The use of multiple mobile manipulators (MMs) to perform collaborative object transportation is a promising solution for future industry. However, most existing control laws in this field require sensors to measure interactive force-torque between the transported object and the end-effectors of the robots, which is costly and increasing the system complexity. To overcome this problem, the present study considers the interactive force/torque to be unknown nonlinear functions and estimates them using a wavelet neural network (WNN). In particular, an adaptive-wavelet neural network control law is designed to guarantee trajectory tracking for each robot. Then an output synchronization algorithm is additionally used to coordinate the movement of the network MMs. Stability of the proposed control law is proven theoretically using Lyapunov theorem. Furthermore, the effectiveness of the control law is illustrated by simulations.