The aim of this master's thesis is the implementation of optimal trajectory planning for an airplane flying in lower altitudes, which has to avoid collision with obstacles. For the planning we assume static and fully known environment. There are described principals, optimality and complexity for some chosen methods of planning in this thesis. And based on the methods' characteristics it's chosen the best method for implementation.

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Applications such as urban surveillance, search and rescue, agricultural applications, military applications, etc., require miniature air vehicles (MAVs) to fly for a long time. But they have restricted flight duration due to their dependence on battery life, which necessitates optimal path planning. The generated optimal path should obey the curvature limits prescribed by the minimum turn radius/ maximum turn rate of the MAV. Further, in a dynamically changing environment, the final configuration that the MAV has to achieve may change en route, which demands the path to be replanned by an airborne processor in real-time. As MAVs are small in size and light in weight, wind has a very significant effect on the flight of MAVs and the computation of the minimum-time path in the presence of wind plays an important role. The thesis develops feasible trajectory generation algorithms which are fast, efficient, optimal and implementable in an onboard computer for rectilinear and circular path convergence problems and waypoint following problems both in the absence and in the presence of wind. The first part of the thesis addresses the problem of computation of optimal trajectories when MAVs fly on a two-dimensional (2D) plane maintaining a constant altitude. The shortest path is computed for MAVs from a given initial position and orientation to a given final path with a specified direction as required for a given mission. Unlike the classical Dubins problem where the shortest path was computed between two given configurations (position and orientation), the final point in this case is not specified. However, the final path, which can either be a rectilinear path or a circular path, and the direction to which the MAV should converge, is specified. The time-optimal path of MAVs is developed in the presence of wind mainly using the geometric approach although a few important properties are also obtained using optimal control theory, specifically, Pontryagin’s minimum principle (which provides only the necessary condition for optimality) for control-constrained systems. The complete optima l solution to this problem in all its generality is a major contribution of this thesis as existing methods in the literature that address this problem are either not optimal or do not give a complete solution. Further, the time-optimal path for specified initial and final configurations is generated in reasonably short time without computing all the path lengths of possible candidate paths, which is the method that exists in the literature for similar problems. Simulation results illustrate path generation for various cases, including the presence of steady and time-varying wind. Another problem in MAV path planning in 2D addressed in this thesis computes an extremal path that transitions between two consecutive waypoint segments (obtained by joining two way points in sequence) in a time-optimal fashion. This designed trajectory, named as γ-trajectory, is also used to track the maximum portion of waypoint segments in minimum time and the shortest distance between this trajectory and the associated waypoint can be set to a desired value. Another optimal path, called the loop trajectory, that goes through the way points as well as through the entire waypoint segments, is also proposed. Subsequently, the thesis proposes algorithms to generate trajectories in the presence of steady wind and compares these with the optimal trajectory generated using nonlinear programming based multiple shooting method to show that the generated paths are optimal in most cases. In three-dimensional (3D) space, if the initial and final configurations – in terms of (X,Y,Z) position, heading angle and flight path angle- of the vehicle are specified then shortest path computation is an interesting problem in literature. The proposed method in this thesis is based on 3D geometry and, unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this method generates the shortest path in much less time. Due to its simplicity and low computational requirements, this approach can be implemented on a MAV in real-time. But, If the path demands very high pitch angle (as in the case of steep climbs), the generated path may not be flyable for an aerial vehicle with limited range of flight path angles. In such cases numerical methods, such as multiple shooting, coupled with nonlinear programming, are used to obtain the optimal solution. The time-optimal 3D path is also developed in the presence of wind which has a magnitude comparable to the speed of MAVs. The simulation results show path generation for a few sample cases to show the efficacy of the proposed approach as compared to the available approach in the literature. Next, the path convergence problem is studied in 3D for MAVs. The shortest path is generated to converge to a rectilinear path and a circular path starting from a known initial position and orientation. The method is also extended to compute the time-optimal path in the presence of wind. In simulation, optimal paths are generated for a variety of cases to show the efficacy of the algorithm. The other problem discussed in this thesis considers curvature-constrained trajectory generation technique for following a series of way points in 3D space. Extending the idea used in 2D, a γ-trajectory in 3D is generated to track the maximum portion of waypoint segments with a desired shortest distance between the trajectory and the associated waypoint. Considering the flyability issue of the plane a loop-trajectory is generated which is flyable by a MAV with constrained flight path angle. Simulation results are given for illustrative purposes. The path generation algorithms are all based on a kinematic model, considering the vehicle as a point in space. Implementing these results in a real MAV will require the dynamics of the MAV to be considered. So, a 6-DOF SIMULINK model of a MAV is used to demonstrate the tracking of the computed paths both in 2D plane and in 3D space using autopilots consisting of proportional-integral-derivative (PID )controllers .Achieving terminal condition accurately in real-time, if there is noisy measurement of wind data, is also addressed.

Linear Temporal Logic (LTL), as one of the temporal logic, can generate a fully automated correct-by-design controller synthesis approach for single or multiple autonomous vehicles, under much more complex missions than the traditional point-to-point navigation.In this master thesis, a framework which combines model- checking-based robot motion planning with action planning is proposed based on LTL for-mulas. The specifications implicitly require both sequential regions for multi-agent to visit and the desired actions to perform at these regions while avoid-ing collision with each other and fixed obstacles. The high level motion and task planning and low level navigation function based collision avoidance controller are verified by nontrivial simulation and implementation on real quadcopter in Smart Mobility Lab.

[pt] Em veículos de competição com velocidades elevadas, o principal objetivo é chegar em primeiro lugar, o que significa percorrer um determinado número de voltas em uma trajetória fechada fazendo algumas manobras para cumprir o circuito no menor tempo possível, dentro das limitações impostas pelas caracteristicas dinâmicas e de condução destes veículos. A otimização é uma metodologia que pode ser usada para reproduzir trajetórias e técnicas de condução usadas pelos pilotos de corrida, e também para investigar os efeitos de vários parâmetros nas condições limites da estabilidade veicular. Neste trabalho, inicialmente é apresentado o desenvolvimento de um modelo dinâmico do veículo considerando as caracterítiscas suficientes para análise da trajetória, influenciada por parâmetros geométricos e físicos pertinentes. Em seguida é definido o problema de obtenção da trajetória empregando procedimentos de otimização, de modo a determinar como um veículo irá percorrer um traçado, considerando como função objetivo o tempo de percurso, que deverá ser mínimo, e tendo como restrições as condições dinâmicas do veículo e geométricas da pista, implementando rotinas que são usadas em conjunto com os algoritmos existentes na Optimization Toolbox do Matlab. Finalmente apresenta-se o comportamento do veículo, representado pelo modelo desenvolvido anteriormente em uma malha de controle de trajetória, de modo a comparar o comportamento assim obtido com aquele previsto pelo procedimento de otimização. / [en] High speed competition vehicles are required to cover a determined number of laps in a closed trajectory circuit in a time that is the least possible, in the limits of the governing dynamic and driving characteristics of these vehicles. Optimization is a methodology that can be used in order to simulate trajectories and driving techniques of used by the competition pilots and to investigate the effects of several parameters in limit conditions of car stability. In this work it is first presented the development of the vehicle model considering the sufficient characteristics for trajectory analysis, influenced by pertinent geometric and physical parameters. In continuation, the problem of the optimal trajectory is defined using optimization procedures, in order to determine how a vehicle will follow the path, considering as an objective function the time to follow it, that must be the minimum, and having as constraints the vehicle dynamic conditions and the path geometry, implementing routines that are used with the Matlab´s Optimization Toolbox. Finally the behavior of the vehicle is presented, represented by the model developed previously in a trajectory control loop, in such a way to compare the resulting behavior with the one predicted by the optimization procedure.

In this work we present algorithms that are capable of calculating paths to destination for electric vehicles. These paths can be based on the simple metrics such as the distance, time or the paths can be based on more advanced metric such as the minimum energy demanding metric. This metric is parameterizable by the physical construction of the electrical vehicle. We also propose a new algorithm that computes energy optimal paths that are more acceptable by the driver, because it also takes into consideration the time metric while computing the path.