Abstract: Based on reproducing kernel theory,the dynamic control method of coordinated operation for a team of free-flying space robots(FFSRs) in micro-gravity environment of space is presented.Expected trajectory of the target controlled by multi-FFSR is sampled,and the dynamic control of multi-FFSR coordinated operation is realized using dynamic equation of multi-FFSR coordinated operation based on the reproducing kernel theory.Comparing with other methods,the proposed method does not use motion equation to describe the moving trajectory and can control the target to move along an arbitrary and nonlinear curve according to the requirements,so the moving trajectory of the target has no limitations.This method has more advantages than polynomial interpolation and spline interpolation.When a node is increased each time,the approximate error decreases monotonically in the meaning of Sobolev norm.For the node system with intensive density in arbitrary form,the iterative process is uniformly convergent.Its formula is unitary and it can be calculated easily with computer.Simulation results show its effectiveness.