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At least 1,783 records · Page 99

Efficient computation of optimal low thrust gravity perturbed orbit transfers

We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyperbolic tangent smoothing law for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and thus promote convergence. The TPBVP is solved using the method of particular solutions (MPS) shooting method and Picard-Chebyshev numerical integration. Application of Picard-Chebyshev integration affords an avenue for increased efficiency that is not available with step-by-step integrators. We demonstrate that computing the particular solutions with only a low-fidelity force model greatly increases the efficiency of the algorithm while ultimately achieving near machine precision accuracy. A salient feature of the MPS is that it is parallelizable, and thus further speedups are available. It is also shown that, for near Earth orbits and over a small number of en-route revolutions around the Earth, only the zonal perturbation terms are required in the costate equations to obtain a solution that is accurate to machine precision and optimal to engineering precision. The proposed framework can be used for trajectory design around small asteroids and also for orbit debris rendezvous and removal tasks.

Junkins, John L.↗

Evaluation of some significant issues affecting trajectory and control management for air-breathing hypersonic vehicles

Horizontal takeoff airbreathing-propulsion launch vehicles require near-optimal guidance and control which takes into account performance sensitivities to atmospheric characteristics while satisfying physically-derived operational constraints. A generic trajectory/control analysis tool that deepens insight into these considerations has been applied to two versions of a winged-cone vehicle model. Information that is critical to the design and trajectory of these vehicles is derived, and several unusual characteristics of the airbreathing propulsion model are shown to have potentially substantial effects on vehicle dynamics.

Hattis, Philip D.↗

A New Maneuver for Escape Trajectories

This presentation put forth a new maneuver for escape trajectories and specifically sought to find an analytical approximation for medium thrust trajectories. In most low thrust derivations the idea is that escape velocity is best achieved by accelerating along the velocity vector. The reason for this is that change in specific orbital energy is a function of velocity and acceleration. However, Levin (1952) suggested that while this is a locally optimal solution it might not be a globally optimal one. Turning acceleration inward would drop periapse giving a higher velocity later in the trajectory. Acceleration at that point would be dotted against a higher magnitude V giving a greater rate of change of mechanical energy. The author then hypothesized that decelerating from the initial orbit and then accelerating at periapse would not lead to a gain in greater specific orbital energy--however, the hypothesis was incorrect. After considerable derivation it was determined that this new maneuver outperforms a direct burn when the overall DeltaV budget exceeds the initial orbital velocity (the author has termed this the Heinlein maneuver). The author provides a physical explanation for this maneuver and presents optimization analyses.

Adams, Robert B.↗

Optimal force distribution for payload positioning using a planar dual-arm robot

This paper presents a parameter optimization technique for deciding the force distribution on a payload being transported along a predetermined trajectory using two planar manipulator arms. The methodology begins by transforming the singular dynamics of two-arm transport to an ordinary set of differential equations and then proceeds to obtain a relation between the torques exerted by each arm. This relation is then used in a quadratic torque cost which is subsequently minimized to yield an optimal torque distribution. Significant savings in energy were found to occur when the arms were allowed to interact by transmission of forces through the payload. Even more significant are the savings found over one-arm transport of payloads where the arm torques are fixed by the prescribed trajectory.

Carignan, C. R.↗

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

Folta, D. C.↗

An Approach to Realize Generalized Optimal Motion Primitives Using Physics Informed Neural Networks

Autonomous manipulation is a challenging problem in field robotics due to uncertainty in object properties, constraints, and coupling phenomenon with robot control systems. Humans learn motion primitives over time to effectively interact with the environment. We postulate that autonomous manipulation can be enabled by basic sets of motion primitives as well, but do not necessitate mimicking human motion primitives. Here, this work presents an approach to generalized optimal motion primitives using physics-informed neural networks. Our simulated and experimental results demonstrate that optimality is notionally maintained where the mean maximum observed final position percent error was 0.564% and the average mean error for all the trajectories was 1.53%. These results indicate that notional generalization is attained using a physics-informed neural network approach that enables near optimal real-time adaptation of primitive motion profiles.

97 MATHEMATICS AND COMPUTING↗

Overall Traveling-Wave-Tube Efficiency Improved By Optimized Multistage Depressed Collector Design

Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.

Vaden, Karl R.↗

Automatic flare transition penetrating wind shears

In this paper, the development of a digital three-dimensional automatic control law designated to achieve an optimal transition of a large commercial aircraft between the glideslope conditions and the desired final touchdown condition is presented. The linearized equations representing the perturbed motion of the aircraft from the nominal glideslope trajectory are presented. A method of incorporating the spatial, low-level wind shears into these perturbed equations of motion is indicated. It is shown that the system equations then assume the familiar form of the linear regulator problem, acted upon by a constant disturbance. A design procedure is presented to compute a digital, time-invariant, optimal control law for the discrete regulator problem acted upon by a constant disturbance. The response trajectories presented demonstrate the capability of this controller to perform optimal flare maneuvers in the presence of various wind shear conditions.

Nadkarni, A. A.↗

Coordinated Turn Trajectory Generation and Tracking Control for Multi-rotors Operating in Urban Environment

The paper presents an efficient trajectory generation and tracking approach for multi-rotor air vehicles operating in urban environment, which takes into account uncertainties in the urban wind field and in the vehicle's parameters. Generated trajectories are sufficiently smooth, based on the differential flatness of the vehicle's dynamics and optimal in the sense of minimum agility and time. They pass through given set of way points, guarantee flight without a side-slip, and satisfy vehicle's dynamics and actuator constraints. In addition, an algorithm is presented to compute the required power to traverse the generated trajectory. Presented algorithms are implementable in real time using on-board computers. They do not take into account the vehicle's existing flight controller, hence there is no guarantee that the controller will be able to provide acceptable tracking of the generated trajectory, especially in the presence of atmospheric disturbances. To this end, we propose an adaptive augmentation algorithm to improve vehicle's performance by taking into account the effects of disturbances and on-line estimates of vehicle's existing flight controller's gains. The algorithms have been verified by simulations using DJI S1000 octocopter's model.

Stepanyan, Vahram↗

Coordinated Turn Trajectory Generation and Tracking Control for Multi-Rotors Operating in Urban Environment

The paper presents an efficient trajectory generation and tracking approach for multi-rotor air vehicles operating in urban environment, which takes into account uncertainties in the urban wind field and in the vehicle's parameters. Generated trajectories are sufficiently smooth, based on the differential flatness of the vehicle's dynamics and optimal in the sense of minimum agility and time. They pass through given set of way points, guarantee flight without a side-slip, and satisfy vehicle's dynamics and actuators constraints. In addition, an algorithm is presented to compute the required power to traverse the generated trajectory. Presented algorithms are implementable in real time using on-board computers. They do not take into account the vehicle's existing flight controller, hence there is no guarantee that the controller will be able to provide acceptable tracking of the generated trajectory, especially in the presence of atmospheric disturbances. To this end, we propose an adaptive augmentation algorithm to improve vehicle's performance by taking into account the effects of disturbances and on-line estimates of vehicle's existing flight controller's gains. The algorithms have been verified by simulations using DJI S1000 octocopter's model.

Stepanyan, Vahram↗

Modified Newton-Raphson GRAPE methods for optimal control of spin systems

Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Flight Control Role in RLV Configuration Development

A new optimization technique was used to aide in the selection of aerodynamic surfaces and Thrust Vectoring Control (TVC) based on maximizing control margin during ascent and entry portions of the trajectory. In order to meet the mass fraction requirement of RLV (Reusable Launch Vehicle), every substructure needed to be carefully designed to minimize the dry mass. The trajectory was designed to deliver the payload required for each mission subject to thermal and structural constraints. At each point on the trajectory the angle of attack and Mach number pair was used to calculate the control power required to trim and to stabilize the vehicle. The new optimization technique was based on finding the configuration that minimizes the control power peaks along the entire trajectory.

Youssef, Hussein↗

Orbiter Trajectory Analysis for a Two-Stage Reusable Launch Vehicle

Trajectory analysis performed on NASA's reference two-stage-to-orbit launch vehicle upper stage will be presented. The work was completed in support of the Hypersonics Multidisciplinary Analysis and Optimization effort for the NASA-Air Force Joint System Study. Three degree-of-freedom (3-DOF) untrimmed trajectory analysis was performed for the orbiter ascent, closure and re-entry. An iterative closure process resulted in a 333,000 lb initial mass for the orbiter. The re-entry trajectory satisfied heating constraints for all payload out cases and met the constraints with reduced margins for payload in cases. Abort trajectories for engine out at staging, engine out during ascent, and failure to circularize in orbit, gave insight to the robustness of the orbiter. A trimmed ascent trajectory defined an engine gimbal location and the body flap angle best suited for maximizing injected mass. A trimmed re-entry trajectory revealed a need to update the trim routine to accommodate full flap aerodynamic data.

Cowling, Adam L.↗

A neural net approach to space vehicle guidance

The space vehicle guidance problem is formulated using a neural network approach, and the appropriate neural net architecture for modeling optimum guidance trajectories is investigated. In particular, an investigation is made of the incorporation of prior knowledge about the characteristics of the optimal guidance solution into the neural network architecture. The online classification performance of the developed network is demonstrated using a synthesized network trained with a database of optimum guidance trajectories. Such a neural-network-based guidance approach can readily adapt to environment uncertainties such as those encountered by an AOTV during atmospheric maneuvers.

Caglayan, Alper K.↗

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Low-Thrust Mission Design

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on a hypothetical mission to the main asteroid belt.

Optimization↗

TH-AB-BRB-01: Trajectory Modulated Arc Therapy: Application to Partial Breast Irradiation

Current state-of-the art digital C-arm medical linear accelerators are capable of delivering radiation treatments with high level of automation, which affords coordinated motions of gantry, couch, and multileaf collimator (MLC) with dose rate modulations. The new machine capacity has shown the potential to bring substantially improved radiation dosimetry and/or delivery efficiency to many challenging diseases. Combining an integrated beam orientation optimization algorithm with automated machine navigation, markedly improved dose conformity has been achieved using 4ρ therapy. Trajectory modulated radiation therapy (TMAT) can be used to deliver highly conformal dose to partial breast or to carve complex dose distribution for therapy involving extended volumes such as total marrow and total lymph node treatment. Dynamic electron arc radiotherapy (DEAR) not only overcomes the deficiencies of conventional electron therapy in dose conformity and homogeneity but also achieves so without patient-specific shields. The combination of MLC and couch tracking provides improved motion management of thoracic and abdominal tumors. A substantial body of work has been done in these technological advances for clinical translation. The proposed symposium will provide a timely review of these exciting opportunities. Learning Objectives: Recognize the potential of using digitally controlled linacs for clinically significant improvements in delivered dose distributions for various treatment sites. Identify existing approaches to treatment planning, optimization and delivery for treatment techniques utilizing the advanced functions of digital linacs and venues for further development and improvement. Understand methods for testing and validating delivery system performance. Identify tools available on current delivery systems for implementation and control for such treatments. Obtain the update in clinical applications, trials and regulatory approval. K. Sheng, NIH U19AI067769, NIH R43CA183390, NIH R01CA188300, Varian Medical Systems V. Yu, Varian Medical Systems, AAPM Summer Undergraduate Fellowship, NSF graduate fellowship S. Nill, Elekta AB. Cancer Research UK under Programme C33589/A19727, NIHR Biomedical Research Centre at The Royal Marsden and The Institute of Cancer Research.

60 APPLIED LIFE SCIENCES↗

ODIN system technology module library, 1972 - 1973

ODIN/RLV is a digital computing system for the synthesis and optimization of reusable launch vehicle preliminary designs. The system consists of a library of technology modules in the form of independent computer programs and an executive program, ODINEX, which operates on the technology modules. The technology module library contains programs for estimating all major military flight vehicle system characteristics, for example, geometry, aerodynamics, economics, propulsion, inertia and volumetric properties, trajectories and missions, steady state aeroelasticity and flutter, and stability and control. A general system optimization module, a computer graphics module, and a program precompiler are available as user aids in the ODIN/RLV program technology module library.

Hague, D. S.↗