Paper Title
Downrange Constrained Gravity Turn Guidance for Lunar & Mars Landing

Gravity Turn guidance during Lander descent ensures that the thrust vector is always opposite to the velocity vector. By formulation, a thrust to mass ratio can be solved for and applied in real time, which would ensure that Lander reaches the specified altitude with zero velocity. Lander will naturally be vertically oriented at the end. However, the downrange travelled is unconstrained and a free parameter. This paper proposes a scheme to modify the existing guidance law so as to ensure that the Lander travels required downrange. Philosophically, if the thrust angle is slightly modulated for some time from its anti-velocity angle, resultant downrange will be different. The modulation can be on both sides of the anti-velocity vector. Technically this idea is made use to augment the guidance law and get the desired downrange. During ground planning, a time span within the total gravity turn descent can be appropriately selected and the additional thrust angle can be fixed to get a particular downrange. This sensitivity study can be repeated for various downrange. The data set so created can be used to carry out a polynomial fit of downrange versus the thrust angle modulation. The fit can be implemented onboard and used in real flight for having a downrange constrained Gravity Turn descent. Simulation results for typical Mars powered descent and lunar terminal descent have proved the efficacy of method adopted. Keywords - Gravity Turn; Powered Descent; Guidance Law; Lander