Determination of Motion Parameters with Inertial Measurement Units – Part 1: Mathematical Formulation of the Algorithm

The paper tackles the problem of determination of motion parameters of a wheeled mobile robot using the inertial measurement method. By the motion parameters one means: positions, linear velocities and accelerations of characteristic points of the robot, as well as Euler angles and angular velocity and acceleration of a robot body. Existing methods of determination of robot motion parameters, including the inertial method, the satellite navigation method and hybrid methods, are briefly discussed. The method of determination of motion parameters of a wheeled mobile robot with Inertial Measurement Units is described in details. It involves measurement of three components of acceleration of a selected point on the robot using a three-axial accelerometer and three components of angular velocity of the robot body using a three-axial gyroscope. Desired motion parameters are obtained as a result of differentiation, integration and other mathematical transformations. It was assumed that most of the analyzed motion parameters are calculated both in the coordinate system associated with the robot (moving) and in the reference coordinate system (stationary). The presented method is simple, but enables measurement of wide range of 3D motions, and as such it can be used as a benchmark for advanced algorithms of determination of motion parameters. In the Part 2 of this article, the proposed measurement method is verified in empirical experiments with a wheeled mobile robot using the Inertial Measurement Unit based on low-cost MEMS sensors.