This work presents an Artificial Potential Function (APF) developed for the navigation and control of a redundant and nonholonomic mobile manipulator in cluttered 3D spaces. The novelty is to achieve convergent navigation without encountering local minima, a common issue with conventional APFs. This is achieved through a combination of optimal grid-based search to create a discrete APF and subsequent trilinear interpolation for smoothing, which ensures both effective path finding and computational efficiency. The APF navigates the mobile manipulator under a task prioritization scheme, addressing safety and task efficiency by treating the navigation of the mobile base and manipulator arm as primary and secondary tasks, respectively. Implementation details and simulation results show that the method enables safe, efficient and convergent navigation in complex environments.