Development of state dependent factorized optimal control methods with application to spacecraft coulomb formations

Gomroki, Mohammad Mehdi
Among spacecraft formation control techniques, Coulomb tether to control the relative distance is proposed in the literature. A Coulomb tether is similar to physical tether that uses coulomb forces to keep spacecraft at close proximity. It is indicated that a coulomb tether provides an almost a propellantless formation control. The charges loaded to the bodies, can create attractive and repulsive forces between these bodies. Since the forces are relative, coulomb forces cannot change the total linear or angular momentum of the formation. In this thesis, state dependent factorized optimal control methods are applied to control the formation attitude and relative position of the spacecraft Coulomb formation at Earth-moon libration points, Earth circular orbits, and deep space utilizing coulomb forces as well as thrusters. Nonlinear equations of motion of a two-craft Coulomb formation are properly manipulated to obtain a suitable State Dependent Coefficient (SDC) formulation for orbit radial, along-track, and orbit-normal configurations at Earth-Moon libration points, and Earth circular orbits. Moreover, the nonlinear equations of motion and their SDC factorized form of a three-craft Coulomb formation at deep space are discussed. Nonlinear feedback control of radially aligned spacecraft Coulomb formation through numerical simulations are presented in the current work. Moreover, the vi nonlinear optimal control is realized using the Approximating Sequence of Riccati Equations (ASRE) and State Dependent Coefficient Direct (SDC-Direct) methods. The SDC-Direct method is an approached developed and implemented in the current thesis. The present work introduces the SDC-Direct method to solve constrained nonlinear optimal control problems using state dependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as Approximating Sequence of Riccati Equations is used to replace the nonlinear problem by a sequence of linear-quadratic and time-varying approximating problems. The state variables are approximated and expanded in Chebyshev polynomials. Then, the control variables are written as a function of state variables and their derivatives. The constrained nonlinear optimal control problem is then converted to a quadratic programming problem, and a constrained optimization problem is solved. Different final state conditions (unspecified, partly specified, and fully specified) are handled, and the effectiveness of the approaches in reconfiguring the formation and comparison of them is demonstrated through numerical simulations.
Citation Formats
M. M. Gomroki, “Development of state dependent factorized optimal control methods with application to spacecraft coulomb formations,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.