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The recent advent of satellite swarm technologies has enabled space exploration with a massive number of picoclass, low-power, and low-weight spacecraft. However, developing swarm-based satellite systems, from conceptualization to validation, is a complex multidisciplinary activity. One of the primary challenges is how to achieve energy-efficient data transmission between the satellite swarm and terrestrial terminal stations. Employing Lyapunov optimization techniques, we present an online control algorithm to optimally dispatch traffic load among different satellite-ground links for minimizing overall energy consumption over time. Our algorithm is able to independently and simultaneously make control decisions on traffic dispatching over intersatellite-links and up-down-links so as to offer provable energy and delay guarantees, without requiring any statistical information of traffic arrivals and link condition. Rigorous analysis and extensive simulations have demonstrated the performance and robustness of the proposed new algorithm.

To enable robust space exploration, astronautic scientists are exploiting principles and techniques that can help spacecraft systems become more resilient through self-organizing and automatic adaptation. Inspired by the swarming behaviors of animals in nature [

As shown in Figure

Illustration of a small satellite swarm in System F6 [

To address the energy challenges of satellite swarms [

The rest of this paper is organized as follows: Section

We consider a satellite swarm, as shown in Figure

Abstract architecture of the satellite swarm system.

In a swarm, a worker

The current satellite swarm prototypes generally use two different technologies for data communication, that is, the commercial-off-the-shelf wireless technology (e.g., IEEE 802.11) for intersatellite communications within the swarm [

Let

In the following, we assume that satellites can estimate the unfinished traffic load in their queues accurately, and the case when such estimation has errors will be discussed in Section

Our objective is to design a flexible and robust online control algorithm that automatically adapts to the time-varying systems by making decisions on

However, traditional techniques, for example, Markov decision theory and dynamic programming, require substantial statistics of system dynamics and suffer from high computational complexity [

Let

Then, the one-slot conditional Lyapunov drift

If control decisions are made in every slot

A key derivation step is to obtain an upper bound on this term, which is defined as follows.

Under any control algorithm, the drift-plus-penalty expression has the following upper bound for all

Squaring both sides of the queueing dynamic (

Summing the above over

Repeating the above steps for the queue

Combining these two bounds together, and taking the expectation with respect to

Now adding to both sides the penalty expression, that is, the term

Minimizing the right-hand-side of (

(1)

(2)

(3)

The following theorem presents bounds on the time-average energy cost and queue backlogs achieved by the proposed new algorithm.

Define

According to Caratheodory’s theorem [

Because in every time slot

Now we can take expectations on both sides over

Rearranging the terms, and using the fact that

Summing the above over

To prove (

Summing the above over

As mentioned in Section

Suppose there exists an

It suffices to show that using

Now denote the minimum value of

Using this and (

Here

We evaluate the proposed new algorithm with extensive simulations under realistic settings. We simulate a satellite swarm consisting of 5 homogeneous messengers and 50 heterogeneous workers. In every time slot, each messenger can choose to use a specific UDL from at least 3 candidates for transmitting data to ground. According to [

To fully investigate the algorithm performance, we compare it with an intuitive online algorithm called LBMin. In LBMin, each worker dispatches all its data to the messenger currently with the smallest queue backlog, while each messenger chooses the UDL with the lowest energy cost for satellite-ground communication. It represents the current task processing practices in computing and network systems [

We conduct the following analysis on critical factors to characterize their impacts on the algorithm performance.

(1) Impact of control parameter

Time-average energy cost under different

Time-average queue backlog under different

Average service delay under different

(2) Impact of long-term time slot

Time-average energy cost under different

(3) Characterizing algorithm robustness: as mentioned in Section

The impact of estimation errors on time-average energy cost.

The impact of estimation errors on time-average queue backlog.

The impact of estimation errors on average service delay.

(4) Algorithm comparison: we choose to compare LBMin to the proposed new algorithm when

Comparison on time-average energy cost under different

Comparison on time-average throughput under different

In this paper, we propose a new algorithm based on Lyapunov optimization, to reduce the energy consumption on satellite-ground communications for satellite swarm systems. Our approach incorporates traffic scheduling actions on ISLs between workers and messengers and on UDLs between messengers and earth stations, so as to transmit data on high-quality, low-cost UDLs to ground. Through analysis and simulations, we show that this algorithm has provable performance bounds and is very effective in reducing energy costs of satellite-ground communication. We also show that this algorithm can guarantee stable performance over time and is robust to traffic load estimation errors. Moreover, it is computationally efficient and easy to implement in large practical swarming systems.

The number of workers in the swarm

The number of messengers in the swarm

Lyapunov control parameter

The coefficient of energy consumption for transmitting per unit data

Queue backlog of worker

Queue backlog of messenger

The amount of newly generated data at

The maximum value for all

The expectation of

The amount of data traffic sent from

The maximum amount of traffic that can be distributed from

The decision of

The transmission rate of

The maximum transmission rate for all

The error rate of selected UDL of

The energy consumption for transmitting data for

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the State Key Lab of Astronautic Dynamics of China under Grant no. 2014ADL-DW0401, the National Science Foundation of China (NSFC) under Grant no. 61401516 and no. 61202430, the Science and Technology Foundation of Beijing Jiaotong University under Grant no. 2012RC040, and the China Scholarship Council under Grant no. 201308110150. This work has been presented in part at the 16th International Conference on Advanced Communications Technology (ICACT), Pyeongchang, Korea, February 2014.