Initialization algorithm for spatial orientation quaternion in Rodrigues-Hamilton parameters

Introduction. The correction time reduction for the spatial orientation evaluation of a solid under the orientation system initiation is considered. Solid spatial orientation is measured by the integrated values from three orthogonal angular speed sensors. Difference between the actual spatial orientation and the orientation estimated by sensors is adjusted due to the data obtained from other sensors, such as accelerometers and magnetometers. Major existing algorithms deduct data acquired from accelerometers and magnetometers from the evaluation of angular rate through the correction factor thus correcting the spatial orientation assessment error. The higher the solid inclination angle in relation to horizon when the orientation system is switched on, the greater the spatial orientation error is. The algorithm presented herein corrects the spatial orientation evaluation in quaternion components without angular rate sensors which allows minimizing the spatial orientation assessment error within shorter time in comparison with the existing algorithms.

Materials and Methods. To implement the correction algorithm, the MPU6050 sensor is used. It is made with microelectromechanical technology, and its body includes three orthogonally located angular velocity sensors and three orthogonally located accelerometers. The output data from MPU6050 sensor is processed by dsPIC33EP256MU806 microchip. The spatial orientation is calculated by the Rodrigues-Hamilton parameters in the quaternion components. The result is input to the Matlab software package which executes the program of visualizing the dependencies on the time of four quaternion components graphically.

Research Results. In existing algorithms that use the Rodrigues-Hamilton parameters, at the initial initialization of the orientation system, it is suggested to increase the correction factor, or to use the trigonometric formulas to find the Euler angles and translate them into the RodriguesHamilton parameters. In the first case, the initial initialization time remains sufficiently long, in the second case, due to the use of Euler angles, a phenomenon of “gimbal lock” can be observed. The proposed algorithm performs the initial initialization in a time equivalent to the initialization time in the Euler angles parameters, but it applies only the RodriguesHamilton parameters.

Discussion and Conclusions. Using the proposed algorithm will allow a minimum of 5-fold reduction in the initial initialization time of the spatial orientation quaternion. In consequence, the total time required for activating the system will be also reduced due to the fact that the initial initialization is necessary every time the orientation system is switched on. For the correct determination of the spatial orientation according to the proposed algorithm, the necessary condition is the absence of any acceleration on the body other than the gravitational acceleration because the initialization occurs only upon the accelerometer readings. 

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