IMU

Conceptual

An IMU (Inertial Measurement Unit) measures linear acceleration and angular velocity, enabling robots to estimate their orientation and motion. IMUs are essential for state estimation, complementing cameras and LiDAR by providing high-rate proprioceptive data.

What’s Inside an IMU

┌─────────────────────────────────────┐
│              IMU                     │
│  ┌───────────┐  ┌───────────────┐  │
│  │Accelero-  │  │ Gyroscope     │  │
│  │meter (3)  │  │ (3-axis)      │  │
│  │           │  │               │  │
│  │ ax ay az  │  │ ωx ωy ωz     │  │
│  └───────────┘  └───────────────┘  │
│        Optional:                    │
│  ┌───────────────────────────────┐ │
│  │     Magnetometer (3-axis)     │ │
│  │         mx my mz              │ │
│  └───────────────────────────────┘ │
└─────────────────────────────────────┘

• Accelerometer: Measures linear acceleration (m/s²)
• Gyroscope: Measures angular velocity (rad/s)
• Magnetometer: Measures magnetic field (compass heading)

An IMU with magnetometer is sometimes called an AHRS (Attitude and Heading Reference System).

Sensor Characteristics

Accelerometer

Measures specific force (acceleration + gravity).

Reading = True Acceleration - Gravity

At rest: a = [0, 0, 9.81] m/s² (standing upright)

Use: Tilt sensing, vibration, step counting

Gyroscope

Measures angular velocity around each axis.

Reading = [ωx, ωy, ωz] rad/s (roll rate, pitch rate, yaw rate)

Use: Orientation tracking, stabilization

Problem: Drift — small errors accumulate over time

Magnetometer

Measures magnetic field (mostly Earth’s).

Reading = [mx, my, mz] μT

Use: Heading/yaw reference

Problem: Easily disturbed by nearby metal, electronics

Key Specifications

Spec	Description	Good Value
Noise density	Sensor noise level	<0.1 mg/√Hz (accel), <0.01°/s/√Hz (gyro)
Bias stability	How much bias drifts	<10 μg (accel), <1°/hr (gyro)
Sample rate	Output frequency	100-1000 Hz
Range	Maximum measurable	±16g, ±2000°/s

IMU Grades

Grade	Use Case	Gyro Bias	Cost
Consumer	Phones, toys	10-100°/hr	$1-10
Industrial	Drones, robots	1-10°/hr	$50-500
Tactical	Navigation, surveying	0.1-1°/hr	$1,000-10,000
Navigation	Aircraft, ships	<0.01°/hr	$10,000+

Sensor Fusion

Raw IMU data drifts over time. Fusion with other sensors corrects this:

Complementary Filter

Simple, fast — blend gyro (short-term accurate) with accel (long-term accurate):

# Complementary filter for pitch
alpha = 0.98
pitch = alpha * (pitch + gyro_rate * dt) + (1-alpha) * accel_pitch

Kalman Filter / EKF

Optimal fusion, handles noise models:

┌────────────┐     ┌────────────┐
│    IMU     │ ──► │            │
└────────────┘     │   Kalman   │ ──► State Estimate
┌────────────┐     │   Filter   │     (position, velocity,
│   GPS /    │ ──► │            │      orientation)
│ Camera/    │     │            │
│ LiDAR      │     └────────────┘
└────────────┘

Visual-Inertial Odometry (VIO)

Fuse IMU with camera — gold standard for robot state estimation.

Tools: VINS-Mono, ORB-SLAM3, Isaac ROS Visual SLAM

Common IMU Chips

Chip	Grade	Notes
MPU-6050	Consumer	Very cheap, adequate for simple projects
BMI088	Industrial	Good for drones
ICM-42688-P	Industrial	Low noise, Jetson-compatible
ADIS16470	Tactical	High accuracy, SPI interface

ROS 2 Integration

Standard message: sensor_msgs/Imu

# IMU message fields:
orientation         # Quaternion (if filter provides)
angular_velocity    # rad/s (gyro)
linear_acceleration # m/s² (accel)

Launch Example

# Start IMU driver (varies by hardware)
ros2 launch imu_driver imu.launch.py

# View data
ros2 topic echo /imu/data

Fusion Packages

Package	Purpose
robot_localization	EKF/UKF sensor fusion
imu_filter_madgwick	Orientation from IMU
imu_complementary_filter	Simple orientation filter
isaac_ros_visual_slam	VIO with GPU acceleration (Isaac ROS 4.0)

Calibration

IMUs require calibration for best accuracy:

Accelerometer

• Scale factor: Correct gain errors
• Bias: Remove constant offset
• Axis misalignment: Correct non-orthogonal axes

Gyroscope

• Bias: Remove constant offset (changes with temperature!)
• Scale factor: Correct gain

Magnetometer

• Hard iron: Remove constant offset (nearby magnets)
• Soft iron: Correct for nearby metals distorting field

Related Terms

• SLAM — Visual-Inertial SLAM
• LiDAR — Complementary sensor
• Cameras — VIO fusion partner

Sources

• ROS 2 sensor_msgs/Imu — Standard IMU message definition
• robot_localization — EKF/UKF fusion package documentation
• imu_filter_madgwick — Madgwick filter for orientation
• Isaac ROS Visual SLAM — GPU-accelerated VIO with IMU fusion
• TDK InvenSense MPU-6050 — Consumer IMU datasheet
• TDK InvenSense ICM-42688-P — Industrial IMU specifications
• Bosch Sensortec BMI088 — Industrial IMU for drones