The primary problem for multi-robot displacement and motion phase solving requires that the robots prevent themselves from colliding with each other as well as stationary obstacles. In certain situations, robot conflict is unavoidable if one robot views its neighbors as immovable obstacles. Hence, this paper proposes a new NURBs (Non-Uniform Rational B-spline) based algorithm for multi-robot path planning in a crowded environment. First, the proposed technique finds each robot's free, smooth, optimal path while avoiding collision with the existing obstacles. Secondly, the prospect of possible collision between the preplanned trajectories will be computed to allow the robots to navigate in the same workspace and coordinate between them. Then, each robot's time to arrive at potential collision sites is computed based on its speed. As a result, the robots involved in the collision must choose whether to use the robot priority technique to prevent the collision. Simulation results under different scenarios and comparisons with previous works are provided to validate the work. The obtained results prove that the proposed approach is accurate (as the robot's instantaneous speed is taken into consideration), fast (as there is no need to broadcast the robots’ positions), the robots’ paths are optimal and smooth (to avoid jerk movements), and the approach ensures that the robots will not be trapped by local minima problem.