It has recently been shown that minimum-fuel powered descent guidance can be solved onboard as a convex optimization problem.  It therefore presents itself as a promising technology to enable future planetary exploration missions.  However, since this approach is formulated as a deterministic optimal control problem, the resulting guidance law is only designed for a single pair of initial and target states without external disturbances.

We attempt to extend this approach to the more general case of steering initial position and velocity distributions to target distributions, while considering Brownian motion process noise acting on the system.