A relevant task in unmanned aerial vehicles (UAV) flight is path planning in $3D$ environments. This task must be completed using the least possible computing time. The aim of this article is to combine methodologies to optimise the task in time and offer a complete $3D$ trajectory. The flight environment will be considered as a $3D$ adaptive discrete mesh, where grids are created with minimal refinement in the search for collision-free spaces. The proposed path planning algorithm for UAV saves computational time and memory resources compared with classical techniques. With the construction of the discrete meshing, a cost response methodology is applied as a discrete deterministic finite automaton (DDFA). A set of optimal partial responses, calculated recursively, indicates the collision-free spaces in the final path for the UAV flight.

One important challenge in the current research of UAVs is the obstacle avoidance feature, a highly demanded capability in all kinds of UAV applications. Different algorithms that perform sampling tasks in continuous or discrete spaces are widely used in path planning. The Probabilistic Roadmap (PRM) and Rapidly Exploring Random Tree (RRT) variants have a stochastic essence, which allows them to obtain a response even in wide and complex environments. However, they present disadvantages related to computational cost and time convergence of results. In this paper a survey on sampling-based planners is presented, comparing algorithms with continuous and discrete sampling in 3D environments. On the other hand, two new variants are introduced: the Exact Cell Decomposition on Probabilistic Roadmap (ECD-PRM), as an extension of PRM method, and the Modified Adaptive Cell Decomposition (MACD) performing a reduced space decomposition. The comparison is performed attending to several criteria such as path cost, number of generated nodes and number of control points in the final path, whenever it has been reached.

Demand for 3D planning and guidance algorithms is increasing due, in part, to the increase in unmanned vehicle-based applications. Traditionally, two-dimensional (2D) trajectory planning algorithms address the problem by using the approach of maintaining a constant altitude. Addressing the problem of path planning in a three-dimensional (3D) space implies more complex scenarios where maintaining altitude is not a valid approach. The work presented here implements an architecture for the generation of 3D flight paths for fixed-wing unmanned aerial vehicles (UAVs). The aim is to determine the feasible flight path by minimizing the turning effort, starting from a set of control points in 3D space, including the initial and final point. The trajectory generated takes into account the rotation and elevation constraints of the UAV. From the defined control points and the movement constraints of the UAV, a path is generated that combines the union of the control points by means of a set of rectilinear segments and spherical curves. However, this design methodology means that the problem does not have a single solution; in other words, there are infinite solutions for the generation of the final path. For this reason, a multiobjective optimization problem (MOP) is proposed with the aim of independently maximizing each of the turning radii of the path. Finally, to produce a complete results visualization of the MOP and the final 3D trajectory, the architecture was implemented in a simulation with Matlab/Simulink/flightGear.

This paper presents a path planning approach for Unmanned Aerial Vehicles (UAVs) with non-holonomic constraints, such as fixed-wing airplanes. The control scheme is divided in two stages: local planner and kinematic control. In the planning stage, a smooth curve is generated in 3D Euclidean space, using 3D clothoids approximated by Rational Bézier curves. Then, in a second stage, the autonomous flying vehicle is piloted to track references of velocity and orientation. Real flight simulation tests have been carried out to observe the behaviour of the UAV when following 3D clothoids, in order to analyze the properties and benefits of using such smooth curves for path planning of fixed-wing planes.

This paper presents a comparison of two classic path planning techniques, Rapidly-Exploring Random Tree and Modified Adaptive Cell Decomposition applied to 3-Dimensional space path planning generation for UAVs. The study presented focuses on the inclusion of real fixed-wing UAVs maneuverability, where the dynamic and kinematic behaviour introduces hard constraints in real environments. In addition, the inclusion of Dubins and Clotoids curves in 3-Dimensional spaces has been considered in terms of improving the results of these classical methods. Flight simulation results have been included to clarify this comparative study.

Atmospheric temperature describes the specific heat content of the air at particular places and times. In this sense, the presented work proposes a multivariable system that takes data sets of different climatological variables, with the aim of regulating the temperature level. The diversity in climatological variables significantly affects precipitation, humidity, wind speed and temperature. Thus, a study has been carried out on these variables in terms of nonlinear dynamics. The aim of the work is to obtain a better understanding of the dynamics of local climatological variables. On the other hand, due to the fact that the time series analyzed are small, the analysis becomes complex, at the moment of joining all the variables in conjunction, and processing them by means of multivariate statistical prediction methodologies. The results have shown the mean values in the different variables with which a temperature is maintained between and , which shows possible work with multi-objective optimization of the obtained model.