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A planning methodology for nonholonomic mobile manipulators that employs smooth and continuous functions such as polynomials is developed. The method decouples kinematically the manipulator from the platform by constructing admissible paths that drive it to a final configuration and is based on mapping the nonholonomic constraint to a space where it can be trivially satisfied. In addition, the method allows for direct control over the platform orientation. The developed transformation also maps Cartesian space obstacles to transformed ones and allows for obstacle avoidance by increasing the order of the polynomials that are used in planning trajectories. The additional parameters required are computed systematically. It is shown how the method can be extended for avoiding obstacles of any number.