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 article is focused on the search for potential collision of a moving object (as a mobile robot is) with the environment. Application of the proposed and presented method requires existence of the three-dimensional model of the environmental space. In this case, the models are generated automatically with the help of mobile measurement platform developed by authors and are available to other applications. Models of moving objects are loaded by the proposed application from external files. The method is based on data fusion, using data from a laser scanner, global positioning system, and inertial navigation system; however, it can also be used for data obtained by other ways. Its correctness was experimentally proved by several experimental tests. Output is in the form of calculated coordinates of the point in which a moving object would potentially collide with the environment if no avoiding action is taken. Such an object may represent an oversized load transferred by a truck, train, ship, the transport means itself or even a person.

The article deals with sensor fusion and real-time calibration in a homogeneous inertial sensor array. The proposed method allows for both estimating the sensors’ calibration constants (i.e., gain and bias) in real-time and automatically suppressing degraded sensors while keeping the overall precision of the estimation. The weight of the sensor is adaptively adjusted according to the RMSE concerning the weighted average of all sensors. The estimated angular velocity was compared with a reference (ground truth) value obtained using a tactical-grade fiber-optic gyroscope. We have experimented with low-cost MEMS gyroscopes, but the proposed method can be applied to basically any sensor array.

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.

Predictive control seems to be a promising approach that can help to improve properties of existing ventilation systems applied in road tunnels. Advantages of predictive control result mainly from its ability to solve both SISO and MIMO tasks, to have regard for dynamics of process changes in a broad extent, to compensate effect of measurable and non-measurable failures and to formulate the task as an optimization control task considering limiting conditions of control actions, changes of control actions and output variables. Data characterizing the existing ventilation system can be used to analyze and identify the system and create its models. Thereafter the predictive control of ventilation can be designed enabling to predict concentrations of pollutants and optimize system operation.

Each safety-related function must be implemented with a defined safety integrity level (SIL) if the control system implements safety-related functions (SFs) in addition to the standard control functions. The required SIL of the SF depends on the quantity of the risk associated with the failure of this one SF. The SIL against random failure can be expressed through the dangerous failure rate of the SF for an electronic safety-related control system (ESRCS) operating in a continuous mode of operation. The proof must be provided (among other things) that the SIL requirements for the individual SFs are met so the ESRCS can be accepted and implemented. The assessment of the impact of random failures on the SIL of the SF must be performed using the quantitative analysis method. This paper describes the procedure and derives equations for evaluating the impact of random failure on SIL of the SF using Markov chains with two absorption states. The achieved results are presented for SF implemented by ESRCS with dual architecture based on composite fail-safety technique.