This work pertains to the generation of navigation functions for obstacle avoidance and target tracking. One initially defines a so-called spherical world which can be further mapped into many other different topologies using a series of diffeomorphic transformations. This specific configuration further allows one to exploit the main advantages of the sum function approach with respect to the obstacle collision avoidance capabilities of an agent, sum function which is used in order to induce an effective navigation function judging not only from computational perspective, but also from the local minima point of view.