Energy-optimal low-thrust satellite formation manoeuvre in presence of J₂ perturbation

Abstract

This article proposes a method to determine energy-optimal low-thrust trajectories for satellite formation manoeuvre in the presence of the J2 effect. This manoeuvre is cast as a non-linear optimization problem with a desired final satellite formation configuration subjecting to collision avoidance constraint. With this proposed approach, the deputy satellite is manoeuvred into a quasi-periodic desired final formation with respect to the chief satellite in the presence of the J2 effect. Resulting non-linear optimal control problem is converted into non-linear programming (NLP) problem by a direct transcription method called Legendre pseudospectral method. The NLP problem is then solved using a sparse non-linear optimization algorithm. Simulation results validate the proposed optimal trajectory design for formation manoeuvres in the presence of the J2 effect.

Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

“…1 otherwise (15) The term N ⋅ ∈ N denotes the number of finite-time maneuvers along the axis (⋅) within the interval u 0 ; u T , whereas u j c⋅;0 and u j c⋅;f indicate the mean argument of latitude of the chief orbit at the beginning and the end of the jth maneuver, respectively, or alternately the initial and final instant of time of the jth maneuver according to the relationship reported in Eq. (10). By assuming that the relative motion is well described by the linear model [Eqs.…”

“…The reconfiguration problem was posed as a multiplephase nonlinear optimal control problem and is solved via direct transcription using the Gauss pseudospectral method. Wu et al [10] presented a method to determine the fuel-optimal low-thrust trajectories for satellite formation maneuvers in presence of J 2 effect. The resulting nonlinear optimal control problem is converted into nonlinear programming (NLP) problem by the Legendre pseudospectral method.…”

Smooth time-optimal attitude control of spacecraft

“…The smooth approximate time-optimal attitude maneuver problem is then numerically solved by pseudospectral method, which has shown tremendous promise and has been applied to a wide variety of optimal control applications. [2][3][4][5][9][10][11][12][20][21][22][23] In order to attain robust performance, a closed-loop tracking control law is applied to track the optimized reference attitude trajectory.…”

Collision prediction and avoidance for satellite ultra-close relative motion with zonotope-based reachable sets

“…Another hot topic for proximity operations is collision-avoidance maneuver. For this problem, various guidance and path planning technologies have been investigated in literature, such as artificial potential functions, [5][6][7] pseudo-spectral methods, [8][9][10] samplingbased methods, 11,12 heuristic algorithms, 13,14 mixedinteger linear programming, 15 model predictive control (MPC), [16][17][18][19][20] and PDF methods. [21][22][23] Some methods 8,18,19,[21][22][23] have involved the effects of uncertainties.…”