Supercavitating vehicles are characterized by substantially reduced hydrodynamic drag with respect to fully wetted underwater vehicles. Drag is localized at the nose of the vehicle, where a cavitator generates a cavity that completely envelops the body. This causes the center of pressure to be always ahead of the center of mass, thus violating a fundamental principle of hydrodynamic stability. This unique loading configuration, the complex and non-linear nature of the interaction forces between vehicle and cavity, and the unsteady behavior of the cavity itself make the control and maneuvering of supercavitating vehicles particularly challenging. This study represents an effort towards the evaluation of optimal trajectories for this class of underwater vehicles, which often need to operate in unsteady regimes and near the boundaries of the flight envelope. Flight trajectories and maneuvering strategies for supercavitating vehicles are here obtained through the solution of an optimal control problem. Given a cost function and general constraints and bounds on states and controls, the solution of the optimal control problem yields the control time histories that maneuver the vehicle according to a desired strategy, together with the associated flight path. The optimal control problem is solved using the direct transcription method, which does not require the derivation of the equations of optimal control and leads to the solution of a discrete parameter optimization problem. Examples of maneuvers and resulting trajectories are given to demonstrate the effectiveness of the proposed methodology and the generality of the formulation.

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Advances in machine autonomy hold great promise in advancing technology, economic markets, and general societal well-being. For example, the progression of unmanned air systems (UAS) research has demonstrated the effectiveness and reliability of these autonomous systems in performing complex tasks. UAS have shown to not only outperformed human pilots in some tasks, but have also made novel applications not possible for human pilots practical. Nevertheless, human pilots are still favored when performing specific challenging tasks. For example, transportation of suspended (sometimes called slung or sling) loads requires highly skilled pilots and has only been performed by UAS in highly controlled environments. The presented work begins to bridge this autonomy gap by proposing a trajectory optimization framework for operations involving autonomous rotorcraft with suspended loads. The framework generates optimized vehicle trajectories that are used by existing guidance, navigation, and control systems and estimates the state of the non-instrumented load using a downward facing camera. Data collected from several simulation studies and a flight test demonstrates the proposed framework is able to produce effective guidance during autonomous suspended load operations. In addition, variational integrators are extensively studied in this dissertation. The derivation of a stochastic variational integrator is presented. It is shown that the presented stochastic variational integrator significantly improves the performance of the stochastic differential dynamical programming and the extended Kalman filter algorithms. A variational integrator for the propagation of polynomial chaos expansion coefficients is also presented. As a result, the expectation and variance of the trajectory of an uncertain system can be accurately predicted.

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs as previously studied. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient maneuvers. A family of, climb-range paths appears for thrust exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems. Minimizing paths of long duration follow a certain corridor in the V-h chart. The features of the family sharpen for the special case of thrust and drag independent of altitude, and considerable analytical attention is accorded to this for the insight it provides to the more general model. The problem of "steepest climb" is found to be ill-posed with the vehicle model under consideration, straight-vertically-upward maneuver sequences being furnished by a family of paths alternating between upward and downward vertical flight and including a limiting "chattering" member. / Ph. D.

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Tsiotras, Panagiotis; Committee Member: Corban, Eric; Committee Member: Feron, Eric; Committee Member: Johnson, Eric; Committee Member: Vachtsevanos, George.

Thesis (M.S. in Astronautical Engineering)--Naval Postgraduate School, March 2005. / Thesis Advisor(s): I. Michael Ross. Includes bibliographical references (p. 57-58). Also available online.

Consider the problem of developing an algorithm that computes optimal preprogrammed evasive maneuvers for a Maneuvering Reentry Vehicle (MaRV) attacking a target defended with Anti-Ballistic Missiles (ABMs). The problem is large in terms of the number of optimization parameters, and perhaps in terms of the number of nonlinear constraints. Since both MaRV and ABM trajectories are expensive to compute, rapid convergence of the optimization algorithm is of prime concern. This paper examines a discontinuity in the cost function that degrades both the speed and the reliability of optimizer convergence. A solution is offered, proposing that the optimization algorithm be operated in a new parameter space, in which the discontinuity occurs at infinity. Effectively, the mapping prevents the optimization algorithm from crossing the discontinuity thereby improving optimizer convergence. Results comparing convergence with and without the parameter mapping demonstrate the effectiveness of the procedure. / Master of Science

An unmanned aerial vehicle (UAV) swarm allows for a more time-efficient method of searching a specified area than a single UAV or piloted plane. There are a variety of factors that affect how well an area is surveyed. We specifically analyzed the effect both vehicle properties and communication had on the swarm search performance. We used non-dimensionalization so the results can be applied to any domain size with any type of vehicle. We found that endurance was the most important factor. Vehicles with good endurance sensed approximately 90% to 100% of the grid, even when other properties were lacking. If the vehicles lacked endurance, the amount of area the vehicles could sense at a given time step became more important and 10% more of the grid was sensed with the increase in sensed area. The maneuverability of the vehicles was measured as the vehicles' radii of turn compared to the search domain size. The maneuverability mattered the most in the middle-range endurance cases. In some cases 30% more of the grid was searched with improving vehicle maneuverability. In addition, we also examined four communication cases with different amounts of information regarding vehicle location. We found communication increased search performance by at least 6.3%. However, increasing the amount of information only changed the performance by 2.3%. We also studied the impact the range of vehicle communication had on search performance. We found that simulations benefited most from increasing the communication range when the amount of area sensed at a given time step was small and the vehicles had good maneuverability. We also extended the optimization to a multi-objective process with the inclusion of target tracking. We analyzed how the different weightings of the objectives affected the performance outcomes. We found that target tracking performance dramatically changes based on the given weighting of each objective and saw an increase of approximately 52%. However, the amount of the grid that was sensed only dropped by approximately 10%.

The method of singular-perturbation analysis is applied to the determination of range-fuel-time optimal aircraft trajectories. The problem is shown to break down into three sub-problems which are studied separately. In particular, the inner layer containing the altitude path-angle dynamics is analyzed in detail. The outer solutions are discussed in an earlier work. As a step forward in solving the ensuing nonlinear two-point boundary-value problem, linearization of the equations is suggested. Conditions for the stability of the linearized boundary-layer equations are discussed. Also, the question of parameter selection to fit the solution to the split boundary conditions is resolved. Generation of feedback laws for the angle-of-attack from the linear analysis is discussed. Finally, the techniques discussed are applied to a numerical example of a missile. The linearized feedback solution is compared to the exact solution obtained using a multiple shooting method. / Master of Science

Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained. / Master of Science