The paper proposes a path planning algorithm for cluttered environment and maze. The proposed planning algorithm exploits the merit of convex optimization while forming the convex navigable free-spaces, ensuring safety of the vehicle. The contiguous convex free-spaces are iteratively computed from a random-walk based seed generation method to create a contiguous navigable geometry. Inside this contiguous navigable geometry an undirected graph is then created, whose each node and edge belong to at least one convex region which boils down the path planning problem into a graph search problem. In addition, the proposed multiple query planning algorithm can merge the user provided feasible initial and goal configuration with the existing undirected graph in each plan, without deteriorating the planning performance in terms of run-time and path length. Simulation and experimental results confirm the superiority of the proposed planning algorithm jointly in terms of both path length and run-time by a significant margin.