This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)—the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angles and on unit quaternion expressing rotation. Algorithms are compared by their computational efficiency and accuracy of Euler angles estimation. If attitude of the object is computed only from data obtained by the gyroscope, the quaternion-based algorithm seems to be most suitable (having similar accuracy as the matrix-based algorithm, but taking approx. 30% less clock cycles on the 8-bit microcomputer). Integration of the Euler angles’ time derivations has a singularity, therefore is not accurate at full range of object’s attitude. Since the error in every real gyroscope system tends to increase with time due to its offset and thermal drift, we also propose some measures based on compensation by additional sensors (a magnetic compass and accelerometer). Vector data of mentioned secondary sensors has to be transformed into the inertial frame of reference. While transformation of the vector by the matrix is slightly faster than doing the same by quaternion, the compensated sensor system utilizing a matrix-based algorithm can be approximately 10% faster than the system utilizing quaternions (depending on implementation and hardware).

This paper discusses an innovative adaptive heterogeneous fusion algorithm based on estimation of the mean square error of all variables used in real time processing. The algorithm is designed for a fusion between derivative and absolute sensors and is explained by the fusion of the 3-axial gyroscope, 3-axial accelerometer and 3-axial magnetometer into attitude and heading estimation. Our algorithm has similar error performance in the steady state but much faster dynamic response compared to the fixed-gain fusion algorithm. In comparison with the extended Kalman filter the proposed algorithm converges faster and takes less computational time. On the other hand, Kalman filter has smaller mean square output error in a steady state but becomes unstable if the estimated state changes too rapidly. Additionally, the noisy fusion deviation can be used in the process of calibration. The paper proposes and explains a real-time calibration method based on machine learning working in the online mode during run-time. This allows compensation of sensor thermal drift right in the sensor's working environment without need of re-calibration in the laboratory.

A haptic interface is a kinaesthetic link between a human and some real or virtual environment. In this article, we discuss whether the haptic technology (virtually touching objects and feeling forces) could be effectively implemented in the industrial applications. As an example, we will examine the virtual wall which is a fundamental component of almost all virtual objects. Typically, it is based on a simple spring and damper model with constraints that allow the user to make contact with an object. Various factors lead to an unstable behaviour in a controlled system such as the virtual wall. Main causes of disturbances are the sensor (e.g. the signal resolution) and the actuator (e.g. the dynamics of the system which are not covered by the controller design). Some of these disturbance mechanisms can be excluded by mechanical design, and others are more difficult to eliminate – following two are discussed in the article: First one is the zero-order hold effect caused by sampling and the second one is the shifted synchronization of the wall threshold crossings with the sampling times. Both have unwanted effects on the sampled data within the virtual wall system.

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