A new method of collision free motion path planning using Non uniform rational B- Spline curves for mobile robots is addressed in this paper. Obstacles of polygonal nature are used and the navigation occurs in a dynamic environment. Mathematical Modeling with vector addition technique is used to compute the set of points which will form the final path. NURBS technique is applied on the computed set of points which results in smooth curve as the final path, giving the advantage of more efficient motion. NURBS offsets of the computed NURBS path have been defined to avoid collision. Number of obstacles is not a constraint in the model presented. Number and position of obstacles can be changed dynamically which will be encountered by the robot and the path computed will be updated accordingly ensuring the shortest path.