In this paper, we present an approach to local coverage path (CP) planning for a circular mobile sensor. Our family of algorithms provides completed and overlapped coverage control, curvature and path length control, localization, choice of observer’s placement based on sensing range, and first-order differentiable CP. Our family of algorithms begins by partitioning the target region (TR) into several regular triangulations (RTs). Based on the size of the RT and the sensing range, the number and location of observers are determined for all RT. All observers found are then used as waypoints (WPs) to generate baseline CP with the Traveling Salesman Problem’s nearest neighbor algorithm. The proposed algorithm solved the problems of how to design a differentiable and collision-free CP for all sensing range, limited and sufficient, while providing completed coverage control, overlapped coverage control, curvature and path length control, localization, collision avoidance, and the choice of observer’s placement based on sensing range and the environment. The main technical contributions of the proposed approach is to provide a holistic solution that segments any TR, uses triangulation to determine the observation WPs and then compute the smooth and collision-free CP. Computer simulations are provided to validate the effectiveness and correctness of our algorithms.