Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation
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Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation Noble Hatten1
· Ryan P. Russell1
© American Astronautical Society 2016
Abstract A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve efficiency in 3DOF propagation are modified and extended to the 6DOF problem, including the use of variable-fidelity dynamics models. The impact of computing the stage dynamics of a single step in parallel is examined using up to 23 threads and 22 associated GLIRK stages; one thread is reserved for an extra dynamics function evaluation used in the estimation of the local truncation error. Efficiency is found to peak for typical examples when using approximately 8 to 12 stages for both serial and parallel implementations. Accuracy and efficiency compare favorably to explicit Runge-Kutta and linear-multistep solvers for representative scenarios. However, linear-multistep methods are found to be more efficient for some applications, particularly in a serial computing environment, or when parallelism can be applied across multiple trajectories. Keywords Implicit Runge-Kutta · Six degrees of freedom · Attitude · Propagation · Parallel computing
Presented as Paper AAS 16-395 at the 26th AAS/AIAA Space Flight Mechanics Meeting, Feb. 14–18, 2016, Napa, CA. Noble Hatten
[email protected] Ryan P. Russell [email protected] 1
Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin TX, USA
J of Astronaut Sci
Introduction The efficient propagation of space object (SO) trajectories is of vital importance to applications including mission design, conjunction analysis, and trajectory estimation and optimization. In recent years, the astrodynamics community has revisited the viability of implicit Runge-Kutta (IRK) ordinary differential equation (ODE) solvers as accurate, efficient alternatives to the widely used linear multistep and explicit Runge-Kutta (ERK) solvers [6, 14, 21, 26]. Equivalent but alternatively formulated implicit solvers like Modified Chebyshev-Picard Iteration (MCPI) have also been investigated with success [6, 11]. The dynamics model evaluations at each node within an implicit propagation step are independent, allowing such methods to take advantage of modern parallel computing paradigms within a single step – unlike linear multistep and ERK solvers. Additional benefits depend on the specific implementation, but may include, for example, high order, strong stability properties, continuous solutions, symmetry, and symplecticity [6, 11, 19, 20, 26]. In this paper, concepts for propagating three-degree-of-freedom (3DOF) SO trajectories using IRK methods are modified and extended to the propagation of coupled SO trajectory and attitude – the 6DOF problem. Efficient 6DOF propagation is important for a variety of applications, including, perhaps most obviously, determining the orientation evolution of controllable SOs with pointing req
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