Autonomous landing is a vital option for Unmanned Aerial vehicles (UAV), as it can be a fail-safe in many critical cases. This paper demonstrates a complete solution for the soft landing application of a fully autonomous quadrotor on a moving pad considering external disturbance, model uncertainties, and actuators noise. The challenge starts with detecting the specially designed landing pad by an onboard vision system, a robust Algorithm estimates its coordinates precisely using a camera pose estimation. An enhanced Kalman filter by Madgwick data fusion of asynchronous sensors was developed for the best relative pose and heading reference. Different sizes and designs of the ArUco markers were attentively chosen to ensure the best detection at different altitudes and angles of approach. The landing trajectory is dynamically generated based on Jerk optimization, integrating a bio-inspired velocity profile by Fuzzy Logic Controller (FLC) to smoothen the landing. Model Predictive Control (MPC) was opted for quadrotor control to track the generated trajectory in time reference with the rejection of disturbance. The solution presents a soft mechanism for flat surface landing similar to human decision concept and control. The proposed method ensures absorption of the shock of impact, and the optimal tracking of the moving landing pad at less than 4 cm of error in Cartesian coordinates. Experimental results from pad relative pose estimation developed in Python, Data fusion experimentation of Attitude and Heading Reference system (AHRS), and Matlab simulations with a performance comparison between MPC and Proportional Integral Derivative (PID) control validate the effectiveness and reliability of the proposed landing task solution.