Inertia – Another essential ingredient for driverless vehicles

Inertia – Another essential ingredient for driverless vehicles

I know of at least three driverless R&D vehicles which rely on an inertia-based sensor to act as a back-up or supporting technology to other methods of path plotting and navigation (usually a combination of GPS and Lidar, depending on the hardware and software deployed). 

While the systems found in commercial jet liners might cost tens of thousands, and boast extraordinary accuracy over thousands of miles (and have a price tag to match), inertial measurement within a smartphone might have coarser accuracy and cost a few pennies.  Needless to say, the units often found in autonomous vehicles sit somewhere in between – both in terms of cost and resulting accuracy.

As we know, it’s important to have a back-up system to provide a fail-over in case the first one or two fail, or don’t have enough data – that’s the same for navigation as it is for obstacle avoidance or dealing with difficult weather or terrain – but inertial navigation is far from perfect. 

Special thanks to Tiziano Fiorenzani, UAV Design, Guidance and Control Expert, who kindly gave us permission to share his blog on how inertia measurement works.  This is part of a mini series of personal blogs he’s producing about the main sensors that are commonly part of any drone – you can get more updates by following Tiziano on LinkedIn.

What is an IMU?

IMU stands for for Inertial Measurement Unit, and in fact, measures “inertial quantities”, as accelerations and angular velocities. Those quantities can be used directly for  an automatic feedback control loop (eg, the gyro that stabilizes RC helicopters) or we can process their data out and estimate the Attitude (roll, pitch, yaw or quaternion).

What is inside an IMU?

Usually an IMU consists of the following sensors:

  • 3-axis accelerometer: measures the accelerations along its axes
  • 3-axis gyroscope: measures the rotational velocity around its axes
  • 3-axis magnetometer: measures the local magnetic field components along its axes

This setup is made out of 9 sensors (3 sensors on 3 axes), so it is generally referenced as 9-DOF IMU.


Accelerometers sense all the accelerations applied to them, even those due to vibrations or manoeuvres. Isolation is of primary importance as well as an accurate calibration.

There is a simple way to figure how an accelerometer works. Take a scale and put a weight on it, say 1 kg (or 1 lb if you like, but I’ll stick with the International System). The scale will show you 1 kg, because the object’s mass of 1 kg, subject to the gravity acceleration of g = 9.8 m/s^2 (1 g), will experience a force of F = mg = 9.8 N (Newton), that is 1 kg force. Easy enough. Now, if you grab the scale and suddenly moved it upward, you would read that the same object has grown heavier. What does it mean? Well, the scale measures the vertical component of the forces applied to it: naming a the upward acceleration we impressed, the same mass m multiplied by a higher acceleration (g + a) results in a higher force F = m(g+a).

The sensor converts the acceleration into a voltage, which is later translated into a binary number that an autopilot can understand.

There are different types of accelerometers, though the most common are Capacitive and Piezoelectric, which basically measure voltage variations due to the sensor’s deformation. Check the references for more details.

When an accelerometer is used as inclinometer, the gravity vector components at rest are measured in order to evaluate the tilt angle as:

You can verify the effectiveness of an inclinometer with your own smartphone: install an app and verify if a painting has been hanged on the wall on a level plane. It won’t be straight if you move your phone, as the inclinometer is affected by the extra accelerations you cause.

Gyroscopes (usually shortened to ‘gyros’)

Gyros measure the rotational velocity around their axis.

Let’s simplify how it works by imagining a tiny mass, connected to a housing by micro springs and forced to oscillate at a constant frequency. Then imagine the housing connected to the frame by traversal springs.

Any rotation of the system will induce Coriolis force in the mass, pushing it in the direction of the second set of springs (if you are not familiar with Coriolis, check the references below, but basically is a force that applies to something that accelerates in a non inertial frame, like the Foucault pendulum).

The displacement is measured by sensors that are along the mass housing and the rigid structure. As the mass is pushed by the Coriolis force, a differential capacitance will be detected.

Even if the principle is different, and is not based on Coriolis force, one way to visualize a rotational velocity is the swing ride (even though when you kick your partner out he will experience Coriolis force…).

The faster the swing spins, the higher you go. That is because of that fictitious force named centrifugal, that is actually the chain preventing you to fly away. Your altitude is basically a measure of the ride’s speed.

Measuring the rotational velocity is of primary importance, as it can be integrated to obtain an estimate of the actual tilt angle and represents a great signal for feedback control loops. Unfortunately, gyros are noisy and their output at rest varies with the temperature.


Magnetometers… I hate them! Seriously! But, they are the only sensor that can give your heading. A magnetometer measures the local magnetic field components and you can compare those values with the World Magnetic Field Model in order to estimate the attitude, and thus the heading respect to the local magnetic North. Why do I hate them? Because almost everything affects the local magnetic field… electric lines, Sun activities, internal wiring, other sensors, transmitters or even the CPU… That is the reason why you want to put your magnetometer as far from any interference as possible. Still what you measure is your attitude respect to the local magnetic field: the local declination is added up in order to obtain the heading respect to the true North.

If you want to have an idea of how the magnetic field is easily affected by external disturbances, use a compass or install an app on your phone and try to walk in the office, close to the computers or metal objects: you’ll see the needle going nuts.

Miniaturized magnetometers are based on the Anisotropic Magnetoresistance phenomenon: basically the material changes its internal electric resistance when exposed to a magnetic field: check the references for more details.


Sensors would be useless without a proper calibration. For accelerometers and magnetometers you would probably do it once in a while, while gyros need to be calibrated every time before starting.

Why calibrate? Because the output signal is usually as:

measure = scale_factor*signal + bias + noise (m = sf*s + b + n)

The real signal is multiplied by a scale factor and then corrupted by an almost static bias value and a random noise.

While the noise can be easily filtered out, scale factor and bias are almost constant, thus they must be evaluated properly.

For the gyros, the bias is easily estimated before flying, when the vehicle is assumed to be still on the ground, so the actual measured rotational speed is only the bias component.

For accelerometers and magnetometers, the procedure is a little more complex, but basically you want to put your autopilot at different angles and estimate the best fitting sphere out of the measured quantities.

What have we learned

The world of autopilot surely is intriguing. We have just begun to scratch the surface and we still have a long road ahead. IMUs are fundamental to Robotics and Drones just as much as smartphones.


SensorWikiaccelerometersCoriolis forceFoucault pendulumgyrosEarth Magnetic Modelaccelerometer calibrationmagnetometer calibration algorithm