Description:
TECHNOLOGY AREA(S): Info Systems, Space Platforms, Weapons
OBJECTIVE: Develop new techniques for trajectory propagation that are more suited for use in federated simulations than traditional methods
DESCRIPTION: Runge-Kutta methods have been the standard for numerically solving a system of differential equations to propagate rocket vehicle trajectories. While robust with well characterized errors, Runge-Kutta methods have limitations for high-resolution federated simulations. These include extensive computational throughput requirements and large output data sets. Other limitations include the need to perform time-step matching between component simulations and determining the states for federated simulation events between the calculated time-steps. It may be possible to apply new/alternative numerical solution techniques (e.g. Parker-Sochacki method) and/or alternative problem formulations (e.g. Hamiltonian mechanics) to improve computational loading, data storage, and data integrity for rocket vehicle modeling in federated simulations. Desired attributes of alternative propagation methods include: 1. Trajectory generation independent of the time-step requirements of the other component simulations in the federation which consume the trajectory data. 2. Decreased trajectory computational time/hardware loading relative to required resolution, accuracy, and trajectory complexity. 3. Decreased output data storage size relative to resolution and trajectory complexity. 4. Easily tunable resolution accuracy to trade for computational speed and/or decreased output storage size. 5. Implementable common, reproducible, and accurate between-state trajectory estimation methods for trajectory data consuming component simulations within the federation. 6. Decreased between-state trajectory estimation computational time or hardware loading in consuming simulations. 7. Implementable lower accuracy trajectory driven event predictor algorithms for consuming simulations. Viability would not require all improvements in all desired attributes, and would likely be subject to trades of resolution, accuracy, and distributed computer resources. Developed techniques could be applied to other engineering simulations, real-time predictors, and control systems.
PHASE I: Develop the proposed novel propagation technique to a sufficient level to provide a proof-of-concept (e.g. a 3-DoF space launch with spherical rotating Earth with simple atmosphere model). Evaluate its potential value against each of the desired attributes either theoretically, by demonstration, or preferably both. Assess and document potential trades between implementation choices, resolution/accuracy, and numerical/computational efficiencies. Define a software and hardware architecture for using the proposed propagation technique in the government’s Modeling and Simulation Enterprise to be developed as an operational prototype in a Phase II effort.
PHASE II: Develop the proposed technique into an operational prototype rocket vehicle trajectory generation engine, with the basic supporting tools for employing the output data in consuming simulations and simulation frameworks. While medium level of modeling fidelity (e.g. 3+3 DoF, non-spherical Earth, etc.) is expected in the prototype, the prototype’s architecture should be extendable to high-resolution 6-DoF modeling of rocket vehicles. The trajectory generation engine and any post-processing tools must be verified against a design conceptual model with algorithm descriptions, and its output validated against reference systems/trajectories. Source code and executable software should meet government Information Assurance standards to include basic documentation of the conceptual model and algorithms, code structure, verification (vs. conceptual model) and validation results (vs. reference systems/trajectories), Information Assurance checks, and user guidance.
PHASE III: Extend development of the prototype into a fully operational trajectory generation engine for high-resolution 6-DoF modeling of rocket vehicles, with standard supporting tools for employing the output data in consuming simulations and simulation frameworks. Delivery to the government of the trajectory generation engine is expected to be in the form of source code and executable software. The trajectory generation engine and any post-processing tools must be verified against a design conceptual model and algorithm descriptions, and its output validated against reference systems/trajectories. Software should meet government Information Assurance standards. Robust documentation of the conceptual model/algorithms, code structure, verification (vs. conceptual model) and validation results (vs. reference systems/trajectories), Information Assurance checks, and user guidance is required.
REFERENCES:
1: Rudmin. March 1998. "Application of the Parker-Sochacki Method to Celestial Mechanics." Physics Dept., James Madison University. https://arxiv.org/abs/1007.1677.
2: Warne, Polignone Arne, Sochacki, Parker, and Carothers. 2006. "Explicit A-Priori Error Bounds and Adaptive Error Control for Approximation of Nonlinear Initial Value Differential Systems." Computers & Mathematics with Application; Vol. 52: p 1695-1710. http://www.sciencedirect.com/science/article/pii/S089812210600352X.
3: Reilly. May 1979. "Equations of Powered Rocket Ascent and Orbit Trajectory." NRL Report 8237; Communications Sciences Division, Naval Research Laboratory. www.dtic.mil/dtic/tr/fulltext/u2/a069296.pdf.
4: Butcher. 2005. "Numerical Methods for Ordinary Differential Equations." John Wiley & Sons, New York. ISBN 9780470868270.
KEYWORDS: Numerical Methods, Differential Equations, Numerical Integration, Trajectory, Ballistic Missile, Space Launch Vehicle, Simulation
