Closed Loop Guidance Algorithm for Constant Thrust Soft Landing on Lunar Surface

Abstract

Design of a guidance algorithm and an enhanced closed loop Navigation, Guidance and Control (NGC) scheme for the powered descent phase of the proposed unmanned Indian lunar soft landing mission, Chandrayaan-2, is addressed. Powered descent is planned to have a rough braking phase, with five thrust engines, starting at 18km altitude with large horizontal velocity and extends to 3km altitude which is followed by fine braking till 30m above landing site with two engines shutoff and subsequent vertical descent to 2m altitude using constant thrust engine and variable thrust attitude control thrusters. At 2m altitude all engines are shut off to avoid plume hitting lunar surface. Assuming Lander motion in two-dimensional plane and all the thrust engines mounted on a single deck, an open loop guidance algorithm is designed which generates the variable Lander orientation with respect to local vertical axis(till 30m altitude) under the condition that the thrust engines controlling translation motion is operating with full thrust. For the open loop trajectory design, objective function is selected so as to minimize the final state errors and the optimal attitude profile is generated using Steepest Descent algorithm without any linearization on Lander dynamics. In order to tactically fix the simulation time for this method, an existing analytical guidance algorithm which optimizes control effort by modulating both the attitude and thrust engine duty cycle and gives out time-to-go as solution is used as initial reference. For the optimum propellant budget so obtained, time-to-go is recomputed for 100% duty cycle and applied as initial assumption for Steepest Descent algorithm. It is also tuned up to have pitch attitude close to local vertical at 30m altitude before vertical descent. Final vertical descent is planned non-optimally. The NGC scheme proposed strategically tracks the open loop guidance profile along vertical and horizontal direction by augmenting the reference acceleration with error in velocity and position multiplied by suitable gains respectively and then significantly saturated before addition.
Subsequently, modified reference attitude command to orient the thrust engine is generated by comparing the resultant vertical and horizontal acceleration using inverse tan function.