IMU and Sensors

An IMU (Inertial Measurement Unit) combines accelerometers, gyroscopes, and often magnetometers to measure motion. Combined with other sensors (GPS, LiDAR, cameras, barometers), these form the sensory system of any mobile robot.

Why It Matters

Sensors are how robots perceive the world. Every control loop, every SLAM system, every navigation stack starts with sensor data. Understanding sensor characteristics — noise, drift, bandwidth, failure modes — determines whether your robot works reliably or crashes into walls.

IMU Components

Accelerometer (3-axis)

Measures linear acceleration including gravity. At rest, it reads [0, 0, 9.81] m/s² (pointing up).

Principle: a proof mass on a spring. Acceleration displaces the mass; capacitive or piezoresistive sensing measures displacement.

Getting tilt from gravity:

import numpy as np
 
def accel_to_tilt(ax, ay, az):
    roll  = np.arctan2(ay, az)
    pitch = np.arctan2(-ax, np.sqrt(ay**2 + az**2))
    return roll, pitch
# Only valid when not accelerating (e.g., hovering drone, stationary)

Limitation: can’t distinguish tilt from linear acceleration. During movement, readings include both gravity and motion — need Sensor Fusion to separate them.

Gyroscope (3-axis)

Measures angular velocity (°/s or rad/s). Integrate to get angle change:

angle += gyro_rate × dt

Principle: MEMS vibrating structure — Coriolis effect deflects vibration proportional to rotation rate.

Limitation: integration accumulates bias error → drift. A 0.01°/s bias drifts 36°/hour. This is why gyro alone can’t maintain orientation long-term.

Magnetometer (3-axis)

Measures Earth’s magnetic field vector → heading/yaw. Points toward magnetic north.

Limitation: heavily distorted by nearby ferromagnetic materials (steel, magnets, motors). Requires hard-iron and soft-iron calibration before use. Motors running nearby corrupt readings — often unusable on drones during flight.

6-DOF vs 9-DOF

Configuration	Sensors	Can Estimate
6-DOF	Accel + Gyro	Roll, pitch (yaw drifts)
9-DOF	Accel + Gyro + Mag	Roll, pitch, yaw (with mag calibration)

Most flight controllers use 6-DOF + GPS for yaw, since magnetometers are unreliable near motors.

Sensor Noise

Noise Type	Source	Effect	Mitigation
White noise	Random fluctuations	Jittery readings	Averaging, low-pass filter
Bias	Manufacturing offset	Constant error	Calibration (measure at rest, subtract)
Bias drift	Temperature, aging	Slowly changing offset	Sensor Fusion, recalibration
Scale factor error	Sensitivity variation	Readings off by %	Factory or self-calibration

Characterizing Noise: Allan Variance

The Allan variance plot shows noise characteristics vs averaging time:

log(Allan deviation)
     │
     │  ╲  white noise (slope -1/2)
     │    ╲
     │      ──── bias instability (flat region)
     │           ╱
     │          ╱  random walk (slope +1/2)
     └─────────────→ log(averaging time)

The minimum of the Allan deviation curve gives the bias instability — the best achievable stability. Datasheets report this in °/hr for gyros.

Common IMU ICs

Chip	DOF	Gyro Range	Accel Range	Interface	Notes
MPU-6050	6	±2000°/s	±16g	I2C/SPI	Classic, cheap, discontinued
ICM-20948	9	±2000°/s	±16g	I2C/SPI	MPU-9250 successor
BMI270	6	±2000°/s	±16g	SPI	Low power, used in fitness
BNO055	9	±2000°/s	±16g	I2C	Built-in sensor fusion (quaternion output)
LSM6DSO	6	±2000°/s	±16g	I2C/SPI	ST, machine learning core

Other Robot Sensors

Sensor	Technology	Range	Rate	Best For
Ultrasonic	Time-of-flight (sound)	2cm – 4m	10-40 Hz	Short-range obstacle avoidance
2D LiDAR	Time-of-flight (laser)	0.1 – 30m	5-40 Hz	Indoor mapping, SLAM
3D LiDAR	Scanning laser	1 – 200m	10-20 Hz	Autonomous vehicles
Depth camera	IR structured light / ToF	0.3 – 10m	30-90 Hz	Indoor navigation, manipulation
GPS	Satellite triangulation	Global	1-10 Hz	Outdoor position (±2m)
RTK GPS	Differential GPS	Global	10 Hz	Outdoor position (±2cm)
Barometer	Air pressure	Relative altitude	25-100 Hz	Drone altitude hold
Optical flow	Camera motion tracking	Ground texture	30-100 Hz	Velocity estimation (drones)

Calibration

Accelerometer: place IMU in 6 orientations (each axis up and down), record gravity vector, fit to sphere to find offset and scale.

Gyroscope: record data at rest for 60+ seconds. Average = bias offset. Subtract from all future readings.

Magnetometer: rotate in all orientations, fit to ellipsoid (hard-iron = offset, soft-iron = scale/rotation).

Related

• Sensor Fusion — combining IMU data with complementary/Kalman filter
• Kalman Filter — optimal estimation from noisy sensor data
• ADC and DAC — how analog sensor signals are digitized
• UART SPI I2C — digital interfaces to sensor ICs
• SLAM — sensors feed into mapping and localization
• Drone Flight Dynamics — IMU is the primary attitude sensor