Multi-robot systems have begun to permeate into a variety of different fields, but collision-free navigation in a decentralized manner is still an arduous task. Typically, the navigation of high speed multi-robot systems demands replanning of trajectories to avoid collisions with one another. This paper presents an online replanning algorithm for trajectory optimization in labeled multi-robot scenarios. With reliable communication of states among robots, each robot predicts a smooth continuous-time trajectory for every other remaining robots. Based on the knowledge of these predicted trajectories, each robot then plans a collision-free trajectory for itself. The collision-free trajectory optimization problem is cast as a non linear program (NLP) by exploiting polynomial based trajectory generation. The algorithm was tested in simulations on Gazebo with aerial robots.