An explicit terminal acceleration constrained guidance scheme is derived using calculus of variation approach for the lunar landing mission. The proposed guidance scheme not only optimally guide the lander from any initial position and velocity to safe identified site but also ensure required condition for soft vertical landing. To account for various constraints in different segments of the landing sequence, the trajectory is split into braking with rough navigation phase (from 18 km to 8 km), attitude hold phase (holding the attitude for 35 s), braking with precise navigation phase (from end of attitude hold phase to 100 m altitude) and vertical descent phase (from end of braking with precise navigation phase till touchdown). At the end of the mission, the terminal accuracy in position, velocity and attitude is given high importance. Due to unknown initial condition perturbation at braking with rough navigation phase results in error ellipsoid (by Monte-Carlo simulation) at the start of the braking with precise navigation phase. From absolute sensor feedback, knowledge of error in position and velocity is known to take corrective actions using the proposed guidance scheme. Simulation results show that for all cases the trajectory satisfies the demanded terminal acceleration ensuring precise vertical landing on the moon.
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