roll · Y pitch · Z yaw.

12-byte register burst

Signed 16-bit big-endian words: AX AY AZ GX GY GZ. This bench models ±8 g at 4096 LSB/g and ±2000 °/s at 16.4 LSB/(°/s).

00 17 FF D7 10 8C 00 11 FF ED 00 19

1 · MEMSMicroscopic proof masses and vibrating structures respond to acceleration and rotation.

2 · ADCSix analog channels become signed register words at the selected sample rate.

3 · CALIBRATIONStored offsets remove much of the zero-rate bias before integration.

4 · ESTIMATORSGravity gives absolute roll/pitch; gyro integration gives fast relative motion.

5 · FUSIONA complementary filter trades short-term response for long-term stability.

Experiments to try

Freeze the controller without calibrating and watch gyro-only yaw drift from constant bias.
Calibrate while still, zero the estimators, then compare the drift rate.
Set α near 1 for smooth, fast gyro behavior; set it lower to follow noisy gravity more strongly.
Inject a shake and watch the accelerometer angle jump while its fusion trust falls.
Lower the sample rate and compare the stair-stepped response and integration behavior.
Notice that an accelerometer cannot reveal yaw: gravity has no compass heading.