Trajectory Optimization And Control For Far-distance Rapid Cooperative Rendezvous Problem Under Multiple Specific-direction Thrust

This paper aims to solve the trajectory optimization and control problem for fardistance rapid cooperative rendezvous of spacecraft with different optimization objectives.The modified equinoctial elements are used to describe the motion of spacecraft,and the orbital dynamics for spacecraft in the geocentric equatorial coordinate system is established.Later the Hamilton equations for spacecraft are conducted based on the Pontryagin extreme principle,and the optimal control theory for spacecraft under direction-variable continuous thrust and multiple specific-direction thrust are obtained.This paper focuses on the far-distance rapid cooperative rendezvous problem,and aims to achieve the rendezvous task with minimum fuel consumption and dust impacts.It can also realize the fuel sharing between two spacecraft.In the aspect of optimization method,the direct method with the gliding angle and impulse velocity increment to be optimized is used for the multiple specific-direction impulsive thrust model.The indirect method based on switch function is used for multiple specific-direction and variable-direction continuous thrust models,focusing on solving two difficult problems.The first one is the control of thrust amplitude.To solve the integration discontinuity caused by bang-bang control,the homotopy method is used to smooth the problem,that is,starting from solving the relatively simple energy optimization problem to the relatively difficult fuel optimization problem,by changing the homotopy factor.The second problem is the control of thrust direction.In the multiple specific-direction thrust model,the thrust direction always along the radial,circumferential and normal direction of spacecraft.Only two possibilities,positive or negative,need to be judged for the thrust direction.In this paper,we use one integrated variable to control both the thrust amplitude and the thrust direction.The Pontryagin extreme principle is used to judge the value of the control variable.It reduces the number of parameters to be optimized,and solves the problem of doubling the variable number brought by direct methods or other combined methods.In terms of intelligent algorithm,the Quantum-behaved Particle Swarm Optimization(QPSO)algorithm with strong global search ability is used in this paper for the preliminary optimization.Later the Sequential Quadratic Programming(SQP)with strong local search ability is used to modify the optimization results obtained by QPSO,and the final results are obtained.Through the QPSO-SQP combined algorithm with better performance,we can solve complex nonlinear optimal problems,specifically the far-distance rapid cooperative rendezvous problem under multiple specific-direction thrust model,with final rendezvous position and rendezvous time not given.The reasonable and stable results can be obtained,which are difficult to obtain by any other single optimization algorithms.The fuel consumption is taken as a single objective,and one coplanar rendezvous problem and one non-coplanar rendezvous problem are simulated under the multiple specific-direction impulse thrust and the multiple specific-direction continuous thrust,respectively.The optimization results prove the time advantage of cooperative rendezvous mode in solving the far-distance rapid rendezvous of two spacecraft,and also show the advantages of the multiple specific-direction thrust model.Firstly,it can realize the independence of thrust control in each direction,which is suitable for the trajectory optimization of space rendezvous problems that can be completed only with specific-direction thrust.Secondly,it can simplify the dynamical equations and control equations,avoid the emergence of inefficient-direction thrust according to the initial orbit situation,and make the thrust in each direction appear at relatively reasonable position.The circumferential thrust appears near the perigee and apogee of the orbit,and the normal thrust appears near the intersection of the orbital planes of two spacecraft.Besides,the thrusts of two spacecraft are mostly cooperative,i.e.,push in opposite directions during the same time period,theoretically meeting the requirement of minimum fuel consumption of the spacecraft.Finally,through the comparison of optimization results under different thrust model,we find that although the optimal fuel consumption under the multiple specific-direction thrust model increases slightly(<15%),its great significance is the achievability and operability of the thrust model for the rapid cooperative rendezvous problem.On the basis of the content above,the concept of space dust is introduced.Taking the lunar dust,one of the main components of the dust in the Earth-Moon system,as the research object,considering the solar,Earth and lunar gravity,and solar radiation pressure,the dynamic model of ejected dust on the lunar surface is constructed,and the motions of 216,000 dust particles in different initial conditions are simulated for 100 Earth years.The dust number density in Earth-Moon system space is obtained,that is,as long as the position of spacecraft in the Earth-Moon system is determined,the absolute value of dust number density at this position can be obtained.The optimal trajectories for previous examples are discretized to a series of trajectory points.Each trajectory point is placed in the dust number density grid in the Earth-Moon system,to calculate the number of dust particles that spacecraft may collide with.Based on singlefuel-objective optimization problem mentioned above,the number of dust particle that spacecraft may collide with is introduced,and a dual-objective optimization model with the minimum fuel consumption and the minimum number of collision dust is constructed.Through multiple calculations and weighted average processing,the average optimal fuel consumption and the average optimal collision dust amount with different weight factors are explored.The optimization results show a negative correlation between the average optimal fuel consumption and the weight factor,and a positive correlation between the average optimal collision dust amount and the weight factor,which consistent with the assumption of the dual-objective optimization model.From the optimal results of fuel consumption with different weight factors,it can be seen that the weighted method used in this paper can effectively reduce the amount of collision dust while the fuel consumptions are roughly the same.