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Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 117-118). Also available via the Internet.

A widespread use of robotic technology in civilian and military applications has generated a need for advanced motion planning algorithms that are real-time implementable. These algorithms are required to navigate autonomous vehicles through obstacle-rich environments. This research has led to the development of the multilayer trajectory generation approach. It is built on the principle of separation of concerns, which partitions a given problem into multiple independent layers, and addresses complexity that is inherent at each level. We partition the motion planning algorithm into a roadmap layer and an optimal control layer. At the roadmap layer, elements of computational geometry are used to process the obstacle rich environment and generate feasible sets. These are used by the optimal control layer to generate trajectories while satisfying dynamics of the vehicle. The roadmap layer ignores the dynamics of the system, and the optimal control layer ignores the complexity of the environment, thus achieving a separation of concern. This decomposition enables computationally tractable methods to be developed for addressing motion planning in complex environments. The approach is applied in known and unknown environments. The methodology developed in this thesis has been successfully applied to a 6 DOF planar robotic testbed. Simulation results suggest that the planner can generate trajectories that navigate through obstacles while satisfying dynamical constraints.

Advanced connected and automated vehicle technologies offer new opportunities for highway traffic smoothing by optimizing automated vehicle trajectories. As one of the pioneering attempts, this study proposes an efficient trajectory optimization algorithm that can simultaneously improve a range of performance measures for a platoon of vehicles on a signalized highway section. This optimization is centered at a novel shooting heuristic (SH) for trajectory construction that considers realistic constraints including vehicle kinematic limits, traffic arrival patterns, carollowing safety, and signal operations. SH has a very parsimonious structure (e.g., only four acceleration parameters) and a very small computational complexity. Therefore, it is suitable for real-time applications when relevant technologies are in place in the near future. This study lays a solid foundation for devising holistic cooperative control strategies on a general transportation network with emerging technologies.

The use of autonomous UAV’s is a progressively expanding industry. This thesisfocuses on the landing procedure with the main goal to be independent of visualaids. That means that the landing site can be hidden from the air, the landingcan be done in bad weather conditions and in the dark. In this thesis the use ofradio signals is investigated as an alternative to the visual sensor based systems.A localization system is needed to perform the landing without knowing wherethe landing site is. In this thesis an Extended Kalman Filter (EKF) is derived andused for the localization, based on the received signal strength from a radio beaconat the landing site. There are two main goals that are included in the landing,to land as accurate and as fast as possible. To combine these two goals a simultaneoustrajectory optimization and target estimation problem is set up that can bepartially solved while flying. The optimal solution to this problem produces thepath that the UAV will travel to get the best target localization while still reachingthe target. It is shown that trying to move directly towards the estimated landingsite is not the best strategy. Instead, the optimal trajectory is a spiral that jointlyoptimizes the information from the sensors and minimizes the arrival time.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / I would like to acknowledge a number of people who contributed towards the completion of this thesis. Firstly, I thank my supervisor Professor Montaz Ali for his patience, enthusiasm, guidance and teachings. The skills I have acquired during this process have infiltrated every aspect of my life. I remain forever grateful. Secondly, I would like to say a special thank you to Professor Jan Snyman for his assistance, which contributed immensely towards this thesis. I would also like to thank Professor Dominque Orban for his willingness to assist me for countless hours with the installation of CUTEr, as well as Professor Jose Mario Martinez for his email correspondence. A heartfelt thanks goes out to my family and friends at large, for their prayers, support and faith in me when I had little faith in myself. Thank you also to my colleagues who kept me sane and motivated, as well as all the support staff who played a pivotal roll in this process. Above all, I would like to thank God, without whom none of this would have been possible.

An advanced ascent guidance algorithm for rocket-powered launch vehicles is developed. The ascent guidance function is responsible for commanding attitude, throttle and setting during the powered ascent phase of flight so that the vehicle attains target cutoff conditions in a near-optimal manner while satisfying path constraints such as maximum allowed bending moment and maximum allowed axial acceleration. This algorithm cyclically solves the calculus-of-variations two-point boundary-value problem starting at vertical rise completion through orbit insertion. This is different from traditional ascent guidance algorithms which operate in an open-loop mode until the high dynamic pressure portion of the trajectory is over, at which time there is a switch to a closed loop guidance mode that operates under the assumption of negligible aerodynamic forces. The main contribution of this research is an algorithm of the predictor-corrector type wherein the state/costate system is propagated with known (navigated) initial state and guessed initial costate to predict the state/costate at engine cutoff. The initial costate guess is corrected, using a multi-dimensional Newtons method, based on errors in the terminal state constraints and the transversality conditions. Path constraints are enforced within the propagation process. A modified multiple shooting method is shown to be a very effective numerical technique for this application. Results for a single stage to orbit launch vehicle are given. In addition, the formulation for the free final time multi-arc trajectory optimization problem is given. Results for a two-stage launch vehicle burn-coast-burn ascent to orbit in a closed-loop guidance mode are shown. An abort to landing site formulation of the algorithm and numerical results are presented. A technique for numerically treating the transversality conditions is discussed that eliminates part of the analytical and coding burden associated with optimal control theory.

In the past three decades, numerous methods have been proposed to transcribe optimal control problems (OCP) into nonlinear programming problems (NLP). In this dissertation work, a unifying weighted residual framework is developed under which most of the existing transcription methods can be derived by judiciously choosing test and trial functions. This greatly simplifies the derivation of optimality conditions and costate estimation results for direct transcription methods. Under the same framework, three new transcription methods are devised which are particularly suitable for implementation in an adaptive refinement setting. The method of Hilbert space projection, the least square method for optimal control and generalized moment method for optimal control are developed and their optimality conditions are derived. It is shown that under a set of equivalence conditions, costates can be estimated from the Lagrange multipliers of the associated NLP for all three methods. Numerical implementation of these methods is described using B-Splines and global interpolating polynomials as approximating functions. It is shown that the existing pseudospectral methods for optimal control can be formulated and analyzed under the proposed weighted residual framework. Performance of Legendre, Gauss and Radau pseudospectral methods is compared with the methods proposed in this research. Based on the variational analysis of first-order optimality conditions for the optimal control problem, an posteriori error estimation procedure is developed. Using these error estimates, an h-adaptive scheme is outlined for the implementation of least square method in an adaptive manner. A time-scaling technique is described to handle problems with discontinuous control or multiple phases. Several real-life examples were solved to show the efficacy of the h-adaptive and time-scaling algorithm.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 225-232). Also available on the Internet.