It is imperative to find new places other than Earth for the survival of human beings. Mars could be the alternative to Earth in the future for us to live. In this context, many missions have been performed to examine the planet Mars. For such missions, planetary precision landing is a major challenge for the precise landing on Mars. Mars landing consists of different phases (hypersonic entry, parachute descent, terminal descent comprising gravity turn, and powered descent). However, the focus of this work is the powered descent phase of landing. Firstly, the main objective of this study is to minimize the landing error during the powered descend landing phase. The second objective involves constrained optimization in a predictive control framework for landing at non-cooperative sites. Different control algorithms like PID and LQR have been developed for the stated problem; however, the predictive control algorithm with constraint handling’s ability has not been explored much. This research discusses the Model Predictive Control algorithm for the powered descent phase of landing. Model Predictive Control (MPC) considers input/output constraints in the calculation of the control law and thus it is very useful for the stated problem as shown in the results. The main novelty of this work is the implementation of Explicit MPC, which gives comparatively less computational time than MPC. A comparison is done among MPC variants in terms of feasibility, constraints handling, and computational time. Moreover, other conventional control algorithms like PID and LQR are compared with the proposed predictive algorithm. These control algorithms are implemented on quadrotor UAV (which emulates the dynamics of a planetary lander) to verify the feasibility through simulations in MATLAB.