Fast Cooperative Trajectory Optimization for Close-Range Satellite Formation Using Bezier Shape-Based Method

Abstract

Close-range formation flying of multiple satellites is an important technology for future space missions, where formation reconfiguration is a very important field and needs to design suitable flight paths and consider the risk of collisions between satellites. This paper uses the Bezier shape-based (SB) method to rapidly generate the low-thrust collision-avoidance flight paths in the formation reconfiguration. The reconfiguration process of two satellite formations is considered and compared with the finite Fourier series (FFS) method. The simulation results show that the Bezier method spends less computation time to obtain better performance index than the FFS method. In order to verify the applicability of the results obtained by the Bezier method to a direct solver, the results are applied to the Gauss pseudospectral method (GPM) solver as an initial guess. The results show that the Bezier method can take a short time to design suitable initial collision-avoidance flight paths for an direct optimization solver. This is very important for the rapid feasibility evaluation of numerous flight scenarios at the stage of initial mission design and onboard flight paths generation. INDEX TERMS Bezier shape-based method, close-range satellites formation, collision-avoidance, low-thrust trajectory approximation, preliminary mission analysis.

Finite-Time Control Algorithm Based on Modal State Observer for Flexible Satellite Attitude Tracking

“…The proof consists of two parts: 1) The finite time stability when system converges along sliding mode (29); 2) The finite time stability that system could reach sliding mode (29) from any initial condition. In fact, the state observer could get the modal state and its derivative, hence the second derivative could be calculated by equation (1), and the variables in (31) are all claimed.…”

“…Shen [25][26][27] designed state observer for satellite attitude control and his work mainly focused on the structure of state observer under information missing. Some work [28][29][30][31][32] focused on the issue that finite time control under model uncertainty and flexible deformations. Researchers proposed [33][34][35] some state observers to estimate the model uncertainty and disturbance torques for satellite attitude control.…”

Fast cooperative obstacle-avoidance path planning for multiple space manipulators

“…During the motion of the space manipulator, each link is described by three Euler angles. Therefore, to simplify the description, only ϕ i of the i -th link is approximately expanded using the Bezier SB method 33,34 ; the other Euler angles use the same expansion methodwhere τ = t / T (0 ≤ τ ≤ 1) is the dimensionless time, T is the total motion time of the space manipulator, nϕi is the order of the Bezier SB method, Pϕi,k are the unknown coefficients, Bϕi,k is the basis function of the Bezier SB method, and the superscript “′” denotes the derivative with respect to τ …”

“…26–29 The results obtained by the SB method can be used as the initial solution for the direct optimization algorithm. For the generation of a three-dimensional motion path, the FFS SB method 30–32 and the Bezier SB method 33,34 are effective in constraining the maximum thrust acceleration without introducing additional parameters. 35…”

Fast cooperative angular trajectory planning for multiple on-orbit service spacecraft based on the Bezier shape-based method

“…After that, several researchers proposed some other SB methods based on various function shapes. [18][19][20][21][22] In recent years, the FFS SB method [23][24][25][26][27][28][29] and the Bezier SB method [30][31][32] have been put forward. These two methods are very suitable for generating continuous three-dimensional transfer trajectories.…”