This paper describes a recently proposed algorithm in mapping the unknown obstacle in a stationary environment where the obstacles are represented as curved in nature. The focus is to achieve a guaranteed performance of sensor-based navigation and mapping. The guaranteed performance is quantified by explicit bounds of the position estimate of an autonomous aerial vehicle using an extended Kalman filter to track the obstacle and extract its map. The Dubins path planning algorithm is used to provide a flyable and safe path to the vehicle to fly from one location to another. The 2-D Splinegon technique is presented for the mapping of the unknown complex obstacles. This Splinegon technique, which is the most efficient and a robust way to estimate the boundary of a curved-nature obstacles, can provide mathematically provable performance guarantees that are achievable in practice.