Optimal covariance control for lunar surface hop trajectory optimization

Lunar environmental uncertainties and measurement errors can degrade guidance accuracy. To address this issue, an optimal covariance control based method was proposed to incorporate stochastic uncertainties into the trajectory optimization process, thereby enhancing robustness against such disturbances. First, the trajectory optimization problem was formulated as a chance-constrained optimal covariance control problem, with fuel optimality as the performance metric. Stochastic differential equations were used to model dynamic uncertainties, and chance constraints were introduced to represent state and thrust constraints. Subsequently, a successive convex optimization algorithm was developed to solve the problem. The dynamics were discretized using a zero-order hold, and a Kalman filter was employed for real-time state estimation. Based on uncertainty propagation in the filtered closed-loop system, a discrete-time stochastic optimization problem was established. Furthermore, the chance constraints were relaxed into deterministic constraints using Gaussian distribution functions. These constraints were then convexified via successive linearization. An approximate solution to the original problem could thus be obtained by iteratively solving the convex subproblem. In numerical simulations, two scenarios are examined to demonstrate the effectiveness of the proposed algorithm, including hopping on a flat lunar surface and hopping into a pit. Under the same constraints, a comparison with deterministic optimization results shows that the closed-loop optimal trajectory obtained by the proposed method has standard deviations of approximately 2m in position and 1m/s in velocity, which are significantly smaller than those of the open-loop method. The fuel consumption for nominal trajectories increases by less than 0.1kg compared with open-loop method, and is less than the linear quadratic regulator (LQR). Therefore, the proposed method can effectively handle the stochastic uncertainties in measurements and dynamics, and significantly improve landing accuracy.