In this paper, we propose a new scheme to find a free-collision path for complex environment maps. This scheme considers the obstacles in the configuration space as prohibited circular areas. Once the obstacles are modelled, the Non-Linear Algebraic Equation System (NAES) is formulated. Next, we apply a Homotopy Path Planning Method (HPPM) to find a set of points that conforms the solution path on the free-space. HPPM uses the Homotopy Continuation Method (HCM) and the Spherical Algorithm (SA) to obtain the solutions of the NAES emanating from the map. In the present work, we propose a scheme for partitioning complex maps into a set of local maps. This is useful for reducing the computation time. Several simulations of complex environment maps with thousands of obstacles are presented. Furthermore, a strategy to obtain the shortest path is applied. Finally, a simulation of the path tracking on Robot Operating System (ROS) for a differential mobile robot is shown.