In order to meet the requirements of the space environment for the lightweight and load capacity of the manipulator, this paper designs a lightweight space manipulator with a weight of 9.23 kg and a load of 2 kg. It adopts the EtherCAT communication protocol and has the characteristics of high load-to-weight ratio. In order to achieve constant force tracking under the condition of unknown environmental parameters, an integral adaptive admittance control method is proposed. The control law is expressed as a third-order linear system equation, the operating environment is equivalent to a spring model, and the control error transfer function is derived. The control performance under the step response is further analyzed. The simulation results show that the proposed integral adaptive admittance control method has better performance than the traditional method. It has no steady-state error, overcomes the problems caused by nonlinear discrete compensation, and can facilitate analysis in the frequency domain, realize parameter optimization, and improve calculation accuracy.