The article addresses the issue of mobile robotic platform positioning in GNSS-denied environments in real-time. The proposed system relies on fusing data from an Inertial Measurement Unit (IMU), magnetometer, and encoders. To get symmetrical error gauss distribution for the measurement model and achieve better performance, the Error-state Extended Kalman Filter (ES EKF) is chosen. There are two stages of vector state determination: vector state propagation based on accelerometer and gyroscope data and correction by measurements from additional sensors. The error state vector is composed of the velocities along the x and y axes generated by combining encoder data and the orientation of the magnetometer around the axis z. The orientation angle is obtained from the magnetometer directly. The key feature of the algorithm is the IMU measurements’ isolation from additional sensor data, with its further summation in the correction step. Validation is performed by a simulation in the ROS (Robot Operating System) and the Gazebo environment on the grounds of the developed mathematical model. Trajectories for the ES EKF, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms are obtained. Absolute position errors for all trajectories are calculated with an EVO package. It is shown that using the simplified version of IMU’s error equations allows for the achievement of comparable position errors for the proposed algorithm, EKF and UKF.
The article presents the results of mathematical modelling of geomechanical processes that occur during the construction of an escalator tunnel using EPB TBM at the «Mining Institute» station in Saint Petersburg. A numerical model was built using the finite element method implemented in «Plaxis 3D» software. Hardening soil model was used for modelling of soil massif. The analysis of the distribution of displacements and deformations in the main cross-sections of the displacement trough is performed. Issues of assessing the harmful effects of underground construction on undermined buildings and structures are considered. Based on the research, we can conclude that the construction of a tunnel is safe for undermined buildings with strict tunnelling technologies compliance.
The article presents a comparative analysis of the results of mathematical modeling of horizontal tunneling in the Plaxis 3D software package. Two main ways of modeling the tunnel lining were considered: models based on volumetric elements and using the Plate tool. An analysis was made of the distribution of displacements and deformations on the surface: subsidence, inclinations, curvature, horizontal deformations. Comparison of the maximum strain values showed an insignificant deviation (approximately 5%), which proved the applicability of the two models. For further work, a method using the Plate tool could be recommended as being more suitable in the case of complex models with a large number of intersections.
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