Accelerometers and gyroscopes (IMU)

Learn

What you’ll learn

• What accelerometers and gyroscopes measure
• How to get tilt from gravity
• Why gyroscopes drift, and how robots combine both

Accelerometer

Measures acceleration in three directions (x, y, z), including gravity. Lying flat and still, it reads about 9.8 m/s² (1 g) on the axis pointing up and about 0 on the others. Tilt it and gravity shifts between axes, which gives the tilt angle.

Gyroscope

Measures rotation speed around each axis (degrees or radians per second). Add up (integrate) the rotation speed over time and you get the angle turned.

IMU = both together

The popular MPU6050 has a 3-axis accelerometer and a 3-axis gyroscope, and talks over I²C (on an UNO: SDA → A4, SCL → A5).

Drift and noise

• The accelerometer is noisy and gets confused by bumps and turns (they’re acceleration too), but it doesn’t drift.
• The gyroscope is smooth, but tiny errors add up when you integrate, so the angle drifts over time.

Robots combine them with a complementary filter: mostly trust the gyro for quick changes, and slowly correct towards the accelerometer’s angle.

angle = 0.98 * (angle + gyroRate * dt) + 0.02 * accelAngle;

Robot uses

• Turn exactly 90° (gyro)
• Detect when the robot is tipping or has been picked up (accelerometer)
• Balancing robots (both, plus PID control)

Examples

Example: tilt angle from the accelerometer

float pitch = atan2(a.acceleration.x, a.acceleration.z) * 180.0 / PI;

Flat gives about 0°; tilting forward makes it larger.

Example: turning 90° with a gyro

float heading = 0;
unsigned long last = millis();

void loop() {
  sensors_event_t a, g, t;
  mpu.getEvent(&a, &g, &t);
  float dt = (millis() - last) / 1000.0;
  last = millis();
  heading += g.gyro.z * 180.0 / PI * dt;   // rad/s → degrees turned
  if (abs(heading) < 90) {
    // keep spinning
  } else {
    // stop: we've turned 90°
  }
}

Practice

Try it in the virtual Arduino

Press Start simulator. Replace diagram.json with the wiring below, then open the Library Manager tab and add Adafruit MPU6050. Paste the sketch, press ▶, and click the sensor to change its acceleration and rotation. If Wokwi says a library is missing, click its Install button and press ▶ again.

diagram.json

{
  "version": 1,
  "author": "RoboLearn",
  "editor": "wokwi",
  "parts": [
    {
      "type": "wokwi-arduino-uno",
      "id": "uno",
      "top": 0,
      "left": 0,
      "attrs": {}
    },
    {
      "type": "wokwi-mpu6050",
      "id": "imu",
      "top": -90,
      "left": 120,
      "attrs": {}
    }
  ],
  "connections": [
    [
      "imu:VCC",
      "uno:5V",
      "red",
      []
    ],
    [
      "imu:GND",
      "uno:GND.1",
      "black",
      []
    ],
    [
      "imu:SCL",
      "uno:A5",
      "blue",
      []
    ],
    [
      "imu:SDA",
      "uno:A4",
      "green",
      []
    ]
  ],
  "dependencies": {}
}

sketch.ino

#include <Adafruit_MPU6050.h>
#include <Adafruit_Sensor.h>
#include <Wire.h>

Adafruit_MPU6050 mpu;

void setup() {
  Serial.begin(9600);
  if (!mpu.begin()) {
    Serial.println("MPU6050 not found - check wiring");
    while (true) {}
  }
}

void loop() {
  sensors_event_t a, g, temp;
  mpu.getEvent(&a, &g, &temp);
  Serial.print("accel x/y/z (m/s^2): ");
  Serial.print(a.acceleration.x); Serial.print(" ");
  Serial.print(a.acceleration.y); Serial.print(" ");
  Serial.print(a.acceleration.z);
  Serial.print("   gyro z (rad/s): ");
  Serial.println(g.gyro.z);
  delay(250);
}

Tilt with an MPU6050Open full screen ↗

Start simulator

Runs on Wokwi, free, no account needed.

Find gravityEasy

With the virtual sensor still, which axis reads about 9.8 m/s²? What happens when you change the acceleration values?

Tilt alarmMedium

Turn the built-in LED on when the x acceleration is more than 5 m/s² (the board is tilted a lot). After getEvent, add digitalWrite(LED_BUILTIN, abs(a.acceleration.x) > 5 ? HIGH : LOW); and set pinMode(LED_BUILTIN, OUTPUT) in setup().

Why drift?Hard

A gyro has a tiny constant error of 0.5°/s. How far off is the integrated heading after 2 minutes? 0.5 × 120 = 60°. That’s why gyros are combined with other sensors or re-zeroed often.

Quick check

1. Lying still and flat, an accelerometer reads about 9.8 m/s² because of…

Its batteryGravityMagnetismNoise

2. A gyroscope measures…

DistanceRotation speedTemperatureLight

3. Why does a gyro-based angle drift?

Small errors add up when integratingGravity pulls itThe battery drainsIt doesn’t

4. On an UNO, the MPU6050’s SDA connects to…

A4A5Pin 135V

Check my answers