Dynamic Movement Primitive (DMP) which is popular for motion planning of a robot manipulator, has been adapted for a nonholonomic mobile robot to track the desired trajectory. DMP is a simple damped spring model with a forcing function, which learns the trajectory. The damped spring model attracts the robot towards the goal position, and the forcing function forces the robot to follow the given trajectory. Two Radial Basis Function Networks (RBFNs) have been used to learn the forcing function associated with the DMP model. Weight update laws are derived using the gradient descent approach to train the RBFNs. Fuzzy logic based steering angle dynamics is proposed to handle the asymmetric nature of an obstacle. The proposed scheme is capable enough to generate a smooth trajectory in the presence of an obstacle even when start and goal positions are altered, without losing the spatial information embedded while training. The convergence of the robot goal position has been shown using Lyapunov stability theory-based analysis. The approach has been extended to multiple static and dynamic obstacles for the successful convergence of the robot at the goal position. Both simulation and experimental results are provided to confirm the efficacy of the proposed scheme.