Accelerometers and Gyroscopes

An IMU, or inertial measurement unit, holds an accelerometer and a gyroscope. The gyroscope measures how fast the sensor rotates. The accelerometer measures acceleration, and when the sensor sits still, what it feels is gravity.

Roll Pitch Spin rate about z Add sensor noise

Drag the 3D view to look from another angle.

What each sensor measures

The accelerometer reports specific force: the sensor's acceleration $\mathbf{a}$ minus gravity $\mathbf{g}$, written in the sensor frame. The gyroscope reports angular velocity $\boldsymbol{\omega}$:

$$\mathbf{f}_{\text{meas}} = R^\top(\mathbf{a} - \mathbf{g}) + \mathbf{n}_a \qquad \boldsymbol{\omega}_{\text{meas}} = \boldsymbol{\omega} + \mathbf{n}_g$$

With $\mathbf{g} = (0, 0, -9.81)$ and the sensor at rest, the accelerometer reads $+9.81$ on whichever axis points up.

What to notice

Lying flat, the accelerometer reads about 9.81 m/s² on z, even though it is not moving. Tilt it and that reading spreads across x, y, and z, which is how a phone knows which way is down. Press "Shake it" and the reading jumps, since now real motion adds to gravity. That is why an accelerometer alone gives a poor tilt estimate on a moving robot.

The gyroscope reads zero while the sensor sits still, whatever its tilt. Only rotation shows up. Spinning about z shows on the gyro's z axis, not on the accelerometer at all.