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Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of Shuttle and Shuttle derived vehicles) engineering manual

The Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program and its predecessors, the ROBOT and the RAGMOP programs, have had a long history of supporting MSFC in the simulation of space boosters for the purpose of performance evaluation. The ROBOT program was used in the simulation of the Saturn 1B and Saturn 5 vehicles in the 1960's and provided the first utilization of the minimum Hamiltonian (or min-H) methodology and the steepest ascent technique to solve the optimum trajectory problem. The advent of the Space Shuttle in the 1970's and its complex airplane design required a redesign of the trajectory simulation code since aerodynamic flight and controllability were required for proper simulation. The RAGMOP program was the first attempt to incorporate the complex equations of the Space Shuttle into an optimization tool by using an optimization method based on steepest ascent techniques (but without the min-H methodology). Development of the complex partial derivatives associated with the Space Shuttle configuration and using techniques from the RAGMOP program, the ROBOT program was redesigned to incorporate these additional complexities. This redesign created the MASTRE program, which was referred to as the Minimum Hamiltonian Ascent Shuttle TRajectory Evaluation program at that time. Unique to this program were first-stage (or booster) nonlinear aerodynamics, upper-stage linear aerodynamics, engine control via moment balance, liquid and solid thrust forces, variable liquid throttling to maintain constant acceleration limits, and a total upgrade of the equations used in the forward and backward integration segments of the program. This modification of the MASTRE code has been used to simulate the new space vehicles associated with the National Launch Systems (NLS). Although not as complicated as the Space Shuttle, the simulation and analysis of the NLS vehicles required additional modifications to the MASTRE program in the areas of providing additional flexibility in the use of the program, allowing additional optimization options, and providing special options for the NLS configuration.

Lyons, J. T.↗

Coupled Solid Rocket Motor Ballistics and Trajectory Modeling for Higher Fidelity Launch Vehicle Design

Multi-stage launch vehicles with solid rocket motors (SRMs) face design optimization challenges, especially when the mission scope changes frequently. Significant performance benefits can be realized if the solid rocket motors are optimized to the changing requirements. While SRMs represent a fixed performance at launch, rapid design iterations enable flexibility at design time, yielding significant performance gains. The streamlining and integration of SRM design and analysis can be achieved with improved analysis tools. While powerful and versatile, the Solid Performance Program (SPP) is not conducive to rapid design iteration. Performing a design iteration with SPP and a trajectory solver is a labor intensive process. To enable a better workflow, SPP, the Program to Optimize Simulated Trajectories (POST), and the interfaces between them have been improved and automated, and a graphical user interface (GUI) has been developed. The GUI enables real-time visual feedback of grain and nozzle design inputs, enforces parameter dependencies, removes redundancies, and simplifies manipulation of SPP and POST's numerous options. Automating the analysis also simplifies batch analyses and trade studies. Finally, the GUI provides post-processing, visualization, and comparison of results. Wrapping legacy high-fidelity analysis codes with modern software provides the improved interface necessary to enable rapid coupled SRM ballistics and vehicle trajectory analysis. Low cost trade studies demonstrate the sensitivities of flight performance metrics to propulsion characteristics. Incorporating high fidelity analysis from SPP into vehicle design reduces performance margins and improves reliability. By flying an SRM designed with the same assumptions as the rest of the vehicle, accurate comparisons can be made between competing architectures. In summary, this flexible workflow is a critical component to designing a versatile launch vehicle model that can accommodate a volatile mission scope.

Ables, Brett↗

Trajectory optimization for the Atlas/Centaur launch vehicle

A method for finding solutions to complex trajectory optimization problems with detailed hardware and launch vehicle constraints is presented. The trajectory optimization problem is formulated as a constrained function minimization problem by modeling the control by a function of a finite number of parameters. Although any parametric control model may be selected, the natural choice of parameters is the actual parameters of the parametric guidance equations flown on the flight digital computer. A variation of the method of multipliers is presented for performing the constrained function minimization. A functional is proposed that allows incorporation of state variable inequality constraints. Finally, optimization of the HEAO-A direct-ascent trajectory is discussed. The HEAO-A mission demonstrates profile optimization to meet range safety, tracking, heating, structural integrity, and attitude rate constraints.

Brusch, R. G.↗

Trajectory Planning for Mission Survivability of Autonomous Vehicles in Moderately to Extremely Uncertain Environments

Trajectory planning is a particularly challenging task for autonomous vehicles when there are moderate to extreme uncertainties in their operating environment, i.e., where the trajectories of hazards are partially known to completely unknown. In this paper, we propose a receding horizon control strategy with novel trajectory planning policies that enable dynamic updating of the planned trajectories of autonomous vehicles. The proposed policies utilize two metrics: (1) the number of feasible trajectories; and (2) the robustness of the feasible trajectories. We measure the effectiveness of the suggested policies in terms of mission survivability, which is defined as the probability that the primary mission is accomplished or, if that is not possible, the vehicle lands safely at an alternative site. We show that a linear combination of both metrics is an effective objective function when there is a mix of partially known and unknown uncertainties. When the operating environment is dominated by unknown disturbances, maximizing the number of feasible trajectories results in the highest mission survivability. These findings have significant implications for achieving safe aviation autonomy.

aviation autonomy↗

Simulation-Based Analysis of Reentry Dynamics for the Sharp Atmospheric Entry Vehicle

This thesis describes the analysis of the reentry dynamics of a high-performance lifting atmospheric entry vehicle through numerical simulation tools. The vehicle, named SHARP, is currently being developed by the Thermal Protection Materials and Systems branch of NASA Ames Research Center, Moffett Field, California. The goal of this project is to provide insight into trajectory tradeoffs and vehicle dynamics using simulation tools that are powerful, flexible, user-friendly and inexpensive. Implemented Using MATLAB and SIMULINK, these tools are developed with an eye towards further use in the conceptual design of the SHARP vehicle's trajectory and flight control systems. A trajectory simulator is used to quantify the entry capabilities of the vehicle subject to various operational constraints. Using an aerodynamic database computed by NASA and a model of the earth, the simulator generates the vehicle trajectory in three-dimensional space based on aerodynamic angle inputs. Requirements for entry along the SHARP aerothermal performance constraint are evaluated for different control strategies. Effect of vehicle mass on entry parameters is investigated, and the cross range capability of the vehicle is evaluated. Trajectory results are presented and interpreted. A six degree of freedom simulator builds on the trajectory simulator and provides attitude simulation for future entry controls development. A Newtonian aerodynamic model including control surfaces and a mass model are developed. A visualization tool for interpreting simulation results is described. Control surfaces are roughly sized. A simple controller is developed to fly the vehicle along its aerothermal performance constraint using aerodynamic flaps for control. This end-to-end demonstration proves the suitability of the 6-DOF simulator for future flight control system development. Finally, issues surrounding real-time simulation with hardware in the loop are discussed.

Tillier, Clemens Emmanuel↗

Optimum reentry trajectories of a lifting vehicle

Research results are presented of an investigation of the optimum maneuvers of advanced shuttle type spacecraft during reentry. The equations are formulated by means of modified Chapman variables resulting in a general set of equations for flight analysis which are exact for reentry and for flight in a vacuum. Four planar flight typical optimum manuevers are investigated. For three-dimensional flight the optimum trajectory for maximum cross range is discussed in detail. Techniques for calculating reentry footprints are presented.

Chern, J. S.↗

Optimal boost trajectories for the shuttle vehicle.

Solutions of the optimal boost problem for the MSC April 1970 base line shuttle vehicle show significant payload increases may be achieved by flying optimal pitch profiles. Results consistent with aerodynamic and acceleration constraints indicate payload gains of approximately 2.0 per cent of the total injected weight may be achieved. This corresponds to a real payload increase of about 20 per cent. Trajectory parameters for optimal launches under various conditions and a standard gravity turn launch are presented along with a brief discussion of the problem modeling and assumptions. The data are used to support a number of observations and conclusions and to provide some insight into the methods by which payload gains are achieved.

Sullivan, H. C.↗

Evaluation of innovative rocket engines for single-stage earth-to-orbit vehicles

Computer models of rocket engines and single-stage-to-orbit vehicles that were developed by the authors at DFVLR and NASA have been combined. The resulting code consists of engine mass, performance, trajectory and vehicle sizing models. The engine mass model includes equations for each subsystem and describes their dependences on various propulsion parameters. The engine performance model consists of multidimensional sets of theoretical propulsion properties and a complete thermodynamic analysis of the engine cycle. The vehicle analyses include an optimized trajectory analysis, mass estimation, and vehicle sizing. A vertical-takeoff, horizontal-landing, single-stage, winged, manned, fully reusable vehicle with a payload capability of 13.6 Mg (30,000 lb) to low earth orbit was selected. Hydrogen, methane, propane, and dual-fuel engines were studied with staged-combustion, gas-generator, dual bell, and the dual-expander cycles. Mixture ratio, chamber pressure, nozzle exit pressure liftoff acceleration, and dual fuel propulsive parameters were optimized.

Manski, Detlef↗

Demonstration of Linear Covariance Analysis Techniques to Evaluate Entry Descent and Landing Guidance Algorithms, Vehicle Configurations, Analysis Techniques, and Trajectory Profiles

Linear covariance analysis techniques have been previously developed to analyze closed-loop entry, descent, and landing (EDL) scenarios and the initial validation efforts are under-way confirming the generated GN&C system performance results. Given both the theoretical foundation and previous conceptual demonstration, this work begins to flex the potential of linear covariance analysis for atmospheric flight and highlight its versatility and reliability by evaluating multiple entry guidance algorithms, vehicle configurations, trajectory profiles, environment conditions, and analysis techniques for a variety of trade studies. To demonstrate the benefit linear covariance analysis can provide in producing rapid yet accurate performance data, two entry profiles are adopted including the NASA Mars Science Laboratory (MSL) and Exploration Flight Test-1 (EFT-1) while utilizing two different guidance algorithms, the Apollo Final Phase (AFP) and the Fully Numeric Predictor-Corrector Entry Guidance (FNPEG) with different navigation sensor suites in a 6 degree-of-freedom (6-DOF) simulation environment. Results are shown using both linear covariance and Monte Carlo analysis techniques to high-light the consistency between the two methodologies and continue the validation maturation of linear covariance analysis for entry, descent, and landing.

EDL↗

Trajectory Planning for Mission Survivability of Autonomous Vehicles in Moderately to Extremely Uncertain Environments

Trajectory planning is a particularly challenging task for autonomous vehicles when the uncertainties in their operating environment cannot be characterized statistically. In this paper, we propose a receding horizon control strategy with novel trajectory planning policies that enable dynamic updating of the planned trajectories of autonomous vehicles operating in environments where potential conflicts are, from a statistical perspective, either partially known or completely unknown. The proposed policies utilize two metrics: (1) the number of feasible trajectories; and (2) the robustness of the feasible trajectories. We measure the effectiveness of the suggested policies in terms of mission survivability, which is defined as the probability that the primary mission is accomplished or, if that is not possible, the vehicle lands safely at an alternative site. We show that a linear combination of both metrics is an effective objective function when there is a mix of partially known and unknown uncertainties. When the operating environment is dominated by unknown disturbances, maximizing the number of feasible trajectories results in the highest mission survivability. These findings have significant implications for achieving safe aviation. autonomy.

Aviation autonomy↗

Design of a fast crew transfer vehicle to Mars

A final report is made on the trajectory and vehicle requirements for a fast crew transfer vehicle to Mars which will complete an Earth to Mars (and Mars to Earth) transfer in 150 days and will have a stay time at Mars of 40 days. This vehicle will maximize the crew's effectiveness on Mars by minimizing detrimental physiological effects such as bone demineralization and loss of muscle tone caused by long period exposure to zero gravity and radiation from cosmic rays and solar flares. The crew transfer vehicle discussed will complete the second half of a Split Mission to Mars. In the Split Mission, a slow, unmanned cargo vehicle, nicknamed the Barge, is sent to Mars ahead of the crew vehicle. Once the Barge is in orbit around Mars, the fast crew vehicle will be launched to rendezvous with the Barge in Mars orbit. The vehicle presented is designed to carry six astronauts for a mission duration of one year. The vehicle uses a chemical propulsion system and a nuclear power system. Four crew modules, similar to the proposed Space Station Common Modules, are used to house the crew and support equipment during the mission. The final design also includes a command module that is shielded to protect the crew during radiation events.

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