Design and Robust Scheduling of Nano-Satellite Swarm for Synthetic Aperture Radar Applications Chee Khiang Pang, Akash Kumar, Cher Hiang Goh, and Cao Vinh Le Department of Electrical and Computer Engineering National University of Singapore Singapore, Singapore 117583 Email: {justinpang, akash, elegch, cvle}@nus.edu.sg Abstract—This paper presents the design and robust schedul- ing of nano-satellite (nanosat) swarm for synthetic aperture radar (SAR) applications. Based on power budget and bandwidth limit of nanosats, the nanosats’ form factor and swarm size are chosen to ensure requirements on ground resolution and signal-to- noise ratio. An energy-efficient and robust scheduling considering stochastic failures is proposed using scenario optimization with convexification. The effectiveness of our proposed scheduling approach is verified with mathematical rigor as well as extensive simulation results on a realistic SAR application using strip and spot modes. I. I NTRODUCTION With recent advancements in consumer electronics, the ability to operate co-orbital nano-satellites (nanosats) in swarm platforms in the same orbit to replace the more costly and bulkier satellites opens new opportunities and challenges for space industries [1]. As such, power budget and bandwidth limit of nanosats must be carefully taken into account when designing a nanosat swarm. In addition, energy efficiency and reliability are highly essential scheduling objectives. Due to restrictive on-board computational capability, given nanosat specifications and mission details, it is essential for a nanosat swarm to be properly designed and scheduled prior to launch. This is opposite to the traditional synthetic aperture radar (SAR) applications performed by large satellites, where a built- in scheduler is able to receive the jobs submitted by users and perform scheduling online [4]–[6]. To the best of our knowledge, design of a nanosat swarm has only been proposed in [2], considering radar system design and revisit times for nanosat constellation on different orbits. Dy- namic scheduling has been recently proposed for cooperative satellites. In particular, Pemberton and Greenwald identified the need for dynamic scheduling of imaging satellites in the presence of uncertain changes in the environment, desired jobs, as well as the availability of resources [7]. Liao and Yang formulated a satellite scheduling problem considering stochastic weather conditions and proposed a solution using a rolling horizon approach [8]. Wang et al. proposed a heuristic dispatching rules for dynamic scheduling problem of Earth observing satellites to deal with uncertain arrival of new jobs [4]. A satellite mission scheduling problem was studied This work was supported in part by Singapore MOE AcRF Tier 1 Grant R-263-000-A52-112. involving scheduling of jobs to be performed by a satellite in which new job requests can arrive stochastically [5]. A two- phase scheduling method is also proposed for the consideration of emergency jobs in earth observing satellites scheduling [6]. To the best of our knowledge, energy-efficient and robust scheduling of nanosat swarm considering stochastic failures has not been considered in state-of-the-art literature. In ad- dition, the scheduling approaches of existing works were commonly proposed by a dispatching rule [4] and reschedul- ing [8][5]. The former has no baseline schedule and jobs are dispatched online based on a predefined criterion, the latter has a baseline schedule to be revised multiple times online. These approaches require online computation and are not suitable for nanosats. In this paper, design and robust scheduling of a swarm of homogeneous nanosats is presented for SAR applications. Based on power budget and bandwidth limit of nanosats, the nanosats’ form factor and swarm size are properly chosen to ensure minimum requirements on ground resolution and signal-to-noise ratio (SNR). An energy-efficient and robust scheduling approach considering stochastic failures is then proposed using convex scenario optimization (CSO). The key idea of CSO is to find a feasible solution to balance the energy-optimal schedules from individual scenarios of nanosat failures, in which occurrence probabilities of scenarios are formulated using Weibull reliability analysis. Our proposed CSO is applied to SAR applications in Singapore using strip and spot modes. The effectiveness of our proposed CSO is ver- ified with mathematical rigour as well as extensive simulation results. II. DESIGN OF NANOSAT SWARM BASED ON POWER BUDGET AND BANDWIDTH LIMIT In this section, design of a nanosat swarm for SAR ap- plications is presented, which includes the following steps: provision of specifications of nanosats, provision of mission details, and proposal of nanosats’ form factor and swarm size. A. Specifications of Nanosats Nanosats are widely defined as artificial satellites with a wet mass between 1 and 10 kg (2.2 and 22 lb). The most common platform to build a nanosat is cubesat, which measures the 705 Th21.2 2014 13th International Conference on Control, Automation, Robotics & Vision Marina Bay Sands, Singapore, 10-12th December 2014 (ICARCV 2014) 978-1-4799-5199-4/14/$31.00 ©2014 IEEE