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This paper considers the problem of steering and coordinating a group of omnidirectional mobile robots along given paths. Two subproblems, i.e., a path following subproblem and a motion coordination subproblem are solved by using distributed nonlinear model predictive control (NMPC) whose cost function is coupled with neighbors. The distinct features of NMPC are that constraints can be explicitly accommodated, as well as nonlinear and time-varying systems can be easily handled. An idea of morphing is employed to generate intermediate configurations between a source and a target configuration with a desired transition rate. Each mobile robot adjusts its own speed along its reference path to achieve motion coordination. Experiments with three omnidirectional mobile robots are presented to illustrate the validity of our proposed method. Unlike nonholonomic mobile robots, omnidirectional mobile robots have simultaneously and independently controlled rotational and translational motion capabilities.