Desensitizing the Minimum-Fuel Powered Descent For Mars Pinpoint Landing

Abstract

This paper aims at reducing the sensitivity of the minimum-fuel powered descent trajectory on Mars in the presence of uncertainties and perturbations, using the desensitized optimal control methodology. The lander is modeled as a point mass in a uniform gravitational field, and the engine throttle is considered the control variable, which is bounded between two nonzero settings. Unlike the conventional practice of designing separately the nominal trajectory and a feedback tracking controller, desensitized optimal control strategy incorporates the two designs in synergy, delivering a superior performance. Sensitivities of the final position and velocity with respect to perturbed states at all times are derived and augmented onto the minimum-fuel performance index through penalty factors. The linear quadratic regulator technique is used to design the feedback control gains. To reduce the likelihood of the closed-loop throttle exceeding the prescribed bounds, a multiplicative factor is applied to the feedback gains. This reshapes the nominal trajectory from the well-known maximum-minimum-maximum structure in that the nominal throttle is encouraged to stay away from the prescribed bounds, leaving room for the feedback control. Monte Carlo simulations show that the occurrence of out-of-bound closed-loop throttles is significantly reduced, leading to improved landing precision.