Control design for multi-rotor aerial vehicles (MAVs) is quite challenging problem due to their nonlinearitles, unknown dynamics, parametric uncertainties, an underactuated property, a nonlinear coupling dynamics and external disturbances. This paper introduces a first order sliding mode control (FOSMC) for robust stabilization of an under-actuated quad-rotor unmanned aerial vehicle (UAV) operating in the presence of external disturbances. The proposed FOSMC guarantees a finite time convergence of the system trajectories to the sliding surface. Obtained simulations show that the FOSM based approach improves robustness properties compared with the concurrent techniques, and enhance tracking performance of the quad-rotor UAV exposed to external disturbances.

Control design for trajectory tracking of multi-rotor aerial vehicles (MAVs) represents a challenging task due to the under-actuated property, highly nonlinear and cross-coupled dynamics, modeling errors, parametric uncertainties and external disturbances. This paper presents the design of the first order sliding mode control (FOSMC) algorithm for trajectory tracking of the octo-rotor unmanned aerial vehicle (UAV) in the presence of various disturbances. The highly nonlinear octo-rotor UAV dynamics is considered via the generalized framework for MAVs modeling. The stability analysis of the closed-loop system is presented using the Lyapunov based approach. The developed FOSMC exhibits finite-time convergence of the octo-rotor trajec-tories to the sliding manifold and the asymptotic stability of the equilibrium in the presence of vanishing disturbances. Simulation studies show a superior tracking performance and robustness properties of the FOSMC in comparison with the concurrent techniques for trajectory tracking of the octo-rotor UAV in the presence of internal and external disturbances.

The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.

This book provides a solution to the control and motion planning design for an octocopter system. It includes a particular choice of control and motion planning algorithms which is based on the authors' previous research work, so it can be used as a reference design guidance for students, researchers as well as autonomous vehicles hobbyists. The control is constructed based on a fault tolerant approach aiming to increase the chances of the system to detect and isolate a potential failure in order to produce feasible control signals to the remaining active motors. The used motion planning algorithm is risk-aware by means that it takes into account the constraints related to the fault-dependant and mission-related maneuverability analysis of the octocopter system during the planning stage. Such a planner generates only those reference trajectories along which the octocopter system would be safe and capable of good tracking in case of a single motor fault and of majority of double motor fault scenarios. The control and motion planning algorithms presented in the book aim to increase the overall reliability of the system for completing the mission.

The paper addresses the problem of detecting pedestrians using three dimensional data acquired by an autonomous mobile robot equipped with an on-board 3D laser scanner. Previous works in this field have dealt with various approaches for combining 2D and 3D range data features for the use in pedestrian classification. In this paper we propose an image processing pipeline for generating a depth image from point clouds data and then localizing object candidates from the depth image. It involves the image segmentation, feature extraction and human classification processes within unstructured dynamic environments. Three different approaches for the detection of pedestrians, vehicles and cyclists using only 3D range data were employed as a part of this system. We train and test the classifiers in an open environment, with presence of multiple pedestrians, cyclists and vehicles, using only point cloud data. The effectiveness and robustness of the proposed system are verified through experiments with real data. This system is also capable to deal with a real-time framerate (10Hz) with high accuracy.

The paper deals with the mathematical modeling and control of an unmanned aerial vehicle (UAV), called octocopter, based on a linear quadratic regulator (LQR). The complex multivariable and nonlinear UAV model is linearized and represented in the state space form. Optimal LQR control system, which is composed of combination the altitude (UAV height - ${z}$ position) and attitude (orientation) controllers, was first designed. Then, this system is extended to provide an additional control of the translation movement in ${x}$ and ${y}$ directions. The proposed LQR control structure is capable of controlling the UAV for all position and orientation coordinates while tracking desired 3D trajectory. Simulation studies are performed on the UAV model where the designed LQR controller has been compared with previously developed PD controller.

The paper presents a calculation of a system supported on piles according to the second order theory. The influence of piles as supports on the structure is replaced by elastic supports. In the numerical model, the supports are modeled as elastic springs. To compare the calculation results, a system based on rigid and deformable supports was analyzed. The analysis of the system was performed according to the first order theory and the second order theory, which introduces geometric nonlinearity into the calculation. The process of soil modeling around a pile with replacement springs is presented. The applicability of the described procedure is shown in a numerical example. The comparison of the calculation results was done on numerical models of systems with rigid and elastic supports.

The paper presents a procedure for numerical modelling of the rod cross-section bearing capacity. Equilibrium between cross sectional forces and cross-sectional stresses is determined by iterative procedures. According to the described procedure, the load-bearing capacity of the cross-section is determined according to the isotropic linear and nonlinear behavior of the material, for homogeneous and inhomogeneous cross-sections. The nonlinear behavior of the material reduces the stiffness of the cross section of the rod EA and EI, with a significant increase in the deformation values ε and κ. The applicability of the calculation and analysis of obtained results is presented using numerical examples.

Summary: The paper presents a procedure for numerical modelling of the geometric nonlinearity of a rod. The calculation of cross-sectional forces, displacements and rotations of nodes was done by iterative methods on a deformed system. By the described procedure, the equilibrium state is established in the finite position of the rod. In the process of deformation, there is an increase in cross-sectional forces and deformation of the rod. The presented calculation methods are used to model geometric nonlinearity with constant and variable stiffness of the cross section of the rod. The calculations were done numerically, and the results were controlled using the SCIA software package. Through numerical examples, the calculation procedure was presented and the analysis of the results was performed.