For the control of coordinated multiple mobile manipulators, a neural network-based fast terminal sliding mode control scheme is presented in this study. A modified sliding surface (manifold) is devised with the addition of two nonlinear factors in order to strengthen the response, fast convergence rate, and finite time stability. The newly designed fast terminal sliding mode manifold not only improves the rate of convergence more quickly, but also makes sure that tracking errors are stable in finite time. Additionally, the radial basis function neural network architecture is utilized for the estimation of nonlinear terms via online weight adaptation in order to further strengthen the proposed controller as a robust controller. The addition of an adaptive compensator to the controller reduces the impact of factors like friction force, external disturbance, and network reconstruction error. The system has absolute and finite time stability guaranteed by the Lyapunov function approach. Execution analysis has been symbolically resolved, demonstrating that all tracking errors related to motion and forces concurrently converge to zero, and tracking errors related to internal forces remain regulated and can be made arbitrarily small to some desirable values.