Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability. / Ph. D.

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Many potentially useful applications that broadly fall under the umbrella of payload transportation operations have been proposed for aerial towed-cable (ATC) systems, namely the precise capture and delivery of payloads. There remain outstanding issues concerning the dynamics and control of ATC systems that are inhibiting the near-term demonstration of these applications. The development of simplified representations of ATC systems that retain the important dynamics, yet are simple enough for use in control system development is limited. Likewise, little research exists into the development of controllers for ATC systems, especially the development of towing strategies and cable-based control techniques for rendezvous and payload transportation. Thus, this thesis presents novel research into the development of control strategies and simulation facilities that redress these two major anomalies, thereby overcoming a number of hitherto unresolved issues. The primary objective of this thesis is to develop innovative non-linear optimal control systems to manoeuvre a cable towed beneath an aircraft to transport payloads both to and from surface locations. To appropriately satisfy this objective, accurate and efficient modelling capabilities are proposed, yielding the equations of motion for numerous models of the ATC system. A series of techniques for improving the representativeness of simple dynamical models were developed. The benefits of using these procedures were shown to be significant and possible without undue complexity or computational expense. Use of such techniques result in accurate simulations and allow representative control systems to be designed. A series of single and multi-phase non-linear optimal control problems for ATC systems are then formally proposed, which were converted into non-linear programming problems using direct transcription for expedient solution. The possibility of achieving accurate, numerous instantaneous rendezvous of the cable tip with desired surface locations on the ground, in two and three-dimensions, is successfully demonstrated. This was achieved through the use of deployment and retrieval control of the cable and/or aircraft manoeuvring. The capability of the system to safely and accurately transport payloads to and from the surface via control of the cable and/or aircraft manoeuvring is also established. A series of parametric studies were conducted to establish the impact that various parameters have on the ability of the system to perform various rendezvous and payload transportation operations. This allowed important insights into to the nature of the system to be examined. In order for the system to perform rendezvous and payload transportation operations in the presence of wind gusts, a number of simple closed loop optimal feedback controllers were developed. These feedback controllers are based on the linear quadratic regulator control methodology. A preliminary indication of the robustness of ATC systems to wind gusts is provided for through a succession of parametric investigations. The performance of the closed-loop system demonstrates that precise and robust control of the ATC system can be achieved for a wide variety of operating conditions. The research presented in this thesis will provide a solid foundation for further advancing the development of aerial tether payload transportation technology.

Continuous and discrete-time Successive Backward Sweep (SBS) methods for solving nonlinear optimal control problems involving terminal and control constraints are proposed in this dissertation. They closely resemble the Neighboring Extremals and Differential Dynamic Programming algorithms, which are based on the successive solutions to a series of linear control problems with quadratic performance indices. The SBS methods are relatively insensitive to the initial guesses of the state and control histories, which are not required to satisfy the system dynamics. Hessian modifications are utilized, especially for non-convex problems, to avoid singularities during the backward integration of the gain equations. The SBS method requires the satisfaction of the Jacobi no-conjugate point condition and hence, produces optimal solutions. The standard implementation of the SBS method for continuous-time systems incurs terminal boundary condition errors due to an algorithmic singularity as well as numerical inaccuracies in the computation of the gain matrices. Alternatives for boundary error reduction are proposed, notably the aiming point and the switching between two forms of the sweep expansion formulae. Modification of the sweep formula expands the domain of convergence of the SBS method and allows for a rigorous testing for the existence of conjugate points. Numerical accuracy of the continuous-time formulation of the optimal control problem can be improved with the use of symplectic integrators, which generally are implicit schemes in time. A time-explicit group preserving method based on the Magnus series representation of the state transition is implemented in the SBS setting and is shown to outperform a non-symplectic integrator of the same order. Discrete-time formulations of the optimal control problem, directly accounting for a specific time-stepping method, lead to consistent systems of equations, whose solutions satisfy the boundary conditions of the discretized problem accurately. In this regard, the second-order, implicit mid-point averaging scheme, a symplectic integrator, is adapted for use with the SBS method. The performance of the mid-point averaging scheme is compared with other methods of equal and higher-order non-symplectic schemes to show its advantages. The SBS method is augmented with a homotopy- continuation procedure to isolate and regulate certain nonlinear effects for difficult problems, in order to extend its domain of convergence. The discrete-time SBS method is also extended to solve problems where the controls are approximated to be impulsive and to handle waypoint constraints as well. A variety of highly nonlinear optimal control problems involving orbit transfer, atmospheric reentry, and the restricted three-body problem are treated to demonstrate the performance of the methods developed in this dissertation.

This dissertation introduces a Dynamical Neural Network (DNN) model based adaptive inverse optimal control design for a class of nonlinear systems. A DNN structure is developed and stabilized based on a control Lyapunov function (CLF). The CLF must satisfy the partial Hamilton Jacobi-Bellman (HJB) equation to solve the cost function in order to prove the optimality. In other words, the control design is derived from the CLF and inversely achieves optimality when the given cost function variables are determined posterior. All the stability of the closed loop system is ensured using the Lyapunov-based analysis. In addition to structure stability, uncertainty/ disturbance presents a problem to a DNN in that it could degrade the system performance. Therefore, the DNN needs a robust control against uncertainty. Sliding mode control (SMC) is added to nominal control design based CLF in order to stabilize and counteract the effects of disturbance from uncertain DNN, also to achieve global asymptotic stability. In the next section, a DNN observer is considered for estimating states of a class of controllable and observable nonlinear systems. A DNN observer-based adaptive inverse optimal control (AIOC) is needed. With weight adaptations, an adaptive technique is introduced in the observer design and its stabilizing control. The AIOC is designed to control a DNN observer and nonlinear system simultaneously while the weight parameters are updated online. This control scheme guarantees the quality of a DNN's state and minimizes the cost function. In addition, a tracking problem is investigated. An inverse optimal adaptive tracking control based on a DNN observer for unknown nonlinear systems is proposed. Within this framework, a time-varying desired trajectory is investigated, which generates a desired trajectory based on the external inputs. The tracking control design forces system states to follow the desired trajectory, while the DNN observer estimates the states and identifies unknown system dynamics. The stability method based on Lyapunov-based analysis is guaranteed a global asymptotic stability. Numerical examples and simulation studies are presented and shown for each section to validate the effectiveness of the proposed methods.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23888号 / 工博第4975号 / 新制||工||1777(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 加納 学, 准教授 丸田 一郎, 教授 松野 文俊 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

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<p>NR 20140805</p>

Collision avoidance is an essential component of autonomous shipping. As ships begin to advance towards autonomy, developing an advisory system is one of the first steps. An advisory system with a strong collision avoidance component can help the crew act more quickly and accurately in dangerous situations. One way to avoid colission is to make the vessel stop as fast as possible. In this work, two scenarios are studied, firstly, stopping along a predefined path, and secondly, stopping within a safe area defined by surrounding obstacles. The first scenario was further worked with to formulate a real-time solution. Movements of a vessel, described in three degrees of freedom with continuous dynamics, were simulated using mathematical models of the forces acting on the ship. Nonlinear optimal control problems were formulated for each scenario and solved numerically using discretization and a direct multiple shooting method. The results for the first problem showed that the vessel could stop without much deviation from the path. Paths with different curvatures were tested, and it was shown that a slightly longer distance was traveled when the curvature of the path was greater. The results for the second problem showed that the vessel stays within the safe area and chooses a relatively straight path as the optimal way of stoping. This results in a shorter distance traveled compared to the solution of the first problem. Two different real-time approaches were formulated, firstly a receding-horizon approach and secondly a lookup-based approach. Both approaches were solved with real-time feasibility, where the receding-horizon approach gave a better solution while lookup-based approach had a shorter computational time.

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