This paper addresses the problem of deriving attitude estimation and trajectory tracking strategies for unmanned aerial vehicles (UAVs) using exclusively on-board sensors. The perception of the vehicle position and attitude relative to a structure is achieved by robustly comparing a known pier geometry or map with the data provided by a LiDAR sensor, solving an optimization problem and also robustly identifying outliers. Building on this information, several methods are discussed for obtaining the attitude of the vehicle with respect to the structure, including a nonlinear observer to estimate the vehicle attitude on SO(3). A simple nonlinear control strategy is also designed with the objective of providing an accurate trajectory tracking control relative to the structure, and experimental results are provided for the performance evaluation of the proposed algorithms.