Convex programming based method for stochastic optimal powered descent guidance with Wasserstein terminal cost

For powered descent guidance (PDG) problems, chance constrained covariance control can improve the closed-loop performance of the fuel-optimal trajectories in the presence of stochastic uncertainties. However, there are no feasible trajectories if the desired distribution is unreachable. To handle the problem, this paper proposes a novel Wasserstein terminal cost (WTC)-based covariance control method, which steers the states to the final distribution with the minimum terminal Wasserstein distance. For the linear WTC-based covariance control, a relaxation is proposed and further proven to be lossless using the first-order optimality conditions. Subsequently, the stochastic PDG is formulated within the WTC-based framework. The original stochastic nonconvex problem is intractable and is therefore handled via a successive convex programming (SCP) algorithm by iteratively solving a sequence of convex subproblems. To derive the subproblems, the stochastic dynamics are linearized via change of variables, and the propagation of the first two moments is relaxed via slack variables. Additionally, chance constraints are conservatively converted into deterministic forms and further convexified by linearization techniques. The convexification is numerically exact upon the convergence of the SCP algorithm. Numerical simulations on Mars PDG demonstrate that the proposed method can generate feasible trajectories with near minimal Wasserstein distance.