An anytime branch and bound algorithm for agile earth observation satellite onboard scheduling
Introduction
The task of recognizing targets over sea is typically treated as an acquisition of a large area target with all interesting moving targets included inside. To realize a full covering of this large area, a large number of high resolution satellites are required to work coordinately. This is rather resource consuming and inefficient as a large portion of the area contains nothing interesting especially when the moving targets are sparsely distributed. With the development of satellite autonomy techniques, the efficiency of targets recognition over sea can be greatly improved. This can be realized by, for instance, a bi-satellite cluster, composed of a low resolution satellite (LRS for short) leading the formation for targets detection and a trailing high resolution satellite (HRS for short) for targets recognition. The LRS detects the precise locations of the moving targets when it flies over the sea area and then sends the information to the trailing HRS which generates onboard a plan to be executed in a timely manner. This avoids observing uninteresting areas and enhances the utilization efficiency of the rare satellite resources.
There have been increasing research attentions on autonomous agile earth observation satellites in last decades (Davies et al., 2016), resulting in a number of successful missions such as EO1 spacecraft (Sherwood et al., 2005), FireBird (Reile et al., 2013) and OptiSAR (Fabrizio, 2016). The EO1 from NASA is capable to detect and respond to the scientific events occurring on Earth such as volcanic eruptions, growth and retreat of ice caps, cloud detection, and crust deformation (Sherwood et al., 2005, Tran et al., 2004a). EO1 generates onboard an abstract long-term plan and creates detailed short-term plans autonomously with an iterative repair method which resolves state, resource, and temporal conflicts. The FireBird is able to derive fire parameters such as the location and size of burning areas (Reile et al., 2013). FireBird has limited onboard autonomy where the initial routine acquisition request is generated on ground and the onboard planning is triggered by auto-detected events. The OptiSAR™, a constellation from Canadian company UrtheCast, consists of 8 tandem pairs from two orbital planes. Each tandem pairings contains a SAR (Synthetic Aperture Radar) sensor and an optical sensor separated by only a couple of minutes (Pirondini, 2016). The constellation was designed not only to allow for near-simultaneous acquisition of SAR and optical data (Denis et al., 2017), but also to make the optical satellite take cloud-free images with the aid of the leading SAR satellite which is able to capture real-time cloud information.1
Another famous constellation worth mentioning is Pleiades (Gleyzes et al., 2012) which consists of two non-autonomous agile satellites. Although without onboard autonomy, the constellation is able to access any point on the globe within one day (Gleyzes et al., 2012). Three mission plans are generated per day for each satellite by the ground segment, which can integrate last-minute customer requests up to 2 h before the plans are uploaded. Although the responsive ability of Pleiades is quite excellent due to the use of a bi-satellite constellation, it is believed that the ability could be further improved if autonomy is used. Also, autonomy can help to reduce operating costs (Chien et al., 2005).
Onboard mission planning and scheduling is a critical functionality of autonomous systems which helps spacecraft to exploit its autonomous ability in an efficient way (LaVallee et al., 2006, Tran et al., 2004b).
CASPER (Continuous Activity Scheduling, Planning, Execution, and Replanning) (Knight et al., 2001) is used by EO1 as its onboard mission planning software, whose reasoning capability is inherited from ASPEN (Automated Scheduling and Planning Environment), one of the most successful frameworks for automated planning and scheduling of spacecraft control and operations (Fukunaga et al., 1997). CASPER employs an iterative repair method to continuously modify and update a current working plan in light of changing operating context (Rabideau et al., 1999, Chien et al., 2000).
A reactive-deliberate architecture is studied in Lemaître and Verfaillie (2007), which is another well-known autonomous planning architecture for agile earth observation satellites (Beaumet et al., 2008). The reactive task is in charge of the interaction between the environment and the decisional architecture, which is at any time able to provide an action-commitment. When triggered by the reactive task, the deliberative one is to generate an activity plan to be sent to the reactive task as a decision proposal (Pralet and Verfaillie, 2008). Beaumet et al. (2011) proposed an iterated stochastic greedy algorithm for the deliberative task, and they argued that a look-ahead mechanism could further improve the algorithm along some directions they envisaged.
Apart from the famous ASPEN and reactive-deliberate architecture, a number of dedicated onboard planning techniques were proposed in the literature under various settings. Damiani et al. (2004) proposed an anytime planning approach for the management of a non-agile satellite. Lenzen et al. (2014) developed a VAMOS (Verification of Autonomous Mission Planning Onboard a Spacecraft) system consisting of an onboard component and an on-ground component. VAMOS, which is the planning and scheduling system used in FireBird mission, uses resource bounds to address inaccurate on-ground resource propagation. Liu et al. (2016) proposed an autonomous onboard scheduling algorithm for single agile satellite scheduling problem where they considered an over-simplified model that does not involve time dependent transition constraint.
In this paper, a bi-satellite cluster consisting of an autonomous low resolution satellite (LRS) leading the formation and a trailing agile high resolution satellite (HRS) is considered in the setting of targets recognition over sea. The LRS can look a small amount of time ahead of the HRS and continuously send the latest information it acquired to HRS. To quickly response to the constantly updating information, it is particularly important for the HRS to be equipped with onboard mission planning and scheduling ability. For this purpose, an anytime branch and bound onboard scheduling algorithm (AB&B) is proposed. AB&B always decides the next observation to be performed during the execution of the current observation. The next observation is the first one selected in a schedule plan which is generated by a branch-and-bound subroutine (B&B) with the targets in the look ahead horizon of the LRS as input. B&B solves an agile earth observation satellite (AEOS) scheduling problem whose prominent feature is its time-dependent maneuver time constraint (Pralet and Verfaillie, 2012). Experiments on a set of representative scenarios are presented to validate the efficacy of the proposed AB&B and the bi-satellite cluster.
The remainder of this paper is organized as follows. In Section 2, a mathematical model of the AEOS scheduling problem is proposed. Section 3 presents the main scheme of the anytime branch and bound online scheduling algorithm (AB&B) and the details of the branch and bound subroutine. Experimental results are presented in Section 4 to validate the efficiency of the bi-satellite cluster and the effectiveness of the proposed AB&B. Concluding remarks are drawn in Section 5.
Section snippets
Problem description
As is shown in Fig. 1, in a bi-satellite cluster, the LRS ahead is in charge of detecting targets with a wide swath camera and computing the profits and locations of the targets, which are then sent to the trailing HRS. The HRS constantly generates online schedule plans with the purpose of maximizing the total profits of the selected observations subject to a number of imperative constraints. The cluster is capable to recognize a large number of targets via a single fly-over opportunity. As
Main scheme of the anytime branch and bound algorithm
An anytime branch and bound (AB&B) algorithm is proposed for the autonomous decisional system onboard the HRS. The main scheme of the AB&B is shown in Algorithm 1. AB&B basically determines the next observation to be performed during the execution of the current observation. The next observation is the first one selected in the plan generated by a branch-and-bound (B&B) subroutine with a time limit of ( where is the imaging time of the current observation), taking into account
Test data
The efficacy of the proposed anytime branch and bound algorithm (AB&B) was validated on a large number of instances. These instances were generated based on an assumption and a set of parameters.
It is assumed that the high resolution satellite in the bi-satellite cluster uses the latest China’s agile satellite platform CAST30003 produced by the China Academy of Space Technology. With this platform, the maneuver process includes three phases:
Conclusion
This paper describes a bi-satellite cluster for targets recognition over sea, which is composed of a low resolution satellite leading the formation for targets detection and a trailing agile high resolution satellite for targets recognition. The high resolution satellite generates onboard a schedule plan to be executed given the target locations provided by the low resolution satellite. A mathematical model of the agile earth observation satellite scheduling problem was proposed and an anytime
Acknowledgments
We are grateful to the reviewers for their insightful comments which helped us to improve the paper. This work was supported by the National Natural Science Foundation of China (Grant numbers: 71690233, 61473301, 71201171, 71501179 and 71501180).
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
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