Stabilization of Spacecraft in Spatial Periodic Orbits using Linear Quadratic Regulator (LQR)

Pushparaj, Nishanth; Hayashi, Yuta; Bando, Mai

Abstract

Mission design for exploring minor celestial bodies and planetary satellites presents significant technical challenges, particularly in highly perturbed dynamical environments. The weak and complex gravitational fields of small bodies, along with perturbations caused by factors such as irregular shape, gravity field, solar radiation pressure, and gravitational attraction from nearby planets, can disrupt spacecraft trajectories and lead to collisions. This paper focuses on the Circular Restricted Three-Body Problem (CRTBP) and proposes linear quadratic regulators (LQR) to stabilize spacecraft in periodic orbits around planetary satellites, such as the Moon. Prograde and retrograde families of periodic orbits are computed numerically, and bifurcation analysis is performed to identify out-of-plane bifurcation points. The LQR theory is applied to stabilize periodic orbits by minimizing a quadratic cost function while stabilizing out-of-plane unstable prograde and retrograde orbits. The paper primarily discusses the LQR control application to spatial periodic orbit families and presents station-keeping results. The research provides insights into station-keeping of such periodic orbits, which are potential candidates for several missions like the Martian Moons eXploration mission and any small planetary satellite exploration missions. Results suggest that three-dimensional prograde and retrograde orbits can be maintained at less than 12 mm/s for two months.

Citation

Pushparaj, N., Hayashi, Y., & Bando, M. (2023, June). Stabilization of Spacecraft in Spatial Periodic Orbits using Linear Quadratic Regulator (LQR). Paper presented at 34th International Symposium on Space Technology and Science & 12th Nano-Satellite Symposium, Kurume, Fukuoka, Japan

• Presentation Conference Type: Conference Paper (unpublished)
• Conference Name: 34th International Symposium on Space Technology and Science & 12th Nano-Satellite Symposium
• Start Date: Jun 3, 2023
• End Date: Jun 9, 2023
• Deposit Date: Jun 6, 2023
• Keywords: CRTBP; Linear Quadratic Regulator; Bifurcations; QSOs; Low Prograde Orbits; Periodic Orbits
• Public URL: https://nottingham-repository.worktribe.com/output/21635055
• Related Public URLs: https://ists.ne.jp/