Solutions to trajectory optimization problems are carried out by the direct and indirect methods. Under broad heading of these methods, numerous algorithms such as collocation, direct, indirect and multiple shooting methods have been developed and reported in the literature. Each of these algorithms has certain advantages and limitations. For example, direct shooting technique is not suitable when the number of nonlinear programming variables is large. Indirect shooting method requires analytical derivatives of the control and co-states function and a poorly guessed initial condition can result in numerical unstable values of the adjoint variable. Multiple shooting techniques can alleviate some of these difficulties by breaking down the trajectory into several segments that help in reducing the non-linearity effects of early control on later parts of the trajectory. However, multiple shooting methods then have to handle more number of variables and constraints to satisfy the defects at the segment joints. The sie of the nonlinear programming problem in the collocation method is also large and proper locations of grid points are necessary to satisfy all the path constraints. Stochastic methods such as Genetic algorithms, on the other hand, also require large number of function evaluations before convergence. To overcome some of the limitations of the conventional methods, improved solution techniques are developed. Three improved methods are proposed for the solution of trajectory optimization problems. They are • a genetic algorithm employing dominance and diploidy concept. • a collocation method using chebyshev polynomials , and • a hybrid method that combines collocation and direct shooting technique A conventional binary-coded genetic algorithm uses a haploid chromosome, where a single string contains all the variable information in the coded from. A diploid, as the name suggests, uses pair of chromosomes to store the same characteristic feature. The diploid genetic algorithm uses a dominant map for decoding genotype into a stable, consistent phenotype. In dominance, one allele takes precedence over another. Diploidy and dominance helps in retaining the previous best solution discovered and shields them from harmful selection in a changing environment. Hence, diploid and dominance affect a king of long-term memory in the genetic algorithm. They allow alternate solutions to co-exist. One solution is expressed and the other is held in abeyance. In the improved diploid genetic algorithm, dominant and recessive genes are defined based on the fitness evaluation of each string. The genotype of fittest string is declared as the dominant map. The dominant map is dynamic in nature as it is replaced with a better individual in future generations. The concept of diploidy and dominance in the improved method mimics closer to the principles used in human genetics as compared to any such algorithms reported in the literature. It is observed that the improved diploid genetic algorithm is able to locate the optima for a given trajectory optimization problem with 10% lower computational time as compared to the haploid genetic algorithm. A parameter optimization problem arising from an optimal control problem where states and control are approximated by piecewise Chebyshev polynomials is well known. These polynomials are more accurate than the interpolating segments involving equal spaced data. In the collocation method involving Chebyshev polynomials, derivatives of two neighboring polynomials are matched with the dynamics at the nodal points. This leads to a large number of equality constraints in the optimization problem. In the improved method, derivative of the polynomial is also matched with the dynamics at the center of segments. Though is appears the problem size is merely increased, the additional computations improve the accuracy of the polynomial for a larger segment. The implicit integration step size is enhanced and overall size of the problem is brought down to one-fourth of the problem size defined with a conventional collocation method using Chebyshev polynomials. Hybrid method uses both collocation and direct shooting techniques. Advantages of both the methods are combined to give more synergy. Collocation method is used in the starting phase of the hybrid method. The disadvantage of standalone collocation method is that tuning of grid points is required to satisfy the path constraints. Nevertheless, collocation method does give a good guess required for the terminal phase of the hybrid method, which uses a direct shooting approach. Results show nearly 30% reduction in computation time for the hybrid approach as compared to a method in which direct shooting alone is used, for the same initial guess of control. The solutions obtained from the three improved methods are compared with an indirect method. The indirect method requires derivations of the control and adjoint equations, which are difficult and problem specific. Due to sensitivity of the costate variables, it is often difficult to find a solution through the indirect method. Nevertheless, these methods do provide an accurate result, which defines a benchmark for comparing the solutions obtained through the improved methods. Trajectory design and optimization of a RLV(Reusable Launch Vehicle) Demonstrator mission is considered as a test problem for evaluating the performance of the improved methods. The optimization problem is difficult than a conventional launch vehicle trajectory optimization problem because of the following two reasons. • aerodynamic lift forces in the RLV add one more dimension to the already complex launch vehicle optimization problem. • as RLV performs a sub orbital flight, the ascent phase trajectory influences the re-entry trajectory. Both the ascent and re-entry optimization problem of the RLV mission is addressed. It is observed that the hybrid method gives accurate results with least computational effort, as compared with other improved techniques for the trajectory optimization problem of RLV during its ascent flight. Hybrid method is then successfully used during the re-entry phase and in designing the feasible optimal trajectories under the dispersion conditions. Analytical solutions obtained from literature are used to compare the optimized trajectory during the re-entry phase. Trajectory optimization studies are also carried out for the off-nominal performances. Being a thrusting phase, the ascent trajectory is subjected to significant deviations, mainly arising out of solid booster performance dispersions. The performance index during rhe ascent phase is modified in a novel way for handling dispersions. It minimizes the state errors in a least square sense, defined at the burnout conditions ensure possibilities of safe re-entry trajectories. The optimal trajectories under dispersion conditions serve as a benchmark for validating the closed-loop guidance algorithm that is developed for the ascent phase flight. Finally, an on-line trajectory command-reshaping algorithm is developed which meets the flight objectives under the dispersion conditions. The guidance algorithm uses a pre-computed trajectory database along with some real-time measured parameters in generating the optimal steering profiles. The flight objectives are met under the dispersion conditions and the guidance generated steering profiles matches closely with the optimal trajectories.

Continuous Descent Arrival (CDA) is a procedure where aircraft descend, at or near idle thrust, from their cruise altitude to their Final Approach Fix without leveling off. By eliminating inefficient leveling off at low altitude, CDA provides benefits such as fuel savings, flight time savings, and the significant noise reduction near airports, but the usage of CDAs has been limited in low traffic condition due to difficulty in the separation management. For the successful CDA without degradation of the runway throughput, air traffic controllers should know the performance bound of the CDA trajectory and control the time of arrival for each aircraft, which is interpreted as Required Time of Arrival (RTA) from the aircraft standpoint. This thesis proposes a novel trajectory optimization methodology to meet RTA constraint. The CDA trajectory optimization problem in the flight management system is modeled as a path constrained optimal control problem of switched dynamical system. A sequential method that performs mode sequence estimation and parameter optimization, sequentially, is proposed to solve this problem. By analyzing the relaxed optimal solution with simplified dynamics, a computationally efficient algorithm to find the optimal switching structure is proposed and applied for the mode sequence estimation. This thesis also proposes a performance-bound analysis methodology using optimal control techniques to help controllers make a feasible schedule for CDA operations at a meter fix. The feasible time range analysis for a wide variety of aircraft is performed by using the proposed methodology. Based on the analysis result, a single flight time strategy is proposed for the application of CDA in high traffic conditions. The simulation with real traffic data has been shown that the single flight time strategy, combined with the proposed fixed RTA trajectory optimization, guarantees the conflict free CDA operation.

<p>Constrained optimization is used to derive human postures and movements. In the first study a static 3D model with 30 muscle groups is used to analyse postures. The activation levels of these muscles are minimized in order to represent the individual's choice of posture. Subject specific data in terms of anthropometry, strength and orthopedic aids serve as input. The aim is to study effects from orthopedic treatment and altered abilities of the subject. Initial validation shows qualitative agreement of posture strategies but further details about passive stiffness and anthropometry are needed, especially to predict pelvis orientation. In the second application, the athletic long jump, a problem formulation is developed to find optimal movements of a multibody system when subjected to contact. The model was based on rigid links, joint actuators and a wobbling mass. The contact to the ground was modelled as a spring-damper system with tuned properties. The movement in the degrees of freedom representing physical joints was described over contact time through two fifth-order polynomials, with a variable transition time, while the motion in the degrees of freedom of contact and wobbling mass was integrated forwards in time, as a consequence. Muscle activation variables were then optimized in order to maximize ballistic flight distance. The optimization determined contact time, end configuration, activation and interaction with the ground from an initial configuration. The results from optimization show a reasonable agreement with experimentally recorded jumps, but individual recordings and measurements are needed for more precise conclusions.</p><p> </p>

This thesis explores how an Asteroid Sample Return Mission might make use of solar electric propulsion to send a spacecraft on a journey to the asteroid 1989ML and back. It examines different trajectories that can be used to get an asteroid sample return or similar spacecraft to an interplanetary destination and back in the most fuel-efficient manner. While current plans call for keeping such a spacecraft on the asteroid performing science experiments for approximately 90 days, it is prudent to inquire how lengthening or shortening this time period may affect mission fuel requirements. Using optimal control methods, various mission scenarios have been modeled and simulated. The results suggest that the amount of time that the spacecraft may spend on the asteroid surface can be approximated as a linear function of the available fuel mass. Furthermore, It can be shown that as maximum available thrust is decreased, the radial component of the optimal thrust vector becomes more pronounced.

Trajectory planning is an important component of autonomous driving. It takes the result of route-level navigation plan and generates the motion-level commands that steer an autonomous passenger vehicle (APV). Prior work on solving this problem uses either a sampling-based or optimization-based trajectory planner, accompanied by some high-level rule generation components.

Approved for public release, distribution is unlimited / problem, with engine thrust as the only possible perturbation. The optimal control problems are solved using the general purpose dynamic optimization software, DIDO. The dynamical model together with the fuel optimal control problem is validated by simulating several well known orbit transfers. By replicating the single satellite model, this thesis shows that a multi-satellite model which optimizes all vehicles concurrently can be easily built. The specific scenario under study involves the injection of multiple satellites from a common launch vehicle; however, the methods and model are applicable to spacecraft formation problems as well. / Major, United States Air Force

Forestry machines have the power to lift heavy logs, but they are not so smart at providing information, or help operators perform better work. The main reason to this problem is the low level of technology applied to forestry machines, which has not changed so much since the forestry machines were first introduced in the 1960’s. But starting 2013, machines manufacturers got inspired by developments in the automation and robotics industry, several of new technologies have been developed in the market - computerized hydraulics, feedback controllers for vibration damping, sensor-based motion control systems, improvements in mechanical design, smart suspension controller, etc. Largely, this development is attributed to better hardware and software developed during the last decade by researchers of Scandinavian institutes. In this thesis, we introduce a new type of forestry machine, the harwarder, which can perform the work of two machines (harvester and forwarder) by a single one. The forwarder is a forestry vehicle that carries big felled logs. The harvester is a type of heavy forestry manipulator employed in cut-to-length logging operations for felling, and bucking trees. Both the manipulator and vehicle should work synchronized to get the best out of this design. To benefit out of its design, in the first part of thesis we will analyze the kinematics and dynamics of machine, and design a time optimal coordinated motion via virtual holonomic constraints, to solve a particular task of forestry crane. The second part consists on applying optimization to reduce energy consumption during the motion. Result of thesis work: 1) By using coordinated motion, consequently the energy consumptions are drastically reduced comparing to traditional motion of the crane. 2) By applying optimization, the energy efficiency is improved.

Asteroid mining is rapidly becoming a popular topic amongst space community, primarily due to the potential resources that the asteroids can provide for future spacefaring. One of the interesting resources that can be obtained from asteroids is water, which can also be processed into oxygen and fuel. An intriguing concept would be to process fuel from asteroid, and establish a fuel depot in an Earth-centered orbit. This thesis considers a mission concept consisting of travelling to an Arjuna near-Earth asteroid from a lunar distant retrograde orbit as a depot orbit, processing fuel in-situ from the water on the asteroid, and bringing back 100 tons of fuel to the depot orbit. In order to minimize fuel consumption for such a trip, the thesis develops an optimization method that can obtain the best trajectory for different phases of the round trip, given certain constraints to ensure the spacecraft successfully reaches the asteroid and comes back to the Earth system. The optimization model consists of four steps, i.e., the outbound trip, the first phase of the return trip, the second phase of the return trip, and the optimization for the combined phases of return trip. The outbound trip is the trajectory from the depot orbit to the asteroid. After at least three months of mining, the spacecraft brings back the processed fuel to the vicinity of the Moon. This phase is called the first phase of the return trip. The spacecraft is then captured without an insertion burn to an Earth-centered orbit by a lunar gravity assist maneuver, and travels to the point where the insertion maneuver to the depot orbit begins. This is the second phase of the return trip. The last step of the optimization is the combination of the two phases of return trip, in addition to the final maneuver for entering the lunar distant retrograde orbit. The optimization method uses MATLAB fmincon solver, and it was applied to 29 synthetic asteroids. There were 19 converged solutions, but for 10 asteroids the optimizations was not able to converge. The lowest minimum fuel consumption for a trip is 19965.5 kg, and the highest minimum fuel consumption is 61821.4 kg. For the lowest minimum fuel consumption, the duration of the trip is nearly 7 years, and the duration for the highest minimum fuel consumption is about 2.6 years.

Thesis (M.S.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 23, 2007) Includes bibliographical references.

Aircrafttrajectory optimization is traditionally used forminimizing fuel consumption or time when going from one flightstate to another. This thesis presents a possible approach toincorporate tactical constraints in aircraft trajectoryoptimization. The stealth technology of today focuses on making thetactics already in use more effective. Since tactics andstealth are closely interrelated, new and better results may beobtained if both aspects are considered simultaneously. Simplyreducing the radar cross section area in some directionswithout considering tactical aspects may result in little, ifany, improvement. Flight tests have been performed in cooperation withEricsson Microwave Systems and the Swedish Air Force FlightAcademy. The aircraft used was the subsonic jet trainer Saab105, designated SK60 by the Swedish Air Force. The results showa decrease of 40% in the time interval between the instant theaircraft was first detected until it could pass above the radarstation. This corresponds to a reduced radar cross section(RCS) in the direction from the aircraft to the radar of almost90%, if classical RCS reduction techniques would have beenapplied. If a modern aircraft with stealth properties would be used,the proposed methodology is believed to increase the possibleimprovements further. This is because the variation of themagnitude of RCS in different directions is greater for a shapeoptimized aircraft, which is the property exploited by thedeveloped method. The methods presented are indeed an approach utilizing theideas of the network centric warfare (NCW) concept. Themethodology presented depends on accurate information about theadversary, while also providing up-to-date information to theother users in the information network. The thesis focuses on aircraft but the methods are generaland may be adapted for missiles, shipsor land vehicles. Theproposed methods are also economically viable since they areuseful for existing platforms without costly modifications. Themethods presented are not limited to radar threats only. Thereasons for using radar in this thesis are the availablenon-classified data and that radar is known to pose a majorthreat against aircraft.