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NASA NTRSDate not supplied

Robust Cislunar Trajectory Optimization Via Midcourse Correction and Optical Navigation Scheduling

This paper presents a new approach to optimal trajectory design that considers uncertainties in the system, referred to herein as robust trajectory optimization. This approach assumes an existing reference trajectory and optimizes the locations of midcourse correction burns and utilization of onboard navigation sensors to minimize dispersions in ∆v or final position. Navigation errors, maneuver execution errors, orbit insertion errors, and environmental modeling errors are considered. The application in this paper is cislunar flight with the goal of injecting into a Near-Rectilinear Halo Orbit for rendezvous with a target vehicle. Two complementary optimization problems are proposed. One problem minimizes the total ∆v dispersion subject to a final position dispersion constraint. The other problem minimizes the final position dispersion subject to a total ∆v dispersion constraint. The results from each optimization problem are shown for a complete mission profile.

Linear Covariance Analysis↗

NASA NTRS1981

Computational methods of robust controller design for aerodynamic flutter suppression

The development of Riccati iteration, a tool for the design and analysis of linear control systems is examined. First, Riccati iteration is applied to the problem of pole placement and order reduction in two-time scale control systems. Order reduction, yielding a good approximation to the original system, is demonstrated using a 16th order linear model of a turbofan engine. Next, a numerical method for solving the Riccati equation is presented and demonstrated for a set of eighth order random examples. A literature review of robust controller design methods follows which includes a number of methods for reducing the trajectory and performance index sensitivity in linear regulators. Lastly, robust controller design for large parameter variations is discussed.

Anderson, L. R.↗

NASA NTRS2014

Potential for Integrating Entry Guidance into the Multi-Disciplinary Entry Vehicle Optimization Environment

The state-of-the-art in vehicle design decouples flight feasible trajectory generation from the optimization process of an entry spacecraft shape. The disadvantage to this decoupled process is seen when a particular aeroshell does not meet in-flight requirements when integrated into Guidance, Navigation, and Control simulations. It is postulated that the integration of a guidance algorithm into the design process will provide a real-time, rapid trajectory generation technique to enhance the robustness of vehicle design solutions. The potential benefit of this integration is a reduction in design cycles (possible cost savings) and increased accuracy in the aerothermal environment (possible mass savings). This work examines two aspects: 1) the performance of a reference tracking guidance algorithm for five different geometries with the same reference trajectory and 2) the potential of mass savings from improved aerothermal predictions. An Apollo Derived Guidance (ADG) algorithm is used in this study. The baseline geometry and five test case geometries were flown using the same baseline trajectory. The guided trajectory results are compared to separate trajectories determined in a vehicle optimization study conducted for NASA's Mars Entry, Descent, and Landing System Analysis. This study revealed several aspects regarding the potential gains and required developments for integrating a guidance algorithm into the vehicle optimization environment. First, the generation of flight feasible trajectories is only as good as the robustness of the guidance algorithm. The set of dispersed geometries modelled aerodynamic dispersions that ranged from +/-1% to +/-17% and a single extreme case was modelled where the aerodynamics were approximately 80% less than the baseline geometry. The ADG, as expected, was able to guide the vehicle into the aeroshell separation box at the target location for dispersions up to 17%, but failed for the 80% dispersion cases. Finally, the results revealed that including flight feasible trajectories for a set of dispersed geometries has the potential to save mass up to 430 kg.

spacecraft guidance↗

NASA NTRS2011

Passive Aerogravity Assisted Trajectories for a Mars Atmospheric Sample Return Mission

A number of studies have demonstrated that aerodynamic lift during a planetary low-altitude atmospheric flyby can increase the V(sub infinity) bending angle and the total delta V achievable from gravity assist. Aero-Gravity Assist (AGA) trajectories of this type require a significantly high spacecraft L/D (lift-to-drag) ratio and a fairly robust closed-loop guidance algorithm capable of providing a desired control authority for level, nearly constant-altitude atmospheric flight. The AGA concept has been described in some previous publications as one of the techniques for Mars and Venus atmospheric sample return mission design strategies. Recent analysis has demonstrated that passive, ballistic (zero-lift) aeropass trajectories could equally satisfy potential future sample return mission objectives and provide quite robust and simple alternatives to a complex guided AGA lifting trajectory design.

sample return missions↗

NASA NTRS2014

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth/Moon L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

James Webb Space Telescope↗

NASA NTRS2014

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

Libration Point Orbit↗

NASA NTRSDate not supplied

Standalone Hazard Evaluation and Refinement From Instrument Findings (S.H.E.R.I.F.)

The Standalone Hazard Evaluation From Instrument Findings or SHERIF is a set of novel algorithms and associated framework designed to support the generation of Digital Elevation Maps (DEMs) from multiple LiDAR scans and perform Hazard Detection (HD) and Safe Site Selection with minimal input from other onboard systems. SHERIF can employ several techniques to perform Point Cloud registration(PCR) on disparate LiDAR scans of a planetary surface to generate a DEM which evolves over the course of a trajectory, with a flow designed to enable robustness. The framework also supports a variety of Hazard Detection and Safe Site Selection algorithms which can be run on the evolving DEM being produced. SHERIF features a robust and modular construction, allowing the user a high degree of flexibility in selecting and implementing whichever PCR and HD/SSL algorithms they may prefer, while maintaining the data products and sensor independence of the core SHERIF framework. SHERIF was recently tested in a hardware in the loop simulation at NASA JSC.

Entry Descent and Landing Guidance Navigation Cont↗

NASA NTRS1999

X-33 Ascent Flight Controller Design by Trajectory Linearization: A Singular Perturbational Approach

The flight control of X-33 poses a challenge to conventional gain-scheduled flight controllers due to its large attitude maneuvers from liftoff to orbit and reentry. In addition, a wide range of uncertainties in vehicle handling qualities and disturbances must be accommodated by the attitude control system. Nonlinear tracking and decoupling control by trajectory linearization can be viewed as the ideal gain-scheduling controller designed at every point on the flight trajectory. Therefore it provides robust stability and performance at all stages of flight without interpolation of controller gains, and eliminates costly controller redesigns due to minor airframe alteration or mission reconfiguration. A prototype trajectory linearization design for X-33 ascent flight controller was designed and tested with 3-DOF and 6-DOF simulations during the 10 weeks SFFP. It is noted that the 6-DOF results were obtained from the 3-DOF design with only a few hours of tuning, which demonstrates the inherent robustness of the design technique. It is this "plug-and-play" feature that is much needed by NASA for the development, test and routine operations of the RLVs. Plans for further research are also presented.

Zhu, J. Jim↗

NASA NTRSDate not supplied

Mission Design Considerations for a Low-Thrust Spacecraft

Developing an executable low-thrust trajectory for use in a spaceflight mission requires the design and optimization of a deterministic trajectory as well as the validation that the selected architecture is robust to some set of uncertainties, execution errors, and potential contingencies. Uncertainty in the ability of the spacecraft and its launch vehicle to execute a trajectory as well as potential deviations such as in-flight anomalies combine with design-to constraints and requirements to complicate the optimization problem. The approach by which robust mission design was accomplished for the initial capability of NASA’s Gateway is presented as well as associated results.

NRHO↗

NASA NTRS2000

X-33 Ascent Flight Controller Design by Trajectory Linearization: A Singular Perturbational Approach

The flight control of X-33 poses a challenge to conventional gain-scheduled flight controllers due to its large attitude maneuvers from liftoff to orbit and reentry. In addition, a wide range of uncertainties in vehicle handling qualities and disturbances must be accommodated by the attitude control system. Nonlinear tracking and decoupling control by trajectory linearization can be viewed as the ideal gain-scheduling controller designed at every point on the flight trajectory. Therefore it provides robust stability and performance at all stages of flight without interpolation of controller gains and eliminates costly controller redesigns due to minor airframe alteration or mission reconfiguration. In this paper, a prototype trajectory linearization design for an X-33 ascent flight controller is presented along with 3-DOF and 6-DOF simulation results. It is noted that the 6-DOF results were obtained from the 3-DOF design with only a few hours of tuning, which demonstrates the inherent robustness of the design technique. It is this "plug-and-play" feature that is much needed by NASA for the development, test and routine operations of the RLV'S. Plans for further research are also presented, and refined 6-DOF simulation results will be presented in the final version of the paper.

Zhu, J. Jim↗

NASA NTRSDate not supplied

Mission Design Considerations for a Low-Thrust Spacecraft

mission design↗

NASA NTRS2019

Investigation of Stiffening Effects on Notch Growth Trajectory of Composite Stiffened Panels with Large Transverse Notches

Design of robust aircraft structure requires consideration of the load-carrying capability with large damage. Large notches, typically introduced as machined cracks (aka “notches”) severing a single skin bay and a central stiffening member, are often used to conservatively address the wide range of possible large damage scenarios. The objective of current effort was to explore the viability of developing preliminary laminate-based methods for predicting crack turning at the adjacent stiffener using traditional fracture mechanics concepts.

Enjuto, Patrick↗

NASA NTRS2019

Low-Thrust Trajectory Design for a Cislunar CubeSat Leveraging Structures from the Bicircular Restricted Four-Body Problem

The upcoming Lunar IceCube (LIC) mission will deliver a 6U CubeSat to a low lunar orbit via a ride-share opportunity during NASAs Artemis 1 mission. This presents a challenging trajectory design scenario, as the vast change in energy required to transfer from the initial deployment state to the destination orbit is compounded by the limitations of the LICs low-thrust engine. This investigation addresses these challenges by developing a trajectory design framework that utilizes dynamical structures available in the Bicircular Restricted Four-Body Problem (BCR4BP) along with a robust direct collocation algorithm. Maps are created that expedite the selection of invariant manifold paths from a periodic staging orbit in the BCR4BP that offer favorable connections between the LIC transfer phases. Initial guesses assembled from these maps are passed to a direct collocation algorithm that corrects them in the BCR4BP while including the variable low-thrust acceleration of the spacecraft engine. Results indicate that the ordered motion provided by the BCR4BP and the robustness of direct collocation combine to offer an efficient and adaptable framework for designing a baseline trajectory for the LIC mission.

Pritchett, Robert↗

NASA NTRS2019

Low-Thrust Trajectory Design for A Cislunar CubeSat Leveraging Structures from the Bicircular Restricted Four-Body Problem

Pritchett, Robert↗

NASA NTRS2022

Analysis and Design of Abort Options for Low Energy LandingTrajectories

Low energy trajectories that enable spacecraft landing on airless bodies using minimum propellant consumption are currently being proposed to support various mission proposals.However, this direct approach to landing poses a risk because the abort options are limited and time-sensitive. A way to deal with this limitation is to declare the approach to landing a critical event, i.e., it must happen as planned or the entire mission is compromised. However,with the appropriate tools and techniques, a number of abort options can be identified, yielding a much more robust design. In this study, multi-body dynamics techniques are exploited to design abort trajectories for low energy transfers, using Earth’s Moon and Jupiter’s moon Europa as examples. As a result, periodic structures are identified for staging purposes in case of emergency, and the propellant cost associated with entering and departing these orbits prior to landing is evaluated.

Hernandez, Sonia↗

NASA NTRS2001

Consideration of Moving Tooth Load in Gear Crack Propagation Predictions

Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two-dimensional analysis of an involute spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.

Lewicki, David G.↗

NASA NTRS2018

Overview of the Spacecraft Design for the Psyche Mission Concept

In January 2017, Psyche and a second mission concept were selected by NASA for flight as part of the 14th Discovery mission competition. Assigned for an initial launch date in 2023, the Psyche team was given direction shortly after selection to research the possibility for earlier opportunities. Ultimately, the team was able to identify a launch opportunity in 2022 with a reduced flight time to its destination. This was accomplished in large part to crosscutting trades centered on the electrical power subsystem. These trades were facilitated through the Psyche mission's planned use of Solar Electric Propulsion (SEP), which enables substantial flexibility with respect to trajectory design. In combination with low-thrust trajectory analysis tools, the team was able to robustly converge to solutions with a higher fidelity and accuracy of results. These trades also took advantage of the 1300 series product line produced by Space Systems Loral (SSL), which enabled power growth while maintaining strong system-level heritage through its modular design that has been utilized on a large number of geostationary (GEO) communications satellites. This paper presents an overview of the Psyche mission concept, and the unique architecture that enables the use of commercially developed electric propulsion and space power systems from Space Systems Loral to provide flexibility in mission design. This paper then discusses the trades that allowed the Psyche team to meet a 2022 launch date.

Prikl, Zachary↗

NASA NTRS1990

Numerical derivative techniques for trajectory optimization

The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.

Hallman, Wayne P.↗