To solve the trajectory planning problem of dual-arm Free Floating Space Robot (FFSR) in space grasping task,a novel FFSR trajectory planning algorithm is designed,which can realize error convergence within predefined arbitrary time.Cuckoo Search（CS） algorithm is used for parameter optimization to realize fast error convergence of the end actuator and obtain a smooth trajectory.Firstly,the FFSR kinematics model based on attitude errors is derived.Then,the cumulative danger field collision avoidance algorithm is applied to the predefined arbitrary time trajectory planning to obtain a quick collision avoidance trajectory with high tracking accuracy.Finally,the CS algorithm is used to optimize the predefined arbitrary time parameters,and the manipulators'trajectory with low joint angular velocity is obtained.The simulation results show that the fast error convergence of the end actuator can be achieved within a predefined time,and a smoother trajectory can be obtained.