A trajectory optimization technique based upon the theory of the second variation.
Optimization of trajectory achieved by successive approximation method based on second variation theory
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Optimization of trajectory achieved by successive approximation method based on second variation theory
A mathematical model describing the generation of aircraft noise is developed with the ultimate purpose of reducing noise (noise-optimizing landing trajectories) in terminal areas. While the model is for a specific aircraft (Boeing 737), the methodology would be applicable to a wide variety of aircraft. The model is used to obtain a footprint on the ground inside of which the noise level is at or above 70 dB.
During the past six months the research objectives outlined in the last semi-annual report were accomplished. Specifically, these are: three-dimensional (3-D) fuel-optimal ascent trajectory of the aerospace plane and the effects of thrust vectoring control (TVC) on the fuel consumption and trajectory shaping were investigated; the maximum abort landing area (footprint) was studied; preliminary assessment of simultaneous design of the ascent trajectory and the vehicle configuration for the aerospace plane was also conducted. The work accomplished in the reporting period is summarized.
An application of the new optimization algorithm called Static/Dynamic Control (SDC) to the design of low-thrust interplanetary trajectories is presented.
Descent retroburns using hydrazine thrusters will generate contaminants in their exhaust that can alter underlying samples, such as water-rich surfaces coinciding with possible life signatures or other science measurements of interest. We present an optimization technique that aims to autonomously minimize contamination during surface approach and landing for propulsive vehicles. In addition to short-range hoppers, the optimization technique is also fully applicable to traditional orbit-to-surface landers. This study addresses scenarios where surface alterations from propulsion events are counterproductive or hazardous to the mission objectives. This is of interest for landers (whether human or robotic), that may rely on pristine soils collected in the immediate vicinity of landing sites to accomplish science investigations, mining, or In Situ Resource Utilization (ISRU) surface operations. Such missions are averse to various surface-plume interactions such as thermal scoring, physical agitation, and contamination. The capability can be applied with minimal impact to the baseline concept.
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A key algorithmic element of a real-time trajectory optimization hardware/software implementation, the quadratic program (QP) solver element, is presented. The purpose of the effort is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter. Many methods of nonlinear programming require the solution of a QP at each iteration. In the trajectory optimization case the QP has a special dynamic programming structure, a LQR-like structure. QP algorithm speed is increased by taking advantage of this special structure and by parallel implementation.
Approximation optimal trajectories - selection of estimation variables in least squares program, and computer program application
The class of hypersonic vehicle configurations with single stage-to-orbit (SSTO) capability reflect highly integrated airframe and propulsion systems. These designs are also known to exhibit a large degree of interaction between the airframe and engine dynamics. Consequently, even simplified hypersonic models are characterized by tightly coupled nonlinear equations of motion. In addition, hypersonic SSTO vehicles present a major system design challenge; the vehicle's overall mission performance is a function of its subsystem efficiencies including structural, aerodynamic, propulsive, and operational. Further, all subsystem efficiencies are interrelated, hence, independent optimization of the subsystems is not likely to lead to an optimum design. Thus, it is desired to know the effect of various subsystem efficiencies on overall mission performance. For the purposes of this analysis, mission performance will be measured in terms of the payload weight inserted into orbit. In this report, a trajectory optimization problem is formulated for a generic hypersonic lifting body for a specified orbit-injection mission. A solution method is outlined, and results are detailed for the generic vehicle, referred to as the baseline model. After evaluating the performance of the baseline model, a sensitivity study is presented to determine the effect of various subsystem efficiencies on mission performance. This consists of performing a parametric analysis of the basic design parameters, generating a matrix of configurations, and determining the mission performance of each configuration. Also, the performance loss due to constraining the total head load experienced by the vehicle is evaluated. The key results from this analysis include the formulation of the sizing problem for this vehicle class using trajectory optimization, characteristics of the optimal trajectories, and the subsystem design sensitivities.
Theory and application of the critical direction method of trajectory optimization
A trajectory-optimization process is described in which the optimum thrust equations are derived using the calculus of variations. The magnitude of the thrust is constrained within an upper and a lower bound, but the thrust direction is arbitrary. This formulation allows both the constant-thrust program and the variable-thrust program to be considered. For the constant-thrust program, certain propulsion-system parameters are optimized for maximum final vehicle mass. This theory has been used to study interplanetary missions to Venus and Mars using a power-limited propulsion system. Both one-way and round trip rendezvous trajectories are considered. The analysis employs a two-body inverse-square force-field model of three dimensions. An iterative routine used to solve the two-point boundary-value problem is described in the Appendix.
Trajectory optimization and linearized pitch computer program for Scout launch vehicle
Trajectory optimization by direct descent to minimum cost using iterative computer solutions
Trajectory optimization by descent process using hybrid computer for direct cost gradient computation
Generalized indirect method solving two-point boundary value problems for rapid optimal trajectory computation
The two methods which are suitable for use in a 4-body trajectory optimization program are both multiconic methods. They include an approach due to Wilson (1970) and to Byrnes and Hooper (1970) and a procedure developed by Stumpff and Weiss (1968). The various steps in a trajectory optimization program are discussed, giving attention to variable step integration, the correction of errors by quadrature formulas, questions of two-impulse transfer, three-impulse transfer, and two examples which illustrate the implementation of the computational approaches.
This paper summarizes various applications of trajectory optimization principles that have been or are being devised by both government and industrial researchers to minimize aircraft direct operating costs (DOC). These costs (time and fuel) are computed for aircraft constrained to fly over a fixed range. Optimization theory is briefly outlined, and specific algorithms which have resulted from application of this theory are described. Typical results which demonstrate use of these algorithms and the potential savings which they can produce are given. Finally, need for further trajectory optimization research is presented.
Algorithms construction for aerospace vehicle trajectory optimization, considering quasi- linearization method for computation of variable time optimum trajectories