The Application Research Of Indirect Method In Multi-specific Directions Thrust Fuel-Optimal Cooperative Rendezvous

Spacecraft orbit maneuver is an important prerequisite for various space missions,so the optimal design of orbit plays a decisive role in the process of space operation.Orbital maneuvers in previous space operations were mainly accomplished under impulse thrust.In recent decades,continuous thrust has attracted more attention because of its strong maneuverability and short time in orbit operation.The initial research on continuous thrust is vector thrust,that is,the thrust model of the spacecraft is mainly continuous variable direction thrust.For fast rendezvous,vector thrust is difficult to accurately control.The multi-specific thrust model studied in this paper is to independently set thrusters in three directions:radial,circumferential and normal.Each thruster has two directions:forward thrust and backward thrust.For different space maneuvering tasks,multiple thrusters finally complete the task through cooperative maneuvering.The fuel optimization problem for unspecified orbital rendezvous of spacecraft is studied in this paper,based on the thrust model of multiple specific directions.For such optimal control problems,the common optimization methods include direct method,indirect method and hybrid method.For the direct method and hybrid method,the optimal control problem is essentially transformed into a parametric optimization problem by discretizing the control variables,and for the multi-specific thrust model,optimize parameters increase sharply compared with the continuous thrust model,and the difficulty of optimization calculation increases sharply,especially for space maneuvering missions under the action of small thrust,spacecraft thrusters need to be switched on and off frequently,and the increase of push and slip sections further increases the difficulty of such discrete optimization methods.Therefore,the indirect method is applied to the optimal orbit control under multi-specific thrust directions in this paper.Based on the Pontriagin extremum principle,the indirect method introduces the costate variable and establishes the Hamiltonian function,thus obtaining the optimal control function equation,because the switching control function and the direction control function are controlled by the corresponding constraint equation,unlike the hybrid method,which requires additional setting of spacecraft engine switching sequence,there are relatively few parameters to be optimized in the optimization process,so it is possible to calculate the difficult space maneuver problem with small thrust.However,the indirect method is faced with many difficulties in solving the optimal fuel rendezvous problem under multi-specific thrust directions.In this paper,a series of improved methods are adopted to improve the feasibility of the indirect method in optimization calculation,and a series of simulation examples are used to verify the advantages of the indirect method over the hybrid method.Because of discontinuous switching control rate in fuel optimization problem,the differential equation of costate variable cannot be smoothly integrated.To solve this problem,homotopy technique is introduced in this paper,as it is a multi-specific thrust model,the optimal control rates of radial,circumferential and normal directions are independent respectively,and the control parameters of linear decline are introduced respectively.Through the common constraints of switching function and control parameters,the judgment of the spacecraft engine switching in a specific direction at each moment is finally obtained,from the energy optimal control problem which is relatively easy to solve,in the form of a linear gradient smooth transition to the fuel optimal problem.Second,due to the lack of corresponding physical meaning of state variables and unknown initial value range,the indirect method is very sensitive to the initial value setting of the covariant variables,and the accuracy of the initial value directly affects the final optimization result.In this paper,the covariant is normalized and its value is limited to a multidimensional sphere,thus improving the efficiency of optimization calculation.Since the research content of this paper is based on the collaborative rendezvous mission of two spacecraft,the final orbit is non-specified orbit,and the rendezvous time is unknown,so the optimization process is difficult,in order to solve this problem,this paper uses the global convergence of the quantum particle swarm intelligence optimization algorithm(QPSO)for energy optimal problem of depending on a parameter optimization,then using the homotopy technology transition to the fuel optimal problem,used in the process of the stronger local search ability but the iterative initial value sensitive series quadratic programming(SQP)algorithm.In this paper,the optimal fuel control theory of the indirect method for spacecraft rendezvous under multi-specific thrust is derived,and a series of simulation and optimization examples are given according to the theory.The simulation results show that the indirect method is slightly better than the mixed method for the relatively simple coplanar collaborative rendezvous problem.Aiming at the complex problem of different surface meeting,under the premise of the same initial condition,three groups of different thrust conditions were set for optimization calculation,the results show that the indirect method can save more fuel than the hybrid method under the condition of roughly the same maneuverability time,which indicates that it is feasible to apply the homotopy technique to the switching function of Pontriagin’s extreme principle for multi-specific thrust directions.At the same time,it can be seen that the advantage of indirect method is not obvious under large thrust.This is because whether the indirect method is used or the mixed method is used,the final push slip section will not exceed the set push slip section of the mixed person,and with the thrust gradually decreases,and hybrid method with full advance slide configuration,increase in the number of parameters among its optimization,optimization difficulty increases,the optimization results obviously than the indirect method;When the thrust is gradually reduced,the preset control strategy of the hybrid method gradually fails to satisfy the optimal control and even fails to obtain the optimal results,and because the indirect method does not need to configure the spacecraft switching strategy in advance,it is not limited to various factors such as the size of the spacecraft thrust and the complexity of rendezvous mission,and the number of optimization parameters is far less than that of the hybrid method,so it is less difficult to calculate.Meanwhile,the indirect method theoretically guarantees the first-order optimality of the optimal solution obtained.