Mars precision landing guidance based on model predictive control approach

Abstract

The purpose of the past Mars exploration missions had been finding trace of water or evidence of life. Thus, the target could be changed to a different scientifically interesting target even if the landing accuracy was not guaranteed. However, the trend of recent missions is changed to investigating the suitability of Mars habitation for Mars human exploration. Follow-ing the trend, higher landing accuracy is required for delivering cargos to a human base and reaching a specific asset or target. Thus, to land precisely to the target, the guidance should be optimal and robust. In this dissertation, the precision landing guidance for Mars powered descent phase is proposed based on Model Predictive Control (MPC) approach. According to the characteristics of the approach, disturbance can be considered at every time step from the optimization pro-cess with new measured states. Moreover, lander’s dynamics is convexificated and linearized to adopt the convex optimization which can guarantee global optimality with a proof of convexi-fication. To use the moving horizon frame, convexificated optimization problem is augmented with Laguerre functions. Because the cost function of the original MPC theory cannot represent fuel-optimal or minimum landing-error exactly, the new cost function that is combined with minimum fuel-consumption and minimum-landing-error is suggested to avoid infeasibility. On the other hand, control input at each time step is calculated from the optimization process at each time step, which means control inputs are independent to each other. Thus, the stability with these independent control inputs is proved by using Lyapunov function for two cases de-pends on the length of the prediction horizon relative to the final time step. To compare the per-formance under the existence of disturbances, navigation error sources and its stochastic mod-els are determined refer to the ‘Altair’ lunar lander’s navigation system which consists of opti-cal sensor, radar and inertial measurement unit. Finally, the numerical simulations are conducted for stability verification, performance analysis and comparison with or without disturbance. The results show that the performance of the proposed guidance law is almost same as that of the convex optimization when disturbance does not exist. Moreover, the proposed guidance can give a feasible command even if the lander has not enough fuel to reach the target by the combined cost function. For the case with disturbances with Monte-Carlo simulation, the landing ellipse which represents the standard de-viation of the final landing position of the proposed guidance is much smaller than even that of the optimal solution.