A cooperative multi-manipulator system is a nonlinear, time-varying, strong coupling system with multiple inputs and outputs. Because of external disturbance, load change and other factors, a cooperative multi-manipulator system needs to address the problems of uncertain environment interaction, feasible control methods and coordinated planning. In this study, the coordinated motion of a multi-manipulator is divided into two types: coupling and superposition motions. An adaptive coordinated motion constraint scheme is proposed for the two different motion forms. The coupled and superposition motions were investigated by coordinating a carrying task and a circle drawing task, respectively, and the effectiveness of the adaptive coordinated motion scheme was verified. Based on the adaptive kinematics constraint algorithm of the multi-manipulator, co-simulation analysis of the multi-manipulator coordinated motion is conducted. Simulation results show that the multi-manipulator preserves the coordination relationship at all points of the trajectory planning path and has a good motion effect. Finally, an experimental platform for a cooperative multi-manipulator system was built to conduct experimental research on the coordinated motion of the multi-manipulator. Experimental results show that the proposed adaptive motion constraint control scheme for cooperative multi-manipulator systems has a good coordination effect, strong adaptivity and high-control precision.