Research On Optimal Orbit Control Of Spacecraft With Specific Thrust Direction

Orbit control design is the basis for a spacecraft to implement the task.In orbit control design,the thrusts in three orthogonal directions are usually provided by multiple thrusters or one thruster by making attitude adjustment to achieve an arbitrary direction.In some special conditions,e.g.,the solar sail,electric sail and magnetic sail,it can be simplified into a radial thrust,when an observation spacecraft keep execute the mission in the phase of orbital transfer it can be considered without the radial thruster,under these circumstances the thrust usually presents in a particular direction.Traditional orbit control methods seldom consider the constraints of the thruster's directions,so this dissertation focuses on the optimal orbital control of spacecraft with specific thrust direction.From the perspective of the relative motion and the absolute motion,the fuel-optimal orbital control using only the radial thrust,the circumferential thrust or the circumferential combined with the normal thrust are studied.The main contributions are as follows.For the time-fixed fuel-optimal orbital maneuver problem with continuous radial thrust,the nonlinear relative motion equations with only radial acceleration are obtained by using the relative direction cosine matrix to transform the chaser's radial thrust to the target's LVLH frame.The circumferential velocity is not controllable by using the weakly controllable method to analyze the controllability of this underactuated nonlinear system.The problem is simplified into a two-dimensional optimal control problem with integral and terminal constraints.A two order generating function with one order term and a constant term is proposed on the basis of the canonical transformation theory and the Hamilton-Jacobi theory,and the differential equations associated with the generating functioninitial and their initial conditions are derived.The proposed optimal control method only requires solving an initial-value ordinary differential equation problem.Two numerical examples of deep space missions are presented to illustrate the effectiveness of the proposed method,and the error of optimal index for is small when compared with the pseudospectral method.For the time-fixed fuel-optimal spacecraft rendezvous and formation reconfiguration problems with continuous circumferential and normal thrust,the nonlinear relative motion equations including the J2 perturbation are derived in the form of state-dependent coefficient.For the rendezvous problem,the optimal feedback control law is obtained by using the SDRE method,and an approximate analytical solution and a numerical solution of the state dependent Riccati differential equation are provided.Moreover,for the formation reconfiguration problem,the optimal feedback control law is adopted for a numerical solution by expanded the SDRE method Based on HJB equation.Compared with the Gauss pseudospectral method,the proposed method does not need an initial guess value.Numerical results show that the analytical solution of Riccati differential equation method has high precision for near circle orbits,and the error of optimal index for numerical method is small even though the eccentricity is 0.3.For the fuel-optimal orbital rendezvous using on-off circumferential thrust,the dynamic equations are established by using polar coordinate system.The two-point boundary value problem and its boundary conditions for both time-fixed final states-fixed and time-constrained final states-constrained cases are derived by using Pontryagin's minimum principle.The variable-step integration combined with the switching detection technique,and analytic Jacobian of the shooting function are used to improve the convergence of the shooting method.Finally,the homotopy method is used to solve the problem from the energy-optimal problem to fuel-optimal problem.The simulation results illustrate the effectiveness of the proposed method for the multiple-revolution “Bang-Bang”control and its robustness to initial value.For the fuel-optimal orbital rendezvous without the radial thrust,the circumferential and normal thrusts are considered as independent and on-off as-1,0,+1,and the dynamic equations are established by using spherical coordinate system.Two steps are introduced to solve the optimal control problem.The first step considers the constant mass and uses the homotopy method to slove the problem from the energy-optimal problem to the fuel-optimal problem.The other step considers variable mass and uses the homotopy method to slove the fuel-optimal control problem.The optimal control strategies in the two steps are derived by using Pontryagin's minimum principle.In order to improve the convergence of the shooting method,the solutions of ODEs combine with variablestep integration with the switching detection technique are proposed,and the analytic Jacobian of the shooting function is also derived.The simulation results show that the proposed method is effective for the multiple-revolution nonplanar orbital transfer and are convergent for zeros initial values.