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.

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.

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%.

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As progress pushes the boundaries of both the performance of new hardware components and the computational capacity of modern computers, the requirements on the performance of robotic systems are becoming more and more demanding. The objective of this thesis is to demonstrate that concurrent design (Co-Design) is the approach to follow to design hardware and control for such high-performance robots. In particular, this work proposes a co-design framework and an algorithm to tackle two main issues: i) how to use Co-Design to benchmark different robotic systems, and ii) how to effectively warm-start the trajectory optimization (TO) problem underlying the co-design problem aiming at global optimality. The first contribution of this thesis is a co-design framework for the energy efficiency analysis of a redundant actuation architecture combining Quasi-Direct Drive (QDD) motors and Series Elastic Actuators (SEAs). The energy consumption of the redundant actuation system is compared to that of Geared Motors (GMs) and SEAs alone. This comparison is made considering two robotic systems performing different tasks. The results show that, using the redundant actuation, one can save up to 99% of energy with respect to SEA for sinusoidal movements. This efficiency is achieved by exploiting the coupled dynamics of the two actuators, resulting in a latching-like control strategy. The analysis also shows that these large energy savings are not straightforwardly extendable to non-sinusoidal movements, but smaller savings (e.g., 7%) are nonetheless possible. The results highlight that the combination of complex hardware morphologies and advanced numerical Co-Design can lead to peak hardware performance that would be unattainable by human intuition alone. Moreover, it is also shown how to leverage Stochastic Programming (SP) to extend a similar co-design framework to design robots that are robust to disturbances by combining TO, morphology and feedback control optimization. The second contribution is a first step towards addressing the non-convexity of complex co-design optimization problems. To this aim, an algorithm for the optimal control of dynamical systems is designed that combines TO and Reinforcement Learning (RL) in a single framework. This algorithm tackles the two main limitations of TO and RL when applied to continuous-space non-linear systems to minimize a non-convex cost function: TO can get stuck in poor local minima when the search is not initialized close to a “good” minimum, whereas the RL training process may be excessively long and strongly dependent on the exploration strategy. Thus, the proposed algorithm learns a “good” control policy via TO-guided RL policy search. Using this policy to compute an initial guess for TO, makes the trajectory optimization process less prone to converge to poor local optima. The method is validated on several reaching problems featuring non-convex obstacle avoidance with different dynamical systems. The results show the great capabilities of the algorithm in escaping local minima, while being more computationally efficient than the state-of-the-art RL algorithms Deep Deterministic Policy Gradient and Proximal Policy Optimization. The current algorithm deals only with the control side of a co-design problem, but future work will extend it to include also hardware optimization. All things considered, this work advanced the state of the art on Co-Design, providing a framework and an algorithm to design both hardware and control for high-performance robots and aiming to the global optimality.

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.

The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include complex nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / Master of Science / The ability of one satellite to perform actions near a second space satellite or other space object is important for understanding the space environment and accomplishing space mission goals. The development of a method to plan the path that one satellite takes near a second satellite such that fuel usage is minimized and other constraints satisfied is important for accomplishing mission goals. This thesis focuses on developing a fast solution method capable of handling complex constraints that can be applied to plan paths satellite relative motion operations. The solution method developed in this thesis is then compared to an existing solution method to determine the efficiency and accuracy of the method.