The proposed program innovates subsurface prospecting by planetary drones to seek a solution to the difficulty of robotic prospecting, sample acquisition, and sample characterization at multiple hazardous locations in a single mission. Innovation focuses on a specific, challenging scenario: sub-surface access of multiple lava tubes by drones far enough from Earth for speed-of-light latency to preclude direct human control. The technology will be broadly applicable to resource prospecting in cold traps, dark craters, cryovolcanoes, asteroids, comets, and other planets. The technology is also applicable to Earth-relevant problems such as the detection of poisonous and explosive gases and flammable dust in mines; and surveying urban canyons; exploring bunkers and caves. The proposed innovation is the development of Anytime Motion Planners that can generate feasible guidance routines to accomplish subsurface prospecting by planetary drones. Anytime Motion Planners are algorithms that can quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. In addition to Anytime Motion Planners, optimal guidance routines will also be innovated in this work by formulating the Generic Autonomous Guidance Optimal Control Problem (Problem G&C) (Pavone, Acikmese, Nesnas, & Starek, 2013) as a convex optimization problem and employing interior-point methods to solve the resulting problem to global optimality. This work will determine whether optimal solutions may be computed quickly enough to be useful in practice.