### IMU Working Principles

Inertial sensors, also called IMUs (Inertial Measurement Unit), are measurement electronic devices that allow estimating the orientation of a body from the inertial forces that the body experiments. Its working principle is based on measuring the forces of acceleration and angular velocity exerted independently on small masses located inside.

The inertial technology is based on the first two Newton’s laws. The first law states that the movement of a body is uniform and linear unless an external force is acting on it. The second law defines that this force exerted on the mass will produce a proportional acceleration. These relationships represent a measurement principle in which sensing devices can be developed able to measure the movement of bodies. Therefore, if we know the magnitude and direction of the force applied to a body and its mass, we can know its acceleration and therefore its speed and position by the first and second mathematical integration of the acceleration versus time.

A conventional IMU has inside a tri-axial accelerometer and a tri-axial gyroscope to estimate its orientation in a three-dimensional Euclidean space (3D). Figure 1 shows a conventional 3D IMU.

Figure 1. Tri-axial Inertial Measurement Unit (IMU).

A uniaxial accelerometer consists on a mass suspended by a spring in a receptacle. The mass can be moved in one direction, which is the measurement direction of the accelerometer. The displacement of this mass is a measure of the difference between acceleration and gravity on the direction of measurement. Thus, a tri-axial accelerometer consists of three uniaxial mounted orthogonally to provide acceleration information in 3D space.

Furthermore, the angular velocity of rotation of the body relative to the inertial reference system can be measured with a device called gyroscope. The construction of the gyroscope can be based on different designs. MEMS gyroscopes (Micro-machined Electro Mechanical System) employ the principle of Coriolis acceleration, based on the vibration of a body for detecting an inertial angular rotation. If the receptacle rotates with an angular velocity perpendicular to the plane, the mass will experience a Coriolis force in the direction perpendicular to the angular velocity. Therefore, displacement caused by Coriolis force is proportional to the angular velocity. Likewise, by integrating the angular velocity, we can obtain the angle of rotation of the body on a single axis. Thus, using three uniaxial gyroscopes perpendicular to each other, a tri-axial gyroscope can measure the rotation of a body in 3D space.

Additionally, current IMUs may incorporate a tri-axial magnetometer. The magnetometer is a magnetic field responsive element, which provides information on the orientation of a body relative to the earth’s magnetic north, e.g. a compass. Since this sensor’s information is absolute, it is often used to reduce measurement errors obtained from the accelerometers and gyroscopes, increasing, this way the accuracy of estimating orientation.

Signals obtained from the accelerometer, gyroscope and magnetometer are fused to obtain the orientation of the IMU, represented by a Direction Cosine Matrix (DCM), also called rotation matrix, or a Quaternion vector. The DCM expresses the orientation of the IMU with respect to a fixed coordinate system in which the X-axis direction points toward magnetic north, and the Zaxis pointing in the same direction as the force of Earth’s gravity (with opposite sign). The process by which the IMU orientation can be estimated, can be divided into two main steps. The first step is the estimation of the initial orientation through the 3D accelerometer (3D Acc) and the 3D magnetometer (Mag 3D) measurements. This process is done only once, when the IMU is stationary and before the user can start any motion. The process could be summarized with the following equations:

The second step is to estimate the orientation of the IMU when movement begins. The 3D gyro sensor is involved in this process. Through the integration of angular velocity signals obtained from the 3D gyro (3D Gyro), it is possible to know the angle of rotation of each axis of the IMU. The previous DCM ( ) is updated by adding the new rotation calculated. The process is summarized in the following equations:

These two steps are used in a robust sensor fusion process to estimate the orientation from the inertial data. An Extended Kalman Filter (EKF), running on the IMU, carries out this process. The following figure shows a block diagram of the process performed by the IMU:

Figure 2. Block Diagram of an IMU internal process to obtain the 3D orientation.

New applications have required the development of low-cost and highly miniaturized sensors. However, size reduction has resulted in several additional technological challenges to achieve adequate accuracy and resolution. In general, miniaturization leads to reduced sensitivity, increased noise and greater temperature dependence. To reduce these technological limitations processing algorithms have been developed to perform a sensory fusion using redundant information for added robustness to the estimation. Advances in the knowledge of this technology and strategies to compensate its limitations have noticeably increased accuracy.

Current miniaturization and availability of IMUs makes it possible to have static or ambulatory measurement devices that can be placed on different body parts (head, limbs, trunk, etc.) to know its position and movement inside or outside a controlled laboratory. Currently, these devices are being employed in many applications, which include monitoring the activities of daily living or the research on the motor control of the body with various pathologies and especially interface control. Thus, this technology allows to extract kinematic patterns of human movement with the advantage of not requiring the implementation of complex algorithms for motion reconstruction as in the case of other interfaces based on computer vision, where obtaining kinematic patterns requires image processing and three-dimensional modelling and requiring certain lighting conditions.