Discussion On Rapid Coordinated Rendezvous Of Spacecraft Of Different Masses Under Continuous Thrust

Spacecraft trajectory optimization is an important problem throughout the whole life cycle of spacecraft,and its research has important practical significance for prolonging the operational life of spacecraft in orbit and increasing the ability of mission execution.Optimized to get better performance indicators such as fuel or time running track,can achieve effective cost savings.In this paper,the spacecraft need to complete the rendezvous mission quickly as the research background.There are two rendezvous modes:active and passive rendezvous and collaborative rendezvous.In the existing space activities,when the space rendezvous mission is limited by time,although the spacecraft can complete the space mission through the active and passive rendezvous,the active and passive rendezvous will face two problems:one is whether the active spacecraft has enough optimization space within the specified time;The second is whether the spacecraft can carry enough fuel to support the entire rendezvous mission.Considering the above two problems,the cooperative rendezvous of two spacecraft will be studied in this paper.The research on spacecraft cooperation rendezvous has been limited to the spacecraft with the same mass(or close to each other).For spacecraft with different mass,it is more reasonable to maneuver with spacecraft with lighter mass under the goal of optimal fuel control.Therefore,earlier studies had concluded that the problem of co-rendezvous between spacecraft of different masses was "meaningless".In this paper,with the minimum fuel consumption as the optimal performance index,we study the different performance of two rendezvous modes when two spacecraft perform emergency space missions with different masses.The trajectory optimization method adopts the indirect method.By introducing the undetermined Lagrange multiplier vector function,The optimal control rate and two-point boundary value problem with constrained control variables are obtained by solving the minimum value of Hamiltonian function based on Pontryagin’s extreme value principle,and then the nonlinear equation is solved by numerical method.Although the theory of indirect method has been mature,many problems still need to be solved to solve the trajectory optimization problem of spacecraft cooperative rendezvous.Among them,the indirect method needs to solve the target function,but the target function requires very high accuracy of the initial value,so it needs to take a series of methods to increase the probability that the guess value falls in the convergence domain of the function.For the above problems,firstly,aiming at the problem that the covariant variable lacks physical significance and its range is unknowable,this paper uses the method of normalizing the covariant variable to limit it to a knowable range.Then,the QPSO algorithm and SQP algorithm are used in series,and the QPSO algorithm is used to search for optimization in a large range within the feasible interval,and the result is used as the initial value of SQP algorithm for local optimization.On the other hand,the solution obtained by the QPSO algorithm can provide a high-quality initial value for SQP algorithm,increase the convergence speed of the algorithm,and obtain a more accurate initial value of the target function.Finally,the initial value is taken as the initial value of the iteration,and a smoothing processing technology--homotopy technology is introduced to smooth the Bang-Bang control problem,so that the initial value of the energy optimal problem can be obtained,and the fuel optimal problem can be iterated gradually in the form of exponential decline.Thus,the optimal admissible control discontinuity problem can be solved.In this paper,coplanar and non-planar continuous thrust models are optimized and simulated respectively,corresponding to three kinds of time limit sets,namely no time limit(or long enough time limit),reasonable time limit and short time limit.The simulation results show that when the mass of two spacecraft is different,and the rendezvous time is not limited,the optimal rendezvous mode is mainly passive rendezvous.Within a reasonable time limit,the optimal control is to use collaborative rendezvous as a more reasonable scheme,and the fuel consumption is shared by two spacecraft.When an emergency space mission is needed,the rendezvous time is limited to a short period of time.Active and passive rendezvous usually cannot complete the rendezvous,but collaborative rendezvous can always complete the rendezvous task despite the increase of fuel consumption.The amount of fuel carried by the spacecraft is limited,so it is necessary to consider whether the light-weight spacecraft has enough fuel to support the completion of the rendezvous mission.This paper explores whether it is feasible to add intervention to the fuel that the spacecraft can consume.The simulation results show that fuel intervention can increase the total fuel consumption of light spacecraft,but it can effectively reduce the fuel consumption of light spacecraft,so that the fuel consumption of spacecraft is more reasonable than the fuel carrying capacity.