With a growing interest in outer space, space robots have become a focus of exploration. To coordinate them for unmanned space exploration, we propose to use the "mother-daughter structure". In this setup, the mother spacecraft orbits the planet, while daughter probes are distributed across the surface. The mother spacecraft senses the environment, computes control commands and distributes them to daughter probes to take actions. They synergistically form sensing-communication-computing-control ($\mathbf{SC^3}$) loops, which are indivisible. We thereby optimize the spacecraft-probe downlink within $\mathbf{SC^3}$ loops to minimize the sum linear quadratic regulator (LQR) cost. The optimization variables are block length and transmit power. On account of the cycle time constraint, the spacecraft-probe downlink operates in the finite block length (FBL) regime. 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 one. Additionally, we derive the approximate closed-form solutions for the proposed scheme and also for the max-sum rate scheme and max-min rate scheme. On this basis, we reveal their different power allocation principles. Moreover, we find that for time-insensitive control tasks, the proposed scheme demonstrates equivalence to the max-min rate scheme. These findings are verified through simulations.

翻译：随着对外太空兴趣的日益增长，空间机器人已成为探索的重点。为了实现无人空间探索中的协同作业，我们提出采用"母-子结构"。在该结构中，母航天器绕行星运行，而子探测器分布于星球表面。母航天器感知环境、计算控制指令并分发至子探测器执行。三者协同形成感知-通信-计算-控制（$\mathbf{SC^3}$）闭环，不可分割。我们据此优化$\mathbf{SC^3}$闭环中的航天器-探测器下行链路，以最小化线性二次型调节器（LQR）总代价。优化变量为块长度与发射功率。受周期时间约束，航天器-探测器下行链路运行在有限块长度（FBL）机制下。为求解该非线性混合整数问题，我们首先确定最优块长度，然后将功率分配问题转化为易解凸问题。此外，我们推导了所提方案及最大和速率方案、最大最小速率方案的近似闭式解。在此基础上，揭示了它们不同的功率分配原则。还发现，对于时间不敏感控制任务，所提方案与最大最小速率方案具有等价性。仿真结果验证了上述发现。