This paper addresses the fault tolerant control problem for an omni-directional mobile platform with four mecanum wheels moving on a well-known flat and constrained workspace with static obstacles. As a fault, we consider the case where a wheel cannot be actuated and hence it rotates freely around its drive shaft owing to the friction with the flat surface. Depending on the multitude of the faults, a robust motion control scheme is developed that achieves any desired configuration within the operational workspace, avoids collisions with the obstacles and does not violate the workspace boundaries despite the presence of dynamic model uncertainties. The challenge with respect to the current state of the art in fault tolerant control for such mobile platforms, where only one faulty wheel has been considered (i.e., the platform still retains its full actuation capabilities), lies in completely compensating up to two faulty wheels (i.e., the model becomes underactuated in this way) despite the dynamic model uncertainty and the presence of static obstacles in the workspace. Navigation Functions are innovatively incorporated with adaptive control techniques to deal with the parametric uncertainty in the robot dynamics, extending thus greatly the current state of the art in robust motion planning and collision avoidance by studying second order dynamics with parametric uncertainty. Finally, an extensive experimental study clarifies the proposed method and verifies its efficiency in various faults.