Optimal control of loose spacecraft formations near libration points with collision avoidance

Abstract

This paper investigates the optimal control of loose leader-following spacecraft formations near libration points. The formation reconfigurations and keepings can be applied at the same time for the loose formations. A loose sphere leader-following formation, i.e., the leader spacecraft moves along the reference Halo orbits while the motions of all follower spacecrafts are restricted to a sphere formation with its center located at the leader, is explored in this study carefully. Collision avoidances among follower spacecrafts are taken into consideration since there are no constraints between followers and then the formation for all followers is loose. A symplectic penalty iteration algorithm is proposed to obtain the optimal solutions with minimization of energy cost. An effective penalty function to avoid collision is developed, and a high efficiency and structure-preserving symplectic method is introduced in the iteration algorithm. Several optimal control problems including formation reconfigurations and formation keepings are solved to show the effectiveness of the proposed algorithm. Numerical results show that errors of formations can be reduced to millimeters or smaller only by few control input and the collision can be avoided successfully by the developed penalty function.

Relative dynamics of charged spacecraft in a magnetic field applied to formation flight

“…The collision avoidance requires more complicated control strategies than the one presented in the present paper; relative distances need to be monitored and more path constraints have to be considered. The control strategy including collision avoidance, as the one developed in [23], will be the focus of our future work.…”

“…Using the same nomenclature as in the computation of matrix A, we can obtain the coefficient vector B q from Eq. ( 16) and (23), which can be expressed in a general form,…”

An efficient intelligent decision method for bionic motion unmanned system

“…28–30 For stochastic nonlinear second-order multi-agent systems, the author in Wen et al 31 combines the leader–follower formation approach and the artificial potential field (APF) method to solve the obstacle avoidance problem. In Li et al, 32 an effective penalty function to avoid collision is developed, and several optimal control problems including formation reconfigurations and formation keepings are solved to show the effectiveness of the proposed algorithm. Besides, formation control laws like trajectory tracking and dual integrator systems based on position estimation were proposed and verified that they can effectively avoid collisions.…”

Charged-Spacecraft Formation: Concept, Deployment and Coulomb-Force Control

“…For Coulomb formation flying research, many static or dynamic configurations are usually proposed with respect to a circular reference orbit. Hogan and Schaub [16], [17] studied the equilibrium of Coulomb formation Equation in two cases of no gravitational forces and libration points of circular restricted three-body gravitational models [18], [19]. Schaub and [20] analyzed the stability of these equilibria and developed continuous feedback controllers to formation-keeping.…”