Welcome to pyqlaw’s documentation!#
pyqlaw is a python implementation of the Q-law feedback control for low-thrust orbital transfers.
Capabilities#
Q-law formulated in Keplerian & SMA-MEE (MEE with semilatus rectum replaced by semimajor axis)
Coasting capabilities with efficiency parameters [3]
Thrust duty cycles
Battery level tracking
Installation#
To install, run:
pip install pyqlaw
and to uninstall:
pip uninstall pyqlaw
Overview of Q-law#
Q-law is a Lyapunov controller defined in terms of orbital elements, and can be used as a feedback controller to construct suboptimal low-thrust, many-revolution transfers. Q-law is very sensitive to the problem (initial & final orbital elements, choice of orbital elements, thruster specs = control authority) as well as its various hyperparamters, which must be chosen carefully. In general, the following should be kept in mind:
For numerical stability, always work with canonical scales.
Be very careful with initial/final orbits not to contain singular elements (e.g. inclination ~ 0 deg in Keplerian elements representation).
Q-law is not suitable for high control authority applications (e.g. interplanetary transfer with 0~very few revolutions).
Taking larger integration time steps t_step (or angle steps, if use_sundman = True) makes the algorithm “faster” (less time until reaching the targeted elements), but may also lead to instability/high jitter once the spacecraft is close to the target; an appropriate value must be found on a problem-to-problem basis.
For more discussions, see for example:
Petropoulos, A. E. (2004). Low-thrust orbit transfers using candidate Lyapunov functions with a mechanism for coasting. Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2(August), 748–762. https://doi.org/10.2514/6.2004-5089
Petropoulos, A. E. (2005). Refinements to the Q-law for low-thrust orbit transfers. AAS/AIAA Space Flight Mechanics Meeting.
Hatten, N. (2012). A Critical Evaluation of Modern Low-Thrust, Feedback-Driven Spacecraft Control Laws.
Some References#
[1] Petropoulos, A. E. (2003). Simple Control Laws for Low-Thrust Orbit Transfers. AAS Astrodynamics Specialists Conference.
[2] Petropoulos, A. E. (2004). Low-thrust orbit transfers using candidate Lyapunov functions with a mechanism for coasting. AIAA/AAS Astrodynamics Specialist Conference, August. https://doi.org/10.2514/6.2004-5089
[3] Petropoulos, A. E. (2005). Refinements to the Q-law for low-thrust orbit transfers. Advances in the Astronautical Sciences, 120(I), 963–982.
[4] Shannon, J. L., Ozimek, M. T., Atchison, J. A., & Hartzell, C. M. (2020). Q-law aided direct trajectory optimization of many-revolution low-thrust transfers. Journal of Spacecraft and Rockets, 57(4), 672–682. https://doi.org/10.2514/1.A34586
[5] Leomanni, M., Bianchini, G., Garulli, A., Quartullo, R., & Scortecci, F. (2021). Optimal Low-Thrust Orbit Transfers Made Easy: A Direct Approach. Journal of Spacecraft and Rockets, 1–11. https://doi.org/10.2514/1.a34949
[6] [Modified Equinoctial Elements (careful with typos in this document!)](https://spsweb.fltops.jpl.nasa.gov/portaldataops/mpg/MPG_Docs/Source%20Docs/EquinoctalElements-modified.pdf)
[7] Hatten, N. (2012). A Critical Evaluation of Modern Low-Thrust, Feedback-Driven Spacecraft Control Laws.
Contents:
Basic Examples:
Advanced Examples: