Module imu mod IFETI_v0.2

Overview

This module is in charge of camera attached orientation frame time integration using a simple explicit numerical scheme. Initial conditions have to be available in order to compute numerical time integration.

Module nomenclature

This stream module waits four physical streams as input. Three physical streams have to carry the three unit vectors three dimensional components that are considered as initial conditions. The last physical stream have to carry IMU angular velocities.

Three physical streams are initiated by the module. Each one stores the three components of one unit vectors integrated over time of the camera attached frame. The synchronization component of the three output streams is identical to the input stream synchronization component.

Module interface

This section gives a summary of the module interface in terms of streams and devices. The order of devices and streams is given as waited by the module. The devices interface is given by :

device( Physical ) IMU sensor

The stream input interface is :

stream( Physical | IMU ) Gyroscopic velocities
stream( Physical | IMU ) Frame initial x-vector
stream( Physical | IMU ) Frame initial y-vector
stream( Physical | IMU ) Frame initial z-vector

and the stream output interface is :

stream( Physical | IMU ) Frame x-vector
stream( Physical | IMU ) Frame y-vector
stream( Physical | IMU ) Frame z-vector

The three last input stream are attached as well as the output streams.

Module operation

The IMU gyroscope sensor provides angular velocities according to devices defined axis. The considered equation of motion, usually called Poisson relation, is given by :

    d(u)/dt = ω × u = ƒ(ω,u,t)

where u is a frame unit vector, ω being the angular velocity vector. The ω vector is provided by the IMU sensor when u is the problem unknown.

Because initial conditions can be provided using different methods, they can be defined anywhere according to time. As a result, numerical integration have to be peformed according to time direction from initial conditions and also against time flow from those same conditions. Two simple explicit numerical schemes are considered for unit vectors components integration :

    uª(i+1) - uª(i) = h(i) ƒ(ω(i),u(i),t(i))

for time direction integration and :

    uª(i) - uª(i-1) = h(i) ƒ(ω(i),u(i),t(i))

for integration against time flow. In the previous relation, a = x, y, z and h(i) designate the time step value for range [i,i+1] and [i-1,i].