  In unmanned space exploration, the cooperation among space robots requires
advanced communication techniques. In this paper, we propose a communication
optimization scheme for a specific cooperation system named the
"mother-daughter system". In this setup, the mother spacecraft orbits the
planet, while daughter probes are distributed across the planetary surface.
During each control cycle, the mother spacecraft senses the environment,
computes control commands and distributes them to daughter probes for actions.
They synergistically form sensing-communication-computing-control
($\mathbf{SC^3}$) loops. Given the indivisibility of the $\mathbf{SC^3}$ loop,
we optimize the mother-daughter downlink for closed-loop control. The
optimization objective is the linear quadratic regulator (LQR) cost, and the
optimization parameters are the block length and transmit power. To solve the
nonlinear mixed-integer problem, we first identify the optimal block length and
then transform the power allocation problem into a tractable convex problem. We
further derive the approximate closed-form solutions for the proposed scheme
and two communication-oriented schemes: the max-sum rate scheme and the max-min
rate scheme. On this basis, we analyze their power allocation principles. In
particular, for time-insensitive control tasks, we find that the proposed
scheme demonstrates equivalence to the max-min rate scheme. These findings are
verified through simulations.
