High-flying unmanned reconnaissance and surveillance systems are now being used extensively in the United States military. Current development programs are producing demonstrations of next-generation unmanned flight systems that are designed to perform combat missions. Their use in first-strike combat operations will dictate operations in densely cluttered environments that include unknown obstacles and threats, and will require the use of terrain for masking. The demand for autonomy of operations in such environments dictates the need for advanced trajectory optimization capabilities. In addition, the ability to coordinate the movements of more than one aircraft in the same area is an emerging challenge. This thesis examines using an analytical reduced order formulation for trajectory generation for minimum time and terrain masking cases. First, pseudo-3D constant velocity equations of motion are used for path planning for a single vehicle. In addition, the inclusion of winds, moving targets and moving threats is considered. Then, this formulation is increased to using 3D equations of motion, both with a constant velocity and with a simplified varying velocity model. Next, the constant velocity equations of motion are expanded to include the simultaneous path planning of an unspecified number of vehicles, for both aircraft avoidance situations and formation flight cases.

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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.

Exploration is a fundamental problem in robotics that requires robots to navigate through unknown environments to autonomously gather information about their surroundings while executing collision-free paths. In this project, we propose a method for producing smooth paths during the exploration process in indoor environments using UAVs to improve battery efficiency and enhance the quality of pose estimation. The developed framework is built by merging two approaches that represent the state of the art in the field of autonomous exploration with UAVs. The overall exploration logic is given by GLocal, a paper that introduces a hybrid, i.e. both sampling-based and frontier-based, framework that is able to cope with the issue of odometry drift when exploring indoor environments due to the absence of absolute localization, e.g. through GNSS. The second approach is FUEL, which introduces a frontier-based exploration methodology which computes the ’drones path as an optimized non-uniform B-Spline. The framework described in this thesis borrows the optimized B-Spline trajectory generation from FUEL and implements it in GLocal. To do this, the original cost function defined by GLocal for each exploration viewpoint was modified and the resulting samples were used to select the initial control points of the B-Spline. Furthermore, we extended the underlying state machine governing the entire algorithm and we revisited the original re-planning logic. The presented system is evaluated in various simulated environments, showcasing the advantages and disadvantages of this method. These evaluations demonstrate its improved state estimation performance and absolute observed volume, albeit at the expense of longer traveled trajectories in big and complex environments. / Utforskning är ett grundläggande problem inom robotteknik som kräver att robotar navigerar genom okända miljöer för att autonomt samla in information om sin omgivning samtidigt som de utför kollisionsfria banor. I det här projektet föreslår vi en metod för att producera jämna banor under utforskningsprocessen i inomhusmiljöer med hjälp av UAV:er för att förbättra batterieffektiviteten och förbättra kvaliteten på posestimeringen. Det utvecklade ramverket bygger på en sammanslagning av två metoder som representerar den senaste tekniken inom autonom utforskning med UAV:er. Den övergripande utforskningslogiken ges av GLocal, en artikel som introducerar en hybrid, i.e. både samplingsbaserad och gränsbaserad, ram som kan hantera problemet med odometridrift vid utforskning av inomhusmiljöer på grund av frånvaron av absolut lokalisering, e.g. genom GNSS. Den andra metoden är FUEL, som introducerar en gränsbaserad utforskningsmetod som beräknar drönarens bana som en optimerad icke-uniform B-Spline. Ramverket som beskrivs i denna avhandling lånar den optimerade B-Spline-banegenereringen från FUEL och implementerar den i GLocal. För att göra detta modifierades den ursprungliga kostnadsfunktionen som definierades av GLocal för varje utforskningspunkt och de resulterande samplen användes för att välja de initiala kontrollpunkterna för B-Spline. Dessutom utökade vi den underliggande tillståndsmaskinen som styr hela algoritmen och vi reviderade den ursprungliga logiken för omplanering. Det presenterade systemet utvärderas i olika simulerade miljöer, vilket visar fördelarna och nackdelarna med denna metod. Dessa utvärderingar visar på förbättrad prestanda för tillståndsuppskattning och absolut observerad volym, om än på bekostnad av längre färdvägar i stora och komplexa miljöer.