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).

The review discusses the possibilities of different driving mechanisms and sensors of spherical robots, and a special kind of mobile robots is introduced and discussed. The sensors discussed can expand robots’ sensing capabilities which are typically very limited. Most spherical robots have holonomic characteristics and protect the inner environment using a shell. Today, there are a diversity of driving mechanisms. Therefore, this article provides a review of all of them and identifies their basic properties. Accordingly, many spherical robots have only inner sensors for moving, balancing, driving, etc. However, a few of them are also equipped with sensors that can measure environmental properties. Therefore, in this paper, we propose the possibility of using such sensors as cameras, LiDARs, thermocouples, and gas sensors, which can be used for special purposes underground, for example, in mines, underground tunnels, or road tunnels. After combining all components are combined, it is possible to design a special type of spherical robot designed for underground exploration, such as accidents in mines or road tunnels.

This paper discusses an innovative adaptive heterogeneous fusion algorithm based on the 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 three-axial gyroscope, three-axial accelerometer, and three-axial magnetometer into attitude and heading estimation. Our algorithm has a similar error performance in the steady state but much faster dynamic response compared with 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. In addition, the noisy fusion deviation can be used in the process of calibration. This 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 recalibration in the laboratory.

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.

Odometry is one of most-used techniques used in mobile robotics and autonomous vehicles, especially when the indoor navigation is required or when robot or vehicle moves inside the tunnel. The output of the odometer is usually a count of pulses corresponding to the distance run by given wheel. Due to the quantization noise, estimation of the velocity (first derivative of the distance) is challenging. This paper is focused on curve-fitting filter used for the speed estimation and optimization of its parameters, considering the physical constraints of the robot, sampling frequency of the system and the quantization step. The paper proposes an empirical formula for estimating the optimal parameters of the curve fitting filter. The optimized filter has been evaluated using both simulation and real experiment and compared with several standard differentiation methods.

The autonomous movement of the mobile robotic system is a complex problem. If there are dynamic objects in the space when performing this task, the complexity of the solution increases. To avoid collisions, it is necessary to implement a suitable detection algorithm and adjust the trajectory of the robotic system. This work deals with the design of a method for the detection of dynamic objects; based on the outputs of this method, the moving trajectory of the robotic system is modified. The method is based on the SegMatch algorithm, which is based on the scan matching, while the main sensor of the environment is a 2D LiDAR. This method is successfully implemented in an autonomous mobile robotic system, the aim of which is to perform active simultaneous localization and mapping. The result is a collision-free transition through a mapped environment. Matlab is used as the main software tool.