With the increase of worldwide space mission, space technology has become a research hotspot and it has beening developing rapidly in recent years.For the general spacecraft trajectory optimization problem, it is a priority to reduce fuel consumption,which is relevant to economic cost of the mission.However, for certain emergencies, it is necessary to complete a specific space task in a relatively short period of time.In this paper, the main content of the study is to gain the optimal trajectory of rapid rendezvous between two or more spacecraft in a determined orbit under finite continuous thrust.The problem of spacecraft trajectory optimization under finite continuous thrust has the characteristics of strong nonlinearity, strong constraint conditions and multi-peak value.So, it is difficult to solve this kind of optimization problem.For the problem of active and passive rendezvous, due to the less spacecraft parameters, using direct collocation method or indirect method can be relatively easy to get good optimization results.However, for the problem of rapid rendezvous between two or more spacecraft,due to the increase of the number of parameters needed to be optimized, especially for non-planar rendezvous problems, extra parameters need to be introduced to represent the time of burn arcs and coast arcs, it is the difficult to obtain the ideal optimization results by using direct method.Due to the particularity of the rendezvous task, the spacecraft need to complete rendezvous task in the determined orbit and the rendezvous point can be any point on the orbit, using orbital elements coordinate system can better depict the constraint conditions than using cartesian coordinate system.For rendezvous between two or more spacecraft, orbital elements coordinate system is used in this paper, and the switching function under orbital elements coordinate system is obtained by using Pontryagin maximum principle and variational principle.In addition, owing to the characteristics of strong nonlinearity, strong constraint conditions and multi-peak value, it is difficult to obtain the ideal optimization result by using the traditional optimization algorithm when dealing with this problem.Therefore,artificial intelligence optimization method is used to search for the initial value, and then the value is used as an initial value in the traditional optimization algorithm, thus the sensibility of traditional optimization algorithm to the initial value can be overcomed.In the part of the artificial intelligence optimization, penalty function method is used to deal with the constraint of the problem.The accuracy of solution obtained by artificial intelligence optimization method is not enough, but it is sufficient used as the initial value of the subsequent optimization.The advantages and disadvantages of indirect method and collocation method are compared and analyzed by comparing the simulation results of several examples,which contain planar and non-planar rendezvous between two or multiple spacecraft.It is found that the simulation results obtained when the two spacecraft semi-cooperative rendezvous are ideal, the total fuel consumption in the task is almost equal to the sum of the fuel consumption when each of the spacecraft transfer to the determined orbit.In the multiple spacecraft semi-cooperative rendezvous task, the fuel consuption of some spacecraft in the rendezvous task may be more than the fuel consuption when the spacecraft transfer to the determined orbit.This is because the spacecraft need to burn in some inappropriate position.It is found that the radial thrust of every spacecraft is much smaller than the tangential thrust and the normal thrust of the spacecraft when solving non-planar rendezvous problems, which deserve attention for the follow-up research.