[MUSIC] In this lesson we are going to discuss the Inertial Measurement Unit or IMU. By the end of this lesson you will be able to describe the operating principles of the two sensors that make up the basic IMU, an Accelerometer and a Gyroscope. You will also be able to model each of these sensors, and account for things like sensor noise and bias. This will be crucial when we incorporate an IMU into a full-state estimator. Let's begin. The inertial measurement unit, or IMU measures the movement of a body in inertial space. Today a certain type of cheap, mass manufactured IMU, is found in nearly every smartphone, such as the iPhone X pictured here. IMUs are often used tasks including, step counting for health tracking, and more recently as augmented reality devices. Despite their ubiquity today, the development of a sensor that could accurately track the motion of a moving body was a significant achievement of the 20th century. The IMU aided transoceanic flights long before GPS, and was crucial to the Apollo missions as part of the on board guidance, navigation, and control system. The Apollo spacecraft relied on an IMU to accurately track both the position, and orientation of the vehicle on the long voyage to the moon. In space there are few landmarks to rely on for guidance. One can track the fixed stars but this is not easy. The onboard IMU which operated without the need for such landmarks Enabled safe navigation to the Moon's surface. In modern self-driving cars, IMUs play a very similar role. Filling in during periods when navigation information from other sensors is either unavailable or unreliable. So what is an IMU? Well, generally, an inertial measurement unit is a composite sensor suite that combines three gyroscopes and three accelerometers to track the exterior free movement of a rigid body. Some IMUs also incorporate magnetometers, or a compass, to help track orientation. IMUs come in many shapes and forms. The sensors found in modern smartphones are relatively cheap, often costing less than a few dollars when purchased in bulk. They are lightweight and require relatively little power but produce quite noisy measurements. More expensive IMUs use more complex components and have more accurate calibration models that can remove the effects of temperature fluctuations, for example. Let's discuss the components of an IMU. The gyroscopes and the accelerometers in more detail. The gyroscope has a long history. The term gyroscope can be quite confusing, because it refers to several concepts all relating to the idea of measuring orientation or change in orientation. The word itself comes from the Greek words Guros, for circle, and skopeo, to look. Historically, a gyroscope was a spinning disk that due to its angular momentum resisted changes in orientation. In the late 19th and early 20th century, engineers realized that this spinning wheel could be used as an orientation reference for marine and aeronautical navigations. This required precise machining, and instead of gimbals, it used high quality jewel or numeric bearings. Although this type of spinning disc gyroscope can be very accurate, it's quite heavy, bulky and often very expensive to manufacture. Nevertheless, it is still using aeronautics and in ballistic applications and can spin it up to 24,000 RPM. In a modern gyroscope, the spinning wheel is typically replaced by a microelectromechanical system that consists of a small silicon tuning fork that changes its resonance properties based on an applied rotation or orientation change. These sensors are much cheaper and can fit in a tiny package. However, they produce noisy measurements and are sensitive to temperature based fluctuations. What's more, they measure rotation rates, and not orientation directly, and so the output signal must be numerically integrated to determine orientation change. This process can introduce additional errors into the final orientation estimate. A self driving car engineer should be aware need to account for issues such as drift and performance variation with temperature introduces substantial additional complexity in the sensor modeling process. One would normally think that a spinning mechanical device would be inferior to a silicon component but this is not always the case. An accelerometer measures acceleration along a single axis. Cheaper MEMS based accelerometers use a miniature cantilever beam with a proof mass attached to it. When the sensor is accelerated, the beam deflects. This deflection can be measured through a capacitive circuit for example, and converted into an acceleration value. More expensive sensors may also use Piezoelectric materials. It's important to note that an accelerometer measures what's called proper acceleration, or specific force. This is the total non-gravitational force per unit mass. The proper acceleration is acceleration with respect to a reference frame in free fall. When you're sitting in your chair, stationary relative to the ground, the proper acceleration you feel will be the value of the gravitational acceleration at your location, but upwards. Another way to say this is that the only non gravitational force acting on you, the normal force, must be equal to the force of gravity. However, of course, for navigational purposes, we often don't care about our proper acceleration. What we care about is acceleration with respect to some fixed reference frame. To compute this acceleration, we need to use the fundamental equation for accelerometers in a gravity field. The second derivative opposition, computed in a fixed frame, is the sum of the specific force, and the acceleration due to gravity. Sometimes this could be sum up and intuitive concept. So let's explore it here An accelerometer in a stationary car measure g upwards, because the coordinate acceleration is zero, ignoring the rotation of the Earth. Since the force of gravity acts downwards its negative is the scalar constant g in the upward direction. Let's look at an example of this on the International Space Station or ISS. Is the value of g less in low Earth orbit? Well, it is, but only by about 10% when compared to the value on the surface of the Earth. The reason why we often hear the term 0 g is because the entire ISS is in free fall together with the astronauts inside it. An accelerometer rigidly attached to the station will have a coordinate acceleration equal to g. This means that the specific force measured by an accelerometer will be 0. Another way of saying this is that the proper acceleration with respect to free fall is 0. The ISS is in free fall. In reality residual atmospheric drag and structural vibrations will create some measured accelerations but they are typically as low as 10 to the -6 g's. Now, that we know about the basic principles of gyroscopes and accelerometers, let's discuss the measurement models we'll need to know in order to incorporate them into a state estimator. [SOUND] Using the notation we discussed in the previous lesson, let's define an expression for what a gyroscope measures. The angular rotation rate, derived from all three gyroscopes, is the angular velocity of the body frame relative to an inertial frame, expressed in the body frame. To it will be add a slowly varying bias term and a white Gaussian additive noise term to model sensor errors. Although gyroscopes do measure the rotation of the Earth, it's often safe to ignore this for applications where we care only about motion over a short duration. Our accelerometer measurement model will have similar noise and bias terms. But now instead of measuring body accelerations directly as we could do with rotational rates, we need to explicitly remove the effect of gravity using our fundamental equation for accelerometers in a gravity field. Since the accelerometers measure acceleration in the IMU body frame, we will need to keep track of the orientation at all times in order to be able to perform the necessary subtraction. Finally, let's discuss a few important limitations of our models. First, an accurate orientation estimate is critical for accurate position estimates. When we convert the measured specific force into an acceleration we have to make sure that the direction of gravity is correct. Otherwise even a small error in orientation can cause us to think that we are accelerating when we're not. Second, both of the models we derived ignore the effects of the Earth's rotation. For longer distance navigation, this is in fact, important. Finally, the models we have derived are for strapdown IMUs. These are IMUs that are physically strapped down to the vehicle and do not incorporate a spinning wheel on gimbals. Although a latter can be much more accurate, they are rarely used in automotive applications because of their bulk and their cost. To summarize, in this video we learned that a 6 degree of freedom IMU is composed of three gyroscopes and three accelerometers. The gyroscopes measure rotational rates in the sensor frame. And accelerometers measure the non-gravitational specific force in the sensor frame as well. Since strapdown IMUs are tricky to calibrate and drift over time, we'll need another sensor to periodically correct our posed estimates. For this, we can use the modern system of global navigation satellites. We'll talk more about this in the next lecture. [MUSIC]
