Desensitizing the Minimum-Fuel Powered Descent for Mars Pinpoint Landing

摘要

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