DESENSITIZING THE MINIMUM-FUEL POWERED DESCENT FOR MARS PINPOINT LANDING

Desensitized Optimal Control (DOC) methodology is applied to the problem of minimum fuel powered descent on Mars, in order to reduce the landing errors in the presence of uncertainties and perturbations. Unlike the conventional practice of designing separately the nominal trajectory and a feedback tracking controller, DOC strategy incorporates the two designs in synergy, delivering better tracking performance. Within this study, a point mass model with a uniform gravitational field is used, with the engine throttle being the control variable which is bounded between two non-zero settings. Most dominating perturbations during the powered descent stage are considered, including the initial deliver errors of the position and velocity, mid-course position update errors, and the uncertainties on the engine thrust. Linear Quadratic Regulator (LQR) technique is used to design the feedback control gains. In order to reduce the likelihood of the closed loop throttle exceeding the prescribed bounds, a multiplicative factor is applied to the feedback gains. In the meantime, sensitivities of the final position and velocity with respect to state perturbations at all times are derived, and augmented onto the minimum fuel performance index through penalty factors. As a result, the nominal trajectory is reshaped from the well-known maximum-minimum-maximum profile with little extra fuel consumption such that the nominal throttle is encouraged to stay away from the bounds. Monte-Carlo simulations show that the occurrence of out of bound throttles are significantly reduced, resulting in improved landing precision. LQR technique is also used to design feedback control laws to guide the lander to a different target detected during the descent, and Monte Carlo simulations are performed to verify the performance of the algorithm.