Planetary landing site detection and selection using multilevel optimization strategy
Introduction
Exploring celestial bodies is an important way for humans to study the origins of the solar system and the universe, and then broaden the boundaries of current knowledge. Currently, the mainstream approach for deep-space exploration is landing, roaming and sample return, which makes it possible to study the extraterrestrial substance qualitatively or quantitatively. However, due to various difficulties, such as landing point detection and selection problems, it is tough to achieve a successful task. Areas of interest for landing or sampling tasks can be bumpy, thus threatening the security of the task. In addition, long term communication delays preclude real-time monitoring. These difficulties inherently require spacecraft's autonomous landing site detection and selection capabilities [1]. As expected, the autonomous technology has attracted the attention of space agencies around the world. The autonomous landing and hazard avoidance technology (ALHAT) project, which was initiated by NASA in the year of 2006, clearly stated that new landing site selection technologies must be further developed to meet the safety and accuracy requirements with the constraints of fuel consumption and security priority level [2]. In the Lunar Lander Mission 2018, the ESA proposed that the lander module should be able to autonomously select safe landing sites and complete precise landings in the areas with complex surroundings [3].
Up to now, a common landing site detection and selection approach is that the potential regions of interest were screened in advance to figure out the zones with high safety probability, and then the safe touchdown site was selected. Most of Mars landers launched by NASA relied on remote-sensing data acquired by previous orbiters for landing site selection, although these data are not sufficient to achieve the pinpoint landing. Even the Phoenix and MSL have achieved the safe landing on Mars successfully, neither has the capability of autonomous hazard detection and landing site selection [[4], [5], [6]]. In addition, even if the terrain information of the landing area is sufficiently accurate, the atmospheric or geological activities may also cause changes of topographical features [7]. Obviously, landing in the predetermined site is likely to cause the landing mission to fail. The Hayabusa-1 prober of JAXA found that one of the candidate sites was unsuitable for landing and sampling due to the existence of excess rocks until its first rehearsal descent [8]. And the ongoing mission Hayabusa-2 encountered a similar situation. A possible landing zone among the planned candidates L08, L07 and M04 is smaller and more rugged, therefore leading the delay of sampling mission to January 2019 [9]. Reviewing the previous planetary landing missions, Apollo 11 was the first spacecraft to conduct a landing site selection during the descent and landing process, but this process was manually implemented by astronauts rather than on-board equipments [10]. Technically, Chang'e−3 is currently the only spacecraft that successfully performed autonomous hazard detection and avoidance (AHDA) on the surface of extraterrestrial objects. The spiral search strategy adopted during the landing site selection phase ensured the safety for the landing site [11]. The ESA also developed the precise intelligent landing using on-board technology system (PILOT), which will be deployed on the Luna-27 lander mission in 2021. And a precursor system of PILOT will be applied to the Luna-25 in 2019 [12].
A lot of methods to solve the optimal landing site selection problem have been put forward. The definition and selection principles for optimal landing sites were gradually improved by Camara, Johnson and Cohenim [1,13]. Initially, the artificial intelligence played an important role in addressing this problem. Serrano N. et al. introduced a fuzzy cognitive engine to select a safe touchdown site from the grayscale image and inferred the safety probability of the landing site based on the Bayesian network as well [14,15]. Furfaro et al. developed an evolutionary fuzzy cognitive technique to imitate the expert decision-making process for Venus and Titan landing site selection [16]. Lunghi et al. used informative indexes extracted from grayscale images as the input of two artificial neural networks (ANNs), and then performed the hazard detection and landing site selection for a lunar scenario by using ANNs [17]. Intelligence algorithms are also employed to solve this problem. Liu et al. adopted the genetic algorithm to identify the safe landing sites from grayscale images [18]. Du et al. used particle swarm optimization to select a safe landing site from digital elevation data [19]. However, these intelligent algorithms are difficult to apply in engineering practice due to large computational burden. Inspired by the spiral search algorithm of Chang'e−3, Jiang et al. developed S-shaped search to find safe areas during the precision obstacle avoidance [20]. Cui et al. integrated terrain safety, fuel consumption, and touchdown performance into an overall index to optimize the landing site selection problem. This approach can search out an applicable zone, but the computation complexity is also greatly increased [21].
In this paper, the multilevel optimization strategy is newly employed to handle the landing site detection and selection problem. The multilevel optimization can decompose the multi-constraint optimization problem into a series of optimization sub-problems and then solve sub-problems in a predetermined sequence. The multi-constrained landing site selection problem can be transcribed into three successive sub-problems: 1) detecting flat candidate landing zones from the digital elevation map (DEM) considering the constraint of terrain hazards; 2) selecting the candidate safe landing zones with minimum fuel consumption; 3) determining the optimal landing site from the optimal fuel consumption landing zone considering the constraints of slope, roughness and minimum landing diameter. In solving the first sub-problem, a novel hazard detection algorithm based on derivatives is proposed to perform the obstacle detection in the optimization process. This algorithm is used to find out relatively flat areas. Data points where the first-order and second-order derivatives satisfy the elevation tolerance at the same time are recognized as flat. Specific steps are described in Section 3. The rest of this paper is organized as follows. A general landing site detection and selection problem with various constraints is reviewed in Section 2. The multilevel optimization strategy based optimal landing site selection method is depicted in Section 3. Comparative numerical simulations and robustness assessments are presented in Sections 4 Comparative numerical simulations, 5 Robustness assessments of multilevel optimization, respectively. Finally, conclusion is in Section 6.
Section snippets
Concept of landing site detection and selection
The primary purpose of landing site selection during the descent and landing is to ensure a safe and accurate landing on regions of interest. Only in this way can rovers perform well on subsequent tasks, such as autonomous roaming, scientific experiments, data transmission and even sampling return. Generally speaking, an ideal landing site should have several topographical features, including no huge boulders and craters, no dramatic terrain slope and roughness. These features or obstacles are
Methodology of multilevel optimization
The idea of multilevel optimization originates from the Stackelberg Leadership Model (1934) in economics [30]. In the strategic game, leader firms optimize outputs firstly to maximize their profits and then followers move sequentially, forming the successive and coupling relation. Later, the multilevel optimization strategy (MOS) is formulated and studied as a mathematic programming method by J. Bracken and J.M McGill in 1973 [31]. Since then, multilevel optimization was applied as a non-convex
Comparative numerical simulations
In this paper, the proposed optimization algorithm is compared with the safety index based optimization method reported in Ref. [21], which can find a landing site without obstacles and guarantee a good landing performance with less fuel consumption. Comparative simulation includes landing site detection and selection simulations using preceding two methods, and safety assessments of optimal landing sites.
Robustness assessments of multilevel optimization
This section investigates the robustness performances of the multilevel optimization strategies in the problem of planetary landing site selection. More specifically, the sensitivity of the multilevel optimization method to the initial positions, guidance methods and landing terrains is evaluated to analyze the impact of the mission scheme and environmental conditions on the entire optimization structure.
Conclusion
In this paper, a multilevel optimization strategy is adopted to deconstruct the landing site detection and selection problem with constraints into three successive sub-problems. In the optimization of first sub-problem, a derivative based hazard detection method is proposed to detect flat area. Meanwhile, important criteria including fuel consumption, terrain slope and roughness are taken into account to minimize relevant indexes in the optimization process. With the going of optimization, the
Acknowledgment
The work described in this paper was supported by the National Natural Science Foundation of China (Grant No. 11672126 and 61673057). The authors fully appreciate their financial supports.
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