Autonomous real-time landing site selection for Venus and Titan using Evolutionary Fuzzy Cognitive Maps

Applied Soft Computing 12 (2012) 3825–3839

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

Autonomous real-time landing site selection for Venus and Titan using Evolutionary Fuzzy Cognitive Maps Roberto Furfaro a,∗ , Wolfgang Fink b , Jeffrey S. Kargel c a

Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA Electrical and Computer Engineering Department and Biomedical Engineering Department, University of Arizona, Tucson, AZ 85721, USA c Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA b

a r t i c l e

i n f o

Article history: Received 13 July 2011 Received in revised form 22 December 2011 Accepted 20 January 2012 Available online 20 March 2012 Keywords: Planetary exploration Planetary landing Autonomous systems Fuzzy Cognitive Maps

a b s t r a c t Future science-driven landing missions, conceived to collect in situ data on regions of planetary bodies that have the highest potential to yield important scientific discoveries, will require a higher degree of autonomy. The latter includes the ability of the spacecraft to autonomously select the landing site using real-time data acquired during the descent phase. This paper presents the development of an Evolutionary Fuzzy Cognitive Map (E-FCM) model that implements an artificial intelligence system capable of autonomously selecting a landing site with the highest potential for scientific discoveries constrained by the requirement of soft landing in a region with safe terrains. The proposed E-FCM evolves its internal states and interconnections as a function of real-time data collected during the descent phase, therefore improving the decision process as more accurate information becomes available. The E-FCM is constructed using knowledge accumulated by planetary experts and it is tested on scenarios that simulate the decision process during the descent phase toward the Hyndla Regio on Venus. The E-FCM is shown to quickly reach conclusions that are consistent with what would be the choice of a planetary expert if the scientist were presented with the same information. The proposed methodology is fast and efficient and may be suitable for on-board spacecraft implementation and real-time decision making during the course of robotic exploration of the Solar System. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Future science-driven and less constrained NASA and ESA missions to explore planetary bodies in the Solar System will require soft landing at sites that have the potential to yield the highest geological and exobiological information. During the planning of any landing mission, scientists and engineers select a landing site on the planetary body of interest using data acquired during the reconnaissance of previously deployed robotic spacecrafts. The completeness of currently available information varies widely from planetary body to planetary body and depends critically on the number of missions deployed on the particular planet and/or natural satellite as well as on their geophysical properties (e.g., dense, thin, or no atmosphere), which may inherently make the acquisition of surface data from orbiting spacecrafts very difficult. For example, instruments onboard spacecrafts currently orbiting Mars (e.g., Mars Reconnaissance Orbiter [18]; Mars Odyssey [36]) have been streaming a wealth of data about the red planet, thus

∗ Corresponding author. Tel.: +1 520 312 7440. E-mail addresses: [email protected] (R. Furfaro), wfi[email protected] (W. Fink), [email protected] (J.S. Kargel). 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2012.01.014

providing a large amount of information to the scientists who can employ all the available data to make the best possible landing site selection. On the contrary, other planetary bodies of high interest, such as Venus and Titan, have less information available and consequently, a priori landing site selection becomes more problematic. For example, due to a dense and opaque atmosphere, which limits the intensity of the reflected electromagnetic signal collected by passive optical instruments, both Venus and Titan have been mainly mapped using Synthetic Aperture Radar (SAR, e.g., Magellan SAR [2] and Cassini SAR [7]), which generates images using the backscattered signal collected by the spacecraft antenna. SAR images have limited spatial resolution (e.g., ∼500 m in the case of Titan SAR mapping mode [7]) and they are harder to interpret. If a safe and accurate landing is desired, images with a spatial resolution of less than 1 m are generally required to resolve features that may be hazardous in nature. Clearly, the exclusive use of currently available SAR data makes any groundbased landing site selection on Venus and Titan extremely difficult. Importantly, even in the case of Mars, a priori selection of a suitable landing site is a complex process which involves the planetary science community at large. For example, NASA’s Jet Propulsion Laboratory has been organizing a series of workshops to actively engage Mars scientists to reach a consensus for the

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selection of the upcoming Mars Science Laboratory (MSL) landing site (http://marsoweb.nas.nasa.gov/landingsites/msl/ workshops/4th workshop/). Whereas ground-based pre-planning and landing site selection is an important activity for any space mission comprising a lander, the final and best landing site selection may be possibly executed in real-time during the Entry, Descent and Landing (EDL) phase itself. Here, we define “best” as the landing site that yields the highest potential for scientific discoveries and that satisfies specific landing safety constraints. Real-time, autonomous selection of such a site requires that the robotic lander is equipped with a system capable of a higher degree of autonomy. Such a system should (1) include software packages that enable fully automated and comprehensive identification, characterization, and quantification of features information within an operational area with subsequent target prioritization and selection for close-up reexamination (e.g., Automated Global Feature Analyzer, AGFA [9,10] for target prioritization); and (2) integrate existing information with acquired, “in transit” spatial and temporal sensor data to automatically perform intelligent planetary landing, which includes identification of sites with the highest potential to yield significant geological and astrobiological information [8,14,15]. The ability to autonomously interpret and make decisions using real-time data collected during the descent toward the planetary body is extremely valuable. A recollection of what happened during the selection process of the landing site for the Phoenix Mission to Mars may help give a clear picture of the problem [40]. During the initial selection phase (2004), scientists based their decision on the best Mars data set available at the time. More specifically, a large variety of landing sites were analyzed using a combination of visible and infrared as well as altimetry data coming from Mars Odyssey THermal EMission Imaging System (THEMIS [6]), Mars Orbiting Laser Altimeter (MOLA [43]) and Mars Global Surveyor (MGS) Mars Orbiting Camera (MOC [29]). Science prioritization within the selected latitude band resulted in establishing four premiere candidate (named A, B, C and D). Region B was initially preferred and was in a very strong position to be the final choice. However, the insertion of Mars Reconnaissance Orbit in September 2006 and the deployment of the camera system with the highest spatial resolution ever sent to another planet (High-Resolution Imaging Science Experiment (HiRISE), up to 25 cm/pixel [30]), provided the Mars science community with additional data. A close inspection of site B showed an unexpected abundance of boulders and rocks. The selection team reinitiated a landing site search using the augmented data set and converged to the final site selection consisting in a sub-area of region D [40]. In this work, we design and simulate an advanced intelligent system capable of autonomously selecting landing sites using data collected in real-time from the lander sensors during the descent toward the planetary body surface. We use Evolutionary Fuzzy Cognitive Maps (E-FCM [5]) to model the cognitive reasoning of a planetary scientist that is presented with the same information available to the lander on-board computer and decides in real-time where to direct the spacecraft for safe landing. While a large number of Artificial Intelligence (AI) methods are available to approach the problem (e.g., fuzzy experts [13–15]), E-FCM techniques for real-time landing decision making were selected because of the map’s ability to dynamically model complex processes comprising a large number of interacting parameters. Importantly, available experience and knowledge accumulated by planetary scientists can be easily translated into a cognitive map that is expressed through the use of concepts connected via causal relationships. Moreover, the ability of the proposed algorithm to reach conclusions in a fast and efficient way (e.g., [46–48]), makes it ideal for real-time implementation on the microprocessor onboard the descending vehicle.

To the best of our knowledge, FCMs have been only recently employed to design algorithms for autonomous interpretation of planetary data [17]. The main goal of this work is to show how FCMs in general, and E-FCMs in particular, can be used to advance the state of the art of autonomous reasoning in planetary exploration by providing an effective inference platform that can be easily understood by planetary scientists. This paper is organized as follows. In Section 2, a theoretical background on autonomous landing on planetary bodies is presented. The problem of landing on Venus and Titan is reviewed and linked to the current interests and needs to develop AI methods for the autonomous exploration of the Solar System. A background on the theory of E-FCM is also provided. In Section 3, the methodology employed to design the proposed E-FCM algorithm for real-time on-board landing site selection is outlined. In Section 4 the proposed algorithm is tested on three possible Venus scenarios and the results of E-FCM Monte Carlo simulations discussed. Section 5 draws conclusions and outlines future research.

2. Theoretical background 2.1. The geology of Venus and Titan Venus and Titan are two of the planetary bodies in the Solar System that have fascinated scientists for centuries. In the planetary science community, Venus is commonly referred to as Earth’s twin sister. Indeed, the second planet from the Sun is the most similar to Earth as they share the same bulk composition and have comparable radius and density. However, Venus highlights a thick, dry, and hazy atmosphere mainly comprised of carbon dioxide (96.5%), which is responsible for a surface pressure 90 times greater than Earth’s and a surface temperature of 468 ◦ C. The upper layer of highly reflective clouds comprising high concentration of sulfuric acid prevents imaging the surface in the visible regime. Our current understanding of the formation of the inner planets during the early history of the Solar System indicates that both Earth and Venus formed from similar materials [31]. However, a major difference between the two planets is marked by their water content. More specifically, whereas Earth is water rich, Venus is extremely dry. Measurements from the Pioneer spacecraft showed that Venus is the planet with the highest Deuterium-to-Hydrogen ratio in the Solar System, which indicates that the planet may have experienced a dramatic loss of water throughout its history. Understanding Venus’ water evolution and fate is critical (a) to characterize the planet’s evolution, and (b) to predict the possible future of Earth and in general the evolution of terrestrial-like planets around stars. On Earth, water is important because it is linked to plate tectonics. Water content on Earth’s interior is responsible for softening the crust and therefore mobilizing the outmost layer through convection. It is accepted that Venus experienced a massive runaway greenhouse [21] and it has been proposed that water recycling on the crust, conducive to plate tectonics, may have happened early in the planet’s history [38]. Currently, because of the lack of water content, which results in a stiff astenosphere, no plate tectonics are observed on Venus. Nevertheless, spacecraft observations reveal an extremely active planet featuring a wealth of volcanic features. Important to mention among the geological features that are unique to Venus are the “tesserae units” (Fig. 1B), which are sets of intersecting fractures covering regions that experienced a higher level of deformation [2]. Such features are important for close-up examination after landing as they represent the oldest material on the surface which may unveil the geological past of the planet. Titan is Saturn’s largest moon and also the only natural satellite in the Solar System with a thick and dense atmosphere. Its bulk

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Fig. 2. Venera 10 Landing ellipse. The area has been divided in three régions, each containing features (real and hypothesized) that are used as ground truth to test the E-FCM algorithm.

Fig. 1. Examples of SAR images from Cassini and Magellan. (A) Cassini SAR image obtained by the spacecraft radar working in image mode during a near-polar flyby on February 22, 2007. The image shows a big island smack in the middle of one of the larger lakes on the northern region of Titan (Credit NASA/JPL). B) Magellan SAR image of a complex ridge terrain (tesserae), centered at 21◦ S, 2.5◦ E in Alpha Regio. The region is characterized by three or more sets of intersecting lineaments (Credit NASA/JPL).

composition is estimated to be 60% rock and 40% water ice. The latter is the main ingredient that comprises the backbone of crust and mantle overlying a rocky core [39]. Titan is very enigmatic. The nature of its hazy atmosphere has been a matter of debate since its discovery in the 1940s [24]. Over the course of the last few decades, using both ground-based, Earth-orbit, and Cassini Spacecraft measurements, it has been established that its atmosphere is comprised mainly of nitrogen with a relatively conspicuous presence of methane (∼4%). Since the methane is continuously being destroyed by the UV photolysis acting on the upper layers of the atmosphere, the source of its resupply has been widely discussed. It has been initially proposed that Titan was covered by a global ocean of methane-ethane [27] with the latter being a product of methane photolytic dissociation. Whereas recent Cassini observations excluded the presence of a global ocean, the on-board SAR instrument operating in imaging mode revealed a complex surface shaped by what seems to be a hydrological cycle: on Titan, methane plays a role similar to that of water on Earth [28]. The surface exhibits a rich variety of features conducive to eolian, pluvial, and fluvial processes including (a) channels carved by liquid methane and/or ethane [26]; (b) vast regions covered by dunes comprised of complex organics [25]; and (c) vast bodies of liquid, reminiscent of lakes or seas on Earth ([19], Fig. 1B). Fig. 1 shows two examples of SAR images that represent the best knowledge we have from orbit about the currently prevailing geological features on the surfaces of both Venus and Titan.

2.1.1. The problem of landing on Venus and Titan Landing on planetary bodies with dense atmospheres such as on Titan and Venus is extremely challenging. In any future science-driven and less constrained landing scenario, including soft precision landing (<100 m landing ellipse diameter) and pin-point landing (<1 m landing ellipse diameter), autonomy will play a more and more critical role in (a) providing autonomous selection of the landing site based on real-time data, (b) implementing a targeting program that will generate a flyable trajectory to the selected target, and (c) executing real-time guidance algorithms to direct the system to the desired location. Current flight-ready technology has been effective in landing a spacecraft on a preselected region within a landing ellipse of 120 km × 20 km (e.g., Phoenix Mission to Mars [37]). Future missions (e.g., MSL [41]) have the potential to shrink the landing ellipse to less than 10 km. Despite such progress in landing technology, autonomous real-time landing site selection has never been implemented. The latter is extremely desirable because the selection takes place in real-time by autonomous reasoning on data collected during the descent to determine sites with the highest potential of scientific discoveries and avoid areas with high hazard potential. In human history only one landing probe has been delivered to the Titan surface, i.e., ESA’s Huygens probe, which landed on the Titan surface on January 14, 2005 [44]. The descent was completely preplanned and unguided due to scarce surface information. The probe landed on what is now interpreted to be a methane-rich outflow channel. During the descent, the camera system collected a set of images showing a plethora of interesting geological features, which may have constituted interesting landing sites in their own right. Landing on Venus has been attempted many times as documented by the results from Russian Venera and Vega missions [3]. The Venus surface has been mapped using the Magellan SAR, which is the only means to probe the surface through its dense atmosphere. Fig. 2 shows the landing ellipse of the region selected by Venera 10 which also represents the planetary area employed to test our E-FCM design (see Section 4). The area is comprised of 8 stratigraphic units [1] and, for our analysis, has been subdivided into three regions. Region #1 is mainly comprised of what is classified as “Tesserae Units”, i.e., ancient terrains featuring dislocated units of tectonic origin. Region #2 is mainly comprised

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of highly fractured plains that exhibit lobate flow field features. Region #3 exhibits a smooth (radar-dark) behavior interpreted as volcanic planes comprising materials that resemble terrestrial volcanic rocks [20]. For all Venera and Vega missions the landing sites were preselected during the planning phase. 2.2. Artificial intelligence for space exploration: the need for fuzzy cognitive models Over the past few decades, the robotic exploration of planetary bodies (i.e., via spacecrafts, orbiters, landers, lake landers, and rovers) has been an effective means of providing scientists with in situ and remote data collection. Indeed, Solar System exploration is focused on understanding the processes and mechanisms that shaped the evolution of planets including their interior and surfaces. Future robotic, less constrained and science-driven planetary reconnaissance will require a much higher degree of autonomy (see for example the NASA-award-winning Tier-Scalable Reconnaissance mission paradigm [8,11,22]). It is expected that truly autonomous systems for space exploration will rely on integrated AI algorithms that are capable of (a) performing fully automated and comprehensive characterization of the features within the operational region, and (b) reasoning over data collected in real-time while en-route to determine the locales with the highest scientific context, i.e., regions that contain relevant geological and exobiological information. Furfaro et al. [13–15,17] proposed the use of fuzzy logic as a framework to design autonomous algorithms that mimic the reasoning process of planetary scientists. Indeed, fuzzy logic is a powerful methodology that can be effectively employed to design expert systems and/or cognitive maps for autonomous reasoning in any kind of space exploration mission architecture. Whereas fuzzy expert systems and FCMs/E-FCMs share the same general framework, they are conceptually different. More specifically, fuzzy experts are systems that acquire knowledge in a structured form via fuzzy-rules [34,42] which comprise the knowledge-base of the algorithm. Conversely, FCMs and their evolutionary extension E-FCMs represent knowledge via a web of causal interconnection between concepts. Importantly, since planetary scientists are required to be at the core of any deployment of robotic devices for Solar System exploration, they should be also critically involved in the design of reasoning algorithms. Indeed, fuzzy logic, which is the foundation of both abovementioned AI schemes, is the basis for human communication and therefore the paradigm makes the interaction between AI domain experts and planetary scientists easier. Any integrated AI scheme of choice should not only make autonomous decisions but also provide sound explanations for its reasoning. Fuzzy logic provides a sound linguistic framework that allows communication between human and machine, also providing scientists with a way to directly implement their proper knowledge-base, thereby incorporating the scientists as an integral part of the design process. Over the past few years, fuzzy expert systems for space exploration have been devised and simulated for Mars and Titan [13–15], and in addition, have been proposed for integration in a framework for the exploration of Titan via a hot-air balloon [16]. FCMs have been proposed and simulated for the autonomous recognition of cryovolcanism on Titan using SAR data [17]. FCMs are very attractive because of their ability to describe causal relationships between qualitative concepts, rendering them valuable for the case of space exploration and planetary reconnaissance. Knowledge is readily available through a visual inspection of the map schematic for an easier interaction between AI experts and planetary scientists during the design process. Importantly, FCMs can also be trained to fine-tune the algorithm against expert conclusions [45]. Whereas FCM are “static” maps in the sense that conclusions are

Fig. 3. Example of a typical E-FCM architecture.

reached when the equilibrium is achieved through an iterative process, the E-FCM may have an additional advantage for situations where the environment is continuously changing over time and decisions have to be made on a timely basis. Concepts and causal relationships are continuously updated according to a clock so that the system is continuously evolving. Such features are important in the landing scenarios investigated in this paper where decisions are time-critical and depend on continuous data streams provided in real-time from the onboard sensors. E-FCMs can be further extended to autonomous agents that work in coordination during the course of planetary exploration (e.g., rovers and boats, see [11,12,22,52]).

2.3. The theory of evolutionary Fuzzy Cognitive Maps Evolutionary Fuzzy Cognitive Maps (E-FCM [4,5]) may be considered an extension of FCMs specifically developed to model variable internal states as well as the dynamic, complex, and causally related context variables (i.e., coming from data acquired during the landing descent). In its basic formulation, FCMs are digraphs designed to capture the cause/effect relationships exhibited by a system [23]. Two basic elements form the backbone of the maps: nodes and arcs. Nodes are the concepts representing factors and attributes of the modeled system, e.g., inputs, outputs, states, variables, events, goals, as well as trends. Arcs are introduced to describe the causal relationships between concepts with a degree of causality. Importantly, FCM models incorporate the available knowledge and expertise by selecting appropriate concepts and causal connections between them. Extending this approach further, in E-FCMs the concept states evolve in real-time as a function of the internal mental state, external inputs, and possibly external causalities. Fig. 3 shows an example of the typical ingredients required to construct an E-FCM. Each concept is equipped with its own update schedule, and subjected to a small self-mutation probability. Moreover, the causal connection between concepts is fired according to a specified conditional probability. The evolutionary extension to FCMs has been chosen due to the highly dynamic nature of the landing selection process. During the EDL phase, data are continuously streamed in real-time and they are processed to determine the landing site using all available information. However, such data are remotely collected and subjected to uncertainty due to the limited resolution of the instrumentation. With the assumption that as the lander gets closer to the targeted region, more accurate information is available, the E-FCM must have the ability to adapt and

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dynamically update the strength of the connections between concepts to account for newly available data. As shown in Fig. 3, the E-FCM is enclosed in a box, which contains all concepts and causal relationships. The updates occur via a reference time or “Clock”, which is the time during which the concepts are updated. The definition of a Clock marks a major difference to conventional FCMs. Concepts and causal relationships are described in detail next. 2.3.1. Concepts Differently than conventional FCMs, concepts are represented by tuples of properties, i.e., A = [AV , T, PS ]. Here, AV denotes the fuzzy values of the concepts C (same as FCM). Concepts values generally range between [−1, 1] or [0, 1]. For a system of N concepts, AV = [AV1 , AV2 , . . ., AVN ] is an evolving vector that represents the time evolution of each of the individual concept values Ci . T = [T1 , T2 , . . ., TN ] is a N × 1 vector that represents, for each concept, the evolving time schedule. The latter accounts for the fact that various concepts may have a different real-time update schedule. PS = [PS1 , PS2 , . . ., PSN ] is the state mutation vector, which accounts for the possibility that each concept may randomly alter its internal state in real time. According to Cai et al. [4], the self-mutation probability must be modeled as a small value to avoid system instability. 2.3.2. Causal relationships The causal relationship between concepts is defined as the tuple R = [W, Pm ], which extends the conventional FCM approach, which uses only the fuzzy connection matrix, to allow the incorporation of uncertainty via fuzziness and randomness. For a system of N concepts, W = {wij } is the N × N weight matrix that represents the causal relationship between two concepts in fuzzy terms (e.g., high, low, medium, absent, etc.). The connections can be either positive or negative. Pm = {pi→j } is the N × N matrix of causal probabilities between the interconnections. Causal probabilities may also be described in fuzzy terms. They represent the uncertainty of connections between concepts. For example, pi→j describes the probability that the concept Ai influences Aj with the strength defined by the correspondent wij . The value Ai of the concept Ci is computed by accounting for all possible influences deriving from interconnected concepts as well as the causal probabilities deriving from Pm . Generally, the probability matrix is not symmetric. At each time interval and according to the predefined time schedule T, the concepts are updated using the following formula:

⎛

Ai (k + 1) = f

⎞

⎜ ⎟  ⎜ ⎟ ⎜Ai (k) + ⎟ A (k)W j ji ⎟ ⎜ ⎝ ⎠ i = 1, N

(1)

i= / j where f(·) is the activation function used to regulate the state variable (bivalent, trivalent or logistic). The weight matrix is evaluated according to the causal probability matrix and the value is randomly changed according to the self-mutation probability. As in conventional FCMs, the E-FCM concepts are initialized using either measurements coming from real data or fuzzy values coming from qualitative expert description of the data. For the landing problem that is under analysis, the information processed by the designed E-FCM is generally extracted from sensor data acquired in real-time. Indeed, images (or other sensor data sets) collected during the descent are processed by appropriate algorithms (e.g., AGFA [10]) to extract the features of interest. However, numerical values representing the collected features fed to the E-FCM must be fuzzified and mapped onto the appropriate interval, i.e., either [−1, 1] or [0, 1]. The initial concept values are used to initialize the iterative process that is generated by free interaction between the map

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concepts. Conventional FCMs are dynamical systems that exhibit the typical behavior of non-linear systems including (a) converging to an equilibrium point (fixed point), i.e., the values of the concepts are stabilized to a fixed numerical value, (b) converging to a limit cycle, i.e., the values of the concepts are cyclically repeated with a fixed time-period, and (c) exhibiting chaotic behavior with concepts changing their values in a non-deterministic fashion. Generally, the asymptotic stability of conventional FCMs is an important parameter that indicates that the map is properly designed. Indeed, it is generally desired that the map reaches a final conclusion and both oscillations and chaotic behaviors are not desirable. E-FCMs can be conceived as dynamical systems that are continuously influenced by the change of environment (external stimuli). Global, long-term stability may be important depending on the length of the simulation and the nature of the problem. For real-time landing time selection, it is mostly important to guarantee the map’s bounded stability during the descent time-period. Indeed, a decision must be generally taken after a set number of seconds depending on the trajectory profile and the ability of the landing vehicle to reach the selected site. 2.3.3. Methods to construct E-FCM The approach employed to design E-FCMs plays a major role in ensuring that the map has the ability to capture the reasoning process with sufficient fidelity. Clearly, the behavior and decisionmaking capability of the proposed E-FCM depends on our team’s understanding of the landing problem. The latter includes (a) understanding geological data to ensure that the system has the ability to select the site that yields the highest scientific return, and (b) understanding surface hazards so that the system avoids sites that have the highest hazard potential, or, as a matter of fact, any hazard that hamper the vehicle safety. Generally, for the case of planetary reconnaissance and space exploration, planetary scientists possess knowledge and understanding of the processes occurring on remote planetary bodies. Consequently, the proposed E-FCM must be designed to incorporate knowledge coming from the planetary science domain to exploit expert knowledge gained by the scientific community over years of analysis of data from previous missions. Our group’s expertise is leveraged to determine the number and typology of concepts comprising the structure of the proposed E-FCM. For the landing problem, the overall expert goals are (a) to identify the concepts important for modeling geomorphological as well as hazardous processes occurring on the surface of Venus and Titan, (b) to define the critical features that can be extracted from remotely sensed data, and (c) to transform the scientific knowledge into a weighted, interconnected dynamic graph. Moreover, the experts must determine the map’s causal probabilities as a function of the descent time during which the E-FCM is actively processing incoming sensor information and recommending navigational and guidance actions. As stated above, the development and construction of the EFCM is executed using knowledge accumulated by field experts who define the type and numbers of concepts, the strength of the connections, and also the causal probability matrix. Various methodologies are available to define the connection strengths. Papageorgiu et al. [33] proposed to define the strength of the connection between concepts using fuzzy IF–THEN rules in the following fashion: IF value of concept Ci is B THEN value of concept Cj is C and the linguistic weight wij is E. Here, B, C, E are linguistic fuzzy values determined via appropriate membership functions with values in the range [0, 1] for direct connection and [−1, 0] for inverse connection. Indeed,

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Very Low

Medium

Low

High

Very High

1

Degree of membership

0.8

0.6

0.4

0.2

0 0

0.1

0.2

0.3

0.4

0.5 0.6 Influence

0.7

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Fig. 4. Membership functions associated with the fuzzy linguistic concepts “Very High”, “High”, “Medium”, “Low”, Very Low”. The selected membership functions are triangular (H, M, L) and trapezoidal (VH, VL).

for any of the established concepts, the experts determine the negative or positive effect of one concept on the others with a fuzzy degree of causation. Importantly, expert opinions can be accounted individually via independent linguistic rules that are subsequently aggregated and de-fuzzified. After detailed discussion, our team converged on the structure of the map so that only one linguistic rule is defined to infer the fuzzy causal connection between concepts (i.e., fuzzy aggregation is not required). Generally, we define the influence between two concepts to be either “Positive” (P) or “Negative” (N). The fuzzy causal connection is determined using the appropriate linguistic fuzzy variable [32,33]. In this case, five variables have been employed: Very Low (VL), Low (L), Medium (M), High (H), Very High (VH). Each linguistic variable is associated with a membership function as shown in Fig. 4. The experts define the interconnection between pairs of concepts using one of the five selected fuzzy variables to describe the relationship between two concepts. The corresponding grade of causality is determined using the centroid method [35].

3. E-FCM design methodology for autonomous real-time landing site selection on Venus The problem of the autonomous selection of a landing site that integrates published knowledge and real-time acquired information on the descent toward the planetary surface is a complex process. Moreover, for a given planetary exploration scenario, establishing the criteria that allow a clear definition of what is the region that yields the maximum possible scientific information is a matter of open debate within the planetary science community. Here, we consider the case of landing on Venus and we focus on designing an E-FCM that autonomously selects the landing site that, among other observables, exhibits the terrain with the most ancient geologic features and hence has the potential to unfold a large portion of the geologic history of the planet [20]. However, the potential for scientific discoveries and geological understanding of any of the considered regions must be consistent with the ability of the spacecraft to safely land at the selected site. Because of the limited SAR resolution and the constant difficulties encountered by planetary data analysts to provide correct SAR image interpretation, a priori, off-line analysis of potential Venus landing regions may yield uncertain and incomplete scenarios. Indeed, many critical features that may increase (or decrease) the potential for scientific discoveries and/or potential hazards may simply not be detected and properly evaluated. Real-time data collected during the descent toward the planetary surface may critically provide additional information, but autonomous reasoning must be implemented considering the short timeline for EDL. Consequently, the overall goal is to construct an E-FCM that ingests data during portions of the EDL, and, for the pre-selected regions, infers what is the potential for scientific discoveries (in the sense clarified above) and potential for hazards, i.e., autonomously selects the best site for a safe landing. The constructed E-FCM evolves in time according to a prescribed schedule (a) to account for data streamed into the landing system from the sensors, and (b) to adapt for reasoning in the presence of data uncertainty and ambiguity. Our team designed an E-FCM model (Fig. 5) that accounts for 33 interconnected concepts, which are reported in Table 1. The selected concepts, which may be determined using real-time feature extraction software (e.g., AGFA [10]), are divided into three

Table 1 Concepts description and concepts values. Concepts

Concept description

Value

C1 , C12 , C23 : landing regions #1, #2, #3 C2 , C13 , C24 : potential for scientific discovery (PSD 1, 2, 3)

Index for landing site selection This concept indicates the potential exhibited by the region to yield significant discoveries This concept indicates the regional potential for landing hazards VPF indicates the level of presence for features associated to volcanic landforms FLF indicates the level of presence for features volcanic flows ATF indicates the level of presence for features associated with ancient terrains ST indicates the level of smoothness of the region RT indicates the level of roughness of the region HST indicates the high slope level of the region LST indicates the level of low slope level of the region FT indicates the level of featureless terrain of the region

Continuous value [0, 1] Five fuzzy values, {VL, L, M, H, VH}

C3 , C14 , C25 : potential for hazards (PHZ 1, 2, 3) C4 , C15 , C26 : volcanic plain features (VPF 1, 2, 3) C5 , C16 , C27 : flow-like features (FLF 1, 2, 3) C6 , C17 , C28 : ancient terrain features (ATF 1, 2, 3) C7 , C18 , C29 : smooth terrain (ST 1, 2, 3) C8 , C19 , C30 : rough terrain (RT 1, 2, 3) C9 , C20 , C31 : high slope terrain (HST 1, 2, 3) C10 , C21 , C32 : low slope terrain (LST 1, 2, 3) C11 , C22 , C33 : featureless terrain (FT 1, 2, 3)

Five fuzzy values, {VL, L, M, H, VH} Six fuzzy values, {A, VL, L, M, H, VH}

Six fuzzy values, {A, VL, L, M, H, VH} Six fuzzy values, {A, VL, L, M, H, VH}

Five fuzzy values, {VL, L, M, H, VH} Five fuzzy values, {VL, L, M, H, VH} Five fuzzy values, {VL, L, M, H, VH} Five fuzzy values, {VL, L, M, H, VH} Six fuzzy values, {A, VL, L, M, H, VH}

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Table 2 Initial weight matrix (33 × 33) expressed in linguistic form. The linguistic values are expressed using the following terms: Very Low (VL), Low (L), Medium (M), High (H), Very High (VH) and can be either Positive (P) or Negative (N). The following numerical values are assigned: VL = 0.1, L = 0.25, M = 0.5, H = 0.75, VH = 0.9. C1 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C20 C31 C32 C33

C2

C3

C4 C5 C6 C7 C8 C9 C10 C11 C12 C13

C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24

NH

C25 C6 C27 C28 C29 C30 C31 C32 C33

NH

PH NL PL PM PVH

NH

NH PH PH NH NH

NH

NH PH NL PL PM PVH

NH NH

NH PH PH NH NH

NH PH NL PL PM PVH

NH

NH PH PH NH NH

Table 3 Initial probability matrix (33 × 33) expressed in numerical form. P1 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22 P23 P24 P25 P26 P27 P28 P29 P20 P31 P32 P33

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

P20

P21

P22

P23

P24

P25

0.5 0.5 0.5 0.5 0.5

0.9

0.5 0.5 0.5 0.5 0.9 0.5 0.5 0.5 0.5 0.5

0.9

0.5 0.5 0.5 0.5 0.9 0.5 0.5 0.5 0.5 0.5

0.9

0.5 0.5 0.5 0.5 0.9

P26

P27

P28

P29

P30

P31

P32

P33

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Evaluaon Landing Region #1 C5: FLF 1 C4: VPF 1

PL P4,2 = 0.5 (in)

PH P31,25 = 0.5 (in)

NH P1,2 = 1

C25: PHZ 3 NH P29,25 , = 0.5 (in)

NL (in) P25,23 = 1

C23: Landing Region #3

C33: FT 3

C28: ATF 3 PVH P28,24 = 0.5 (in)

C24: PSD 3

NH P1,2 = 1

NH P1,2 = 1

PH (in) P24,23 = 1 PL P26,24 = 0.5 (in)

PM P27,24 = 0.5 (in)

C26: VP VPFF 3

Evaluaon Landing Region #3

PH P9,3 = 0.5 (in) C10: LST 1

NH P10,3 = 0.5 (in)

Evaluaon Landing Region #2

C15: VPF 2

NH P32,25 0 5 (in) 32 25 = 0.5

PH P30,25 = 0.5 (in)

C27: FLF 3

C3: PHZ 1

C1: Landing Region #1

C32: LST 3

C30: RT 3

C29: ST 3

C9: HST 1

NL (in) P3,1 31= 1

PH ((in) P2,1 = 1

PH P8,3 = 0.5 (in)

C11: FT 1

C2: PSD 1

C31: HST 3

C8: RT 1

NH P7,3 = 0.5 (in)

PVH P6,2 6 2 = 0.5 (in)

PM P5,2 = 0.5 (in)

C7: ST 1

C6: ATF 1

NH P1,2 = 1 NH P1,2 = 1

NH PL P1,2 = 1 P 15,13 = 0.5 (in) PH (in) P13,12 = 1 C12: Landing Region #2

PM P16,13 = 0.5 (in)

C13: PSD 2

NL (in) P14,12 = 1

C16: FLF 2

PVH P17,13 = 0.5 (in) C17: ATF 2 C22: FT 2

C21: LST 2

NH P18,14 = 0.5 (in)

NH P12,14 = 0.5 (in)

C14: PHZ 2

PH P20,14 20 14 = 0.5 ((in)

C18: ST 2

PH P19,14 = 0.5 0 5 (in) C19: RT 2

C20: HST 2

Fig. 5. E-FCM topological structure. The weights are defined using fuzzy linguistic values (VL = 0.1, L = 0.25, M = 0.5, H = 0.75, VH = 0.9). P and N indicate respectively direct and inverse connection. Initial values of probabilities are indicated as well.

major groups. Each group contains input concepts that account for features of interest on the surface of Venus. Generally such features are required to infer for any of the three regions located within the selected landing area on the southern part of the Venusian Hyndla Regio (see Fig. 2) both the potential for scientific discoveries and the potential for hazards. Indeed, the E-FCM is asked to select one landing site among the three pre-identified landing regions using hypothesized data acquired during a portion of the descent flight. For each of the three regions, a group of 4 variables is identified to influence the potential for scientific discoveries. More specifically, Volcanic Plain Features (VPF, e.g., C4 for landing region #1), Flow-Like Features (FLF, e.g., C16 for Landing region #2), and ancient terrain features (ATF, e.g., C28 for landing region #3) have been selected for their linkage with the geological history of Venus and the influence on the potential for unfolding scientific discovery upon close in situ examination. A fourth feature, called Featureless Terrain (FT, e.g., C11 for landing region #1), has been introduced to account for terrains that do not show features that are relevant to scientific discovery, i.e., influence negatively the potential for scientific discoveries. Conversely, a group of 5 variables has been determined to influence the potential for hazards. For example, smooth terrains (SM, e.g., C7 , for landing region #1) and Low Slope Terrains (LST, e.g., C21 for landing region #2) reduce the potential for landing hazards, whereas Rough Terrains (RT, e.g., C30 for landing region #3) and High Slope Terrains (HST, e.g., C20 for landing region #2) may dramatically increase it. Table 1 also reports the fuzzy values employed to qualitatively describe the selected features. Fig. 5

shows the E-FCM topology as conceived by our team. The selected architecture has a modular structure. For any of the selected three regions, the input concepts (obtained by processing real-time data) influence positively or negatively both the potential for scientific discoveries and for hazards, which in turn affect the potential for landing in the specified region. The “potential for landing” concepts of the three regions are then connected in a loop where they compete against each other. The E-FCM will finally select, within a specified time, the site with the highest landing potential. As with the map’s topology, the weight matrix is selected by our team’s planetary experts. As reported in Table 2, the weights have been established in a linguistic fashion using fuzzy terminology such as “High”, “Low”, “Medium” etc. For example, the link between concept C6 (ATF 1, ancient terrain features for landing site #1) and C2 (PSD 1 or potential for scientific discoveries on landing site #1) is established to be “Positive Very High (PVH)”, i.e., using an IF–THEN formalism:

IF a small change in the value of concept C6 occurs THEN a very high change in the value of the concept C2 is caused. Inference: the influence of C6 on C2 is Positive Very High.

Conversely, the influence between the value of the concept C7 (ST1 or smooth terrain in landing Site #1) and C3 (PHZ 1 or potential for hazards on landing site #1) is “Negative Very High (NVH)” or:

R. Furfaro et al. / Applied Soft Computing 12 (2012) 3825–3839

IF a small change in the value of concept C7 occurs THEN a negative high change in the value of the concept C3 is caused. Inference: the influence of C7 on C3 is Negative Very High. Importantly, in absolute terms, the influence of the potential for scientific discoveries and hazards on the “landing region” concepts has a value of PH and NH, respectively, i.e., a positive (negative) high change in PSD (PHZ) causes a positive (negative) increase on the Landing Region. However, the connection is selected to be time dependent in the following sense: During the descent toward the targeted area, the influence of the potential for scientific discoveries is initially set to be PH and the potential for hazards is initially set to be Negative Low (NL). As the lander gets closer to the surface, the influence (weight) of the hazard on the landing site selection is increased (limit to NH when the final decision is made), whereas the influence (weight) of the potential for scientific discoveries is reduced (limit to PL when the final decision is taken). The goal is to ensure that priority is given to landing safety, especially when less uncertain, higher resolution data are available. The probability matrix Pm is also established by our field experts and for certain connections it is assumed to be time dependent. As a general guideline, the probability of connection between input data and derived concepts (e.g., p4→2 , p11→3 , the probability of connecting with weight w4,2 and w11,3 between concepts C4 , C11 and C2 , C3 , respectively) is assumed to increase with the time of flight to account for the fact that uncertainty in data is less pronounced and therefore the connection is more probable. Table 3 shows the probability matrix at the beginning of the descent phase. 4. Simulations and results A number of scenarios have been considered to simulate the behavior of the E-FCM algorithm in real-time landing site selection situations. It is assumed that the scientific team responsible for soft landing on Venus pre-selects the southern part of Hyndla Regio as the desired landing area (see Fig. 2). The area is subdivided into three landing regions for which the “ground truth” is assumed to be known and established a priori but not available to the planetary analysts before the descent phase is completed. It is also assumed that the mission Guidance, Navigation and Control (GNC) team has designed a descent trajectory such that the lander can autonomously select the landing site using the E-FCM before tF , time after which guidance constraints impose that the other two regions are outside the reachability domain. In this context, the spacecraft is assumed to collect data for 120 s before tF has elapsed. The information is updated every 5 s during which the lander acquires and processes images to extract the features that are input to the E-FCM. For any of the established scenarios, it is assumed that the system collects data with an uncertainty that is a function of the flight time. More specifically, the “ground truth” is set to be the mean value of a data sampling Gaussian distribution with a standard deviation that decreases as tF is approached. Indeed, as the lander gets closer to the surface, the improved instrument resolution yields more accurate data. With the above described setting, data are continuously updated and the E-FCM is run to infer, at each given time interval, what is the best landing region based on the available data and using a specified update schedule, which selects the connection according to the specified probability matrix (see Section 3). Finally, it is noted that all concepts are updated synchronously (same time schedule) and no self-mutation probability is implemented. All simulations have been implemented using the MATLAB® computational environment. In the following, three scenarios are considered.

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Table 4 Ground truth for the landing scenario #1. Scenario #1

Landing region #1

Landing region #2

Landing region #3

VPF FLF ATF ST RT HST LST FT

L L H H L L H VL

L VH A H L L H VL

VH L A H L L H VL

4.1. First scenario For the first scenario, the “ground truth” is constructed using fuzzy linguistic values as reported in Table 4. In this case, the available hypothesized data show a region #1 that is the most suitable for landing. Indeed, the large presence of ancient terrain features makes the region more interesting from the perspective of unfolding the ancient geological history of Venus. All regions are shown to be very safe for landing (high value for smooth and low slopes terrains). Landing regions #2 and #3 have also flow-like features and volcanic terrains, which may be of scientific interest but with lower priority. It is therefore expected that the E-FCM selects landing region #1 as the final landing scenario. A set of 1000 Monte Carlo simulations is executed to evaluate the performance of the E-FCM on the first scenario. Generally, each of the simulations represents an independent descent toward Venus surface. For each case, the initial conditions required to initiate the map are drawn from a sampling Gaussian distribution. More specifically, each simulation is initiated by setting up an initial concept value vector whose numerical values are assigned using a normal distribution with the mean established by the ground truth and a standard deviation of 0.4. Although the selection of the initial standard deviation is arbitrary, it is sufficiently high to model the amount of uncertainty expected at the beginning of the descent phase. Since the initial standard deviation is fairly high, the sampling may yield values outside the [0, 1] range. If that occurs, the concept value is assigned with the value corresponding to the closest boundary (i.e., 0 for negative values and 1 for values higher than 1). The E-FCM evolves both weights and concepts with input values updated every 5 s during the descent. As the time of flight progresses, the flight sensors acquire more precise data, i.e., data closer to the ground truth. Consequently, the standard deviation is assumed to (linearly) decrease with time. Fig. 6 shows the detailed E-FCM behavior for one simulation out of the 1000 cases, reporting for all regions the time evolution of landing concept values (A) as well as the values for potential for scientific discoveries (PSD) (B) and potential for hazard (PHZ) (C). As shown in Fig. 6A, the highest (final) value is reached for region #1, which wins the competition against the other two regions. In this specific case, landing region #1 is constantly selected as the best choice throughout the descent. Fig. 6B indicates that region #1 is the one with the highest potential for scientific discoveries, which is consistent with our expert analysis of the ground truth hypothesized data. The statistics associated with the Monte Carlo simulation are reported in Table 7 and Fig. 7. Out of the 1000 cases, region #1 was selected by the E-FCM 990 times (confidence factor of 99.9%), whereas region #2 and region #3 were selected for landing only 7 (0.07% confidence factor) and 3 times (0.03% confidence factor), respectively. Statistically, region #1 exhibits the highest mean PSD (Fig. 7A), whereas all regions have the same statistical distribution for PHZ with a mean close to 0.05 indicating very low potential for hazards (Fig. 7B).

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A) 700 PSD 1

600

PSD 2 PSD 3

Occu rrence

500 400 300 200 100 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distribution the FCM PSD concept B)

600 PHZ 1 PHZ 2

Occ urrence

500

PHZ 3

400 300 200

100

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Distribution the FCM PHZ concept Fig. 6. Landing scenario #1. The plots report the E-FCM time-dependent output for selected concepts (one sample of the 1000 Monte Carlo simulations). (A) Landing regions concepts values vs. time. The last value (120 s) is employed for autonomous site selection; (B) potential for scientific discoveries (PSD) concept values vs. time; (C) potential for hazards (PHZ) concept values vs. time.

4.2. Second scenario The second scenario is similar to the first one. As reported in the ground truth table (Table 5), landing regions #2 and #3 are identical to the first scenario. Landing region #1 still shows a high presence of ancient terrains, which makes it a more suitable landing site when analyzed from a scientific discovery viewpoint. However, region #1 now indicates a very robust presence of rough terrain and high slope surface, which is a strong indication of potential for hazards. The latter shall discourage the selection of region #1 as preferred landing site. As in the previous case, a set of 1000 Monte Carlo simulations is executed to evaluate the performance of the E-FCM on the second scenario. For each case, the initial conditions required to initiate the map are drawn from a sampling Gaussian distribution. Each simulation is initiated by setting up an initial concept value vector whose numerical values are assigned using a normal distribution with the Table 5 Ground truth for the landing scenario #2. Scenario #2

Landing region #1

Landing region #2

Landing region #3

VPF FLF ATF ST RT HST LST FT

L L H L H H L VL

L VH A H L L H VL

VH L A H L L H VL

Fig. 7. Statistical distribution of the final values of the E-FCM PSD (1, 2, 3, panel A) and PHZ (1, 2, 3, panel B) for the 1000 Monte Carlo simulations of landing scenario #1. On the x-axis the value of the PSD and PHZ concepts for the three regions are reported. Occurrence of the values is reported on the y-axis.

mean established buy the ground truth and a standard deviation of 0.4. Since the initial standard deviation is fairly high, the sampling may yield values outside the [0, 1] range. If that occurs, the concept value is assigned with the value corresponding to the closest boundary (i.e., 0 for negative values and 1 for values higher than 1). The E-FCM evolves both weights and concepts values with input values updated every 5 s and the standard deviation is assumed to be linearly decreasing with time. Fig. 8 shows the detailed E-FCM behavior for one simulation out of the 1000 cases, reporting for all regions the time evolution of landing concept values (A) as well as the values for PSD (B) and PHZ (C). As shown in Fig. 8A, the highest (final) value is reached by region #2, which wins the competition against the other two regions. In this specific case, landing region #2 closely competes with the other two regions especially in the first portion of the descent where priority is given to scientific information. However, in the second part of the descent, where more reliable data about the ground truth are collected, region #2 is selected as the safest. Fig. 8B indicates that region #1 is still the one with the highest potential for scientific discoveries consistently with our expert analysis of the ground truth hypothesized data. However, as reported in Fig. 8C the E-FCM elaborates the streaming of input data consistently increasing the value of the PHZ of region #1. Despite region #2 having a low PSD, the map gives priority to the safety of the landing vs. higher potential for acquiring scientific information. The statistics associated with the Monte Carlo simulation are reported in Table 7 and Fig. 9. Interestingly, out of the 1000 cases, region #2 was selected by the map 715 times (confidence factor of 71.5%) and region #3 was selected for landing 285 times (28.5% confidence factor). The E-FCM did not select region #1 for any of the

R. Furfaro et al. / Applied Soft Computing 12 (2012) 3825–3839

A

3835

700 600

PSD 1 PSD 2 PSD 3

Occ u urrence

500 400 300 200 100 0 0

B

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Distribution the FCM PSD concept

0.8

0.9

1

0.3 0.4 0.5 0.6 0.7 Distribution the FCM PHZ concept

0.8

0.9

1

600 PHZ 1 PHZ 2 PHZ 3

500

Occ urrence

400

300

200

100

0 0

Fig. 8. Landing scenario #2. The plots report the E-FCM time-dependent output for selected concepts (one sample of the 1000 Monte Carlo simulations). (A) Landing regions concepts values vs. time. The last value (120 s) is employed for autonomous site selection; (B) potential for scientific discoveries (PSD) concept values vs. time; (C) potential for hazards (PHZ) concept values vs. time.

1000 simulations. Statistically, both region #2 and region #3 exhibit a similarly low mean for PHZ (Fig. 9B) but region #2 has on average a slightly higher PSD than region #3 (Fig. 9A), which explains the higher confidence factor of the map in choosing region #2. 4.3. Third scenario The third scenario hypothesizes that region #1 and region #2 are relatively full of features indicative of high potential for scientific discoveries. Indeed, region #1 shows a medium level of volcanic plain related features, a very high concentration of flow-like features and an elevated presence of ancient terrains (Table 6). Similarly, region #2 exhibits high presence of volcanic Table 6 Ground truth for the landing scenario #3. Scenario #3

Landing region #1

Landing region #2

Landing region #3

VPF FLF ATF ST RT HST LST FT

M VH H H L L H VL

H VH M H L L H VL

H L A H H M H VL

0.1

0.2

Fig. 9. Statistical distribution of the final values of the E-FCM PSD (1, 2, 3, panel A) and PHZ (1, 2, 3, panel B) for the 1000 Monte Carlo simulations of landing scenario #2. On the x-axis the value of the PSD and PHZ concepts for the three regions are reported. Occurrence of the values is reported on the y-axis.

plane features, very high level of flow-like features and medium concentration of ancient terrain features (Table 6). Both regions #1 and #2 have low concentration of features that are indicative of high PHZ. Conversely, region #3 has only high presence of volcanic plane features and exhibits a high concentration of both smooth and rough terrains, which make the area generally not favorable for landing. As in the previous two scenarios, a set of 1000 Monte Carlo simulations is executed to evaluate the performance of the E-FCM on the third scenario. The simulations are run according to the same standard procedure described in Sections 4.1 and 4.2. Fig. 10 shows the detailed E-FCM behavior for one simulation out of the 1000 cases, reporting for all regions the time evolution of landing concept values (A) as well as the values for PSD (B) and PHZ (C). As reported in Fig. 10A, region #1 and region #2 closely compete for selection throughout the descent. In this specific case, region #1 is selected for landing. As shown in Fig. 10B and C both regions exhibit a similar trend in the PSD and PHZ output values of the E-FCM. Conversely, region #3 exhibits medium-high PSD and high PHZ. The statistics associated with the Monte Carlo simulation are reported in Table 7 and Fig. 11. Interestingly, out of the 1000 cases, region #1 and region #2 are selected almost equally often. More specifically, region #1 was selected by the map 518 times (confidence factor of 51.8%) and region #2 was selected for landing 482 times (48.2% confidence factor). The E-FCM did not select region #3 for any of the 1000 simulations. Statistically, both region #1 and region #2 exhibit a very close low mean for PHZ, whereas region #3

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Fig. 10. Landing scenario #3. The plots report the E-FCM time-dependent output for selected concepts (one sample of the 1000 Monte Carlo simulations). (A) Landing regions concepts values vs. time. The last value (120 s) is employed for autonomous site selection; (B) potential for scientific discoveries (PSD) concept values vs. time; (C) potential for hazards (PHZ) concept values vs. time.

has on average higher PHZ (Fig. 11B). In the same fashion, region #1 and region #2 show a statistically very high mean PDS (Fig. 11A). 5. Discussion and conclusions In this paper the problem of autonomous landing site selection on planetary bodies using real-time data streaming through the vehicle sensors collected on its journey toward the surface has been investigated. It has been shown that careful mission planning and ground-based selection of the best locale that is both safe and has the potential to yield the highest scientific information is possible if and only if remote and in situ data from previously deployed spacecrafts, orbiters, landers, lake landers, and rovers provide a reliable Table 7 Statistics of the E-FCM landing region selections for the three landing scenarios. Landing region #1 Scenario #1 Occurrence Confidence Scenario #2 Occurrence Confidence Scenario #3 Occurrence Confidence

990 99.90%

Landing region #2 7 0.07%.

Landing region #3 3 0.03%

0 0%

715 71.5%

285 28.5%

518 51.8%

482 48.2%

0 0%

Fig. 11. Statistical distribution of the final values of the E-FCM PSD (1, 2, 3, panel A) and PHZ (1, 2, 3, panel B) for the 1000 Monte Carlo simulations of landing scenario #3. On the x-axis the value of the PSD and PHZ concepts for the three regions are reported. Occurrence of the values is reported on the y-axis.

estimation of the properties of the planetary bodies. However, in the case of Venus and Titan, because of a thick and hazy atmosphere that obscure most of the electromagnetic signal passively reflected by the surface, only relatively low resolution SAR images are currently available to evaluate for any given region both scientific and hazardous content. In such cases, the reflected backscattering signal provides only partial and ambiguous information, which is hard to interpret correctly. In principle, one can benefit from data collected during the EDL phase. Indeed, on-board cameras and other instruments that operate in the visible and near-infrared regime may provide valuable information after the vehicle has penetrated deeply into the atmosphere. However, due to the fast nature of the EDL phase (typically on the order of minutes) and the time delay experienced in communicating with Earth, real-time ground-based analysis of the data for real-time site selection is virtually impossible. The only option is to resort to on-board intelligent algorithms that can autonomously reason and take timely and accurate decisions based on the data acquired en-route toward the surface. Here, the theory of Evolutionary Fuzzy Cognitive Maps has been introduced as a premiere AI methodology to address these problems. Indeed, in this work, we focused on developing evolutionary fuzzy cognitive techniques that mimic the planetary scientist process for landing site selection. It has previously been shown that the fuzzy logic framework is ideally suited to deal with reasoning under uncertainty, which is typical of planetary exploration [13–15]. Moreover, fuzzy systems are based on human language, which facilitates the interaction between planetary scientists (who possess the proper knowledge-base) and AI domain experts. The fuzzy logic framework coupled with cognitive maps provides the

R. Furfaro et al. / Applied Soft Computing 12 (2012) 3825–3839

planetary science and mission planning community with a powerful tool for autonomous reasoning during the course of planetary exploration. In the case of landing on a planetary body in the Solar System, since data are continuously collected in real-time, methodologies that continuously adapt to new information are required. Indeed, the evolutionary nature of E-FCM makes it attractive for timecritical decisions in uncertain environments. Here, an example of an E-FCM architecture for real-time autonomous landing site selection has been presented. Focusing on the case of landing on Venus, a map capable of discriminating between three potential regions has been designed and simulated. The proposed E-FCM comprises 33 concepts connected through a web of causal relationships evolving according to a time schedule to account for newly acquired data. Both concepts and connections have been established by our multidisciplinary team, and the proposed E-FCM architecture represents one possible solution to the autonomous landing problem. Importantly, other scientists may have different opinions on how the map should be constructed and which information should be emphasized most. The consideration that different teams of scientists may have decided to devise alternative maps with different reasoning may stimulate research and debate on how to best construct such maps for autonomous reasoning during landing. In principle different concepts can be chosen, although it is our opinion that the qualitative information should have a quantitative root, i.e., input concepts should be connected to features that can be autonomously extracted in real-time using appropriate algorithms (e.g., AGFA [10]). The proposed E-FCM should therefore not be considered as the only possible design but more appropriately as a proof-of-concept architecture and design that illustrate the potential of the methodology. A set of Monte Carlo simulations (1000 runs each) has been executed for three chosen Venus scenarios. In each case, the “ground truth” has been established a priori: each of the input concepts have been assigned a linguistic value that represents an evaluation of the observed feature if high-quality, ideally uncorrupted information was available. Based on such data, which is clearly not available a priori, our team reached a conclusion as to which site would be best for landing. The acquisition of the descent data has been simulated by corrupting the ground truth using a Gaussian (normal) distribution over the assumed ground truth. At each data acquisition interval (i.e., every 5 s) and as the landing site is approached, the input data are updated via sampling from a Gaussian distribution with smaller and smaller standard deviation. For each of the Monte Carlo runs, at a specified time the E-FCM is asked to take a final decision about which site is best for landing (i.e., 120 s of descent time). In any of the three chosen scenarios, statistically the map reasons consistently with human expertise. For example, an analysis of the ground truth for scenario #1 makes apparent that the landing region #1 is the best. Indeed, whereas all sites exhibit features that are safe for landing, the landing region #1 has the highest scientific geological content. At the end of each Monte Carlo simulation, the E-FCM algorithm reaches the same conclusion 99.9% of the times. In the landing scenario #2, an inspection of the ground truth provides a different picture. Here, landing region #1 is the place that would still yield the highest potential for scientific discovery, but exhibits a marked potential for hazards. Landing regions #2 and #3 have low to medium scientific interest but have higher safety factor. During the E-FCM design phase, the map has been specifically designed to give priority to safety, especially when reasoning on less uncertain data (i.e., after the second half of the descent). On average and with similar low potential for hazards, the landing region #2 tends to be more scientifically preferable than #3. Indeed, while region #1 is consistently excluded, the E-FCM selects landing region #2 in 71.5% of all the cases. The third scenario shows two scientifically

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interesting regions (#1 and #2) with globally low hazardous features. Landing in region #3 has some scientifically interesting features but high potential for hazards. The E-FCM consistently excludes #3 from selection and does not show a statistical preference for any of the two before mentioned regions (i.e., #1 and #2). Indeed, landing region #1 is selected in 51.8% of all the cases and landing region #2 is selected in 48.2% of all the cases. As clearly outlined in this summary, the E-FCM reaches the same conclusions as field experts. Moreover, it is fast enough to be suitable for real-time, on-board implementation. Importantly, the explicit design and simulation of E-FCMs for autonomous Titan landing site selection have not been directly discussed. Nevertheless, the E-FCM design principles are similar to the case of Venus landing. It is expected that a Titan-based E-FCM maintains the same structure as in the Venus case and its architecture can be easily adjusted to account for the specifics required by the Titan environment, including the selection of the input concepts that influence the potential for scientific discoveries and the potential for hazards. The details of such a system will be presented in a future paper. In conclusion, we believe that the outlined methodology has the potential to be the premiere AI choice for cognitive reasoning on data collected during the course of planetary exploration especially in scenarios where due to the nature of the mission, real-time human intervention and decision making is virtually impossible. As a general principle, FCMs and their evolutionary extensions, E-FCMs, may be effective in helping scientists and space mission engineers to autonomously handle large amounts of data in realtime, to generate improved and intelligent information, and, in our case, to decide which is the best landing site without the need of human intervention. We envision a future for space exploration and planetary reconnaissance where autonomous agents (spacecrafts, orbiters, landers, lake landers, and rovers) are in close collaboration with humans, helping with sorting and understanding data-rich environments and take autonomous decisions whenever human intervention is not possible. FCMs and E-FCMs can play a critical role at this stage of development, by implementing geological knowledge required to understand planetary environments.

Appendix A. Comparison of fuzzy logic to other AI approaches Any AI scheme available in the literature may be, in theory, adapted to perform integrated functions similar to the ones described in Section 2.2. However, for the given problem of autonomous landing site selection, the selected algorithms must be able to deal with how to adequately represent knowledge and inference. In a broader sense, representation, inference, learning, generalization, explanation, and adaptation capabilities must be carefully analyzed and properly selected to provide a satisfactory solution to the problem of autonomous science during planetary reconnaissance as well as to the problem of autonomously selecting the landing site in real-time. Examples of such algorithms may include symbolic AI [49], fuzzy logic experts [13] and Neural Networks (NN [50]). NNs fall under the category of connectionist systems for which knowledge is distributed among the nodes comprising the network. Indeed, NNs are constructed in such a way that knowledge is unstructured: they learn by examples, by doing or by analogy. Moreover, NNs are capable of good generalization and adaptation. Conversely, symbolic AI and fuzzy systems have been specifically conceived to represent structured knowledge. While inference is exact in symbolic AI, it is approximate in both fuzzy-based and neural network systems. Importantly, symbolic AI systems do not deal very well with missing, corrupted and inexact data. Generally, NNs require training, which implies the availability of a proper training set of input-output pairs

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representing the desired relationship to be learned. Unfortunately, in planetary exploration, data tend to be scarce and ambiguous, making supervised training very problematic if not impossible. One of the critical issues that must be addressed when dealing with the problem of defining AI algorithms for planetary reconnaissance in general, and autonomous landing site selection in particular, is how to represent uncertain knowledge and uncertain data. Fuzzy logic-based methods are inherently capable of dealing with uncertainties. Alternatively, AI algorithms based on probabilistic methods may represent another viable approach (e.g., Bayesian Belief Network (BBN [51])). If one relies on the axioms of probability as a mathematical framework, coherent knowledgebases can be built using (a) data collected in the course of past missions, (b) statistical methods to determine the appropriate conditional probabilities (objective probability), and (c) conditional probabilities that define beliefs unsupported by data (subjective probability). In general, probabilistic methods rely on estimating the posterior probability to assess if a certain conclusion (defined by a rule) may be accepted as correct. The major drawback stems from the fact that such methods cannot deal with ambiguous and contradictory scenarios. Generally, if a condition is asserted as true, Bayes Theorem fails whenever multiple rules reach different conclusions. Conversely, fuzzy systems can deal with contradictory and ambiguous rules by naturally providing a trade-off during the inference process (i.e., rules are fired at the same time). Conflict of interest No conflict of interest to declare. References [1] A.M. Abdrakhimov, Geology and geochemistry of the Venera 8, 9, 10, 13, 14, Vega 1, 2 landing sites, PhD Dissertation, Vernadsky Institute of Geochemistry and Analytical Chemistry, RAS, Moscow, 2000, 143 pp. [2] A.T. Basilevsky, O.V. Nikolaeva, C.M. Weitz, Geology of the Venera 8 site region from Magellan data: morphological and geochemical consideration, J. Geophys. Res. 97 (1992) 16315–16335. [3] A.T. Basilevsky, M.A. Ivanov, J.W. Head, M. Aittola, J. Raitala, Landing on Venus: past and future, Planet. Space Sci. (2007) 55. [4] Y. Cai, C. Miao, A.-H. Tan, Z. Shen, Context modeling with evolutionary fuzzy cognitive map in interactive storytelling, in: IEEE International Conference on Fuzzy Systems, WCCI 2008, Hongkong, China, 2008, pp. 2320–2325. [5] Y. Cai, C. Miao, A.-H. Tan, Z. Shen, B. Li, Creating an immersive game world with evolutionary fuzzy cognitive maps, IEEE Comput. Graph. Appl. 30 (March/April (2)) (2010) 58–70. [6] P.R. Christensen, et al., The thermal emission imaging system (THEMIS) for the Mars 2001 Odyssey Mission, Space Sci. Rev. 110 (2004) 85–130. [7] C. Elachi, S. Wall, et al., Cassini Radar views the surface of Titan, Science 308 (2005) 970–974. [8] W. Fink, J.M. Dohm, M.A. Tarbell, T.M. Hare, V.R. Baker, Next-generation robotic planetary reconnaissance missions: a paradigm shift, Planet. Space Sci. 53 (2005) 1419–1426. [9] W. Fink, Generic prioritization framework for target selection and instrument usage for reconnaissance mission autonomy, in: Proceedings of IEEE World Congress on Computational Intelligence (WCCI) 2006, Vancouver, Canada, 2006, pp. 11116–11119. [10] W. Fink, A. Datta, J.M. Dohm, M.A. Tarbell, F.M. Jobling, R. Furfaro, J.S. Kargel, D. Schulze-Makuch, V.R. Baker, Automated global feature analyzer (AGFA) – a driver for tier-scalable reconnaissance, in: IEEE Aerospace Conference Proceedings, 2008, paper#1273, doi:10.1109/AERO.2008.4526422. [11] W. Fink, M.A. Tarbell, F.M. Jobling, in: L.A. Costas (Ed.), Tier-Scalable Reconnaissance – A Paradigm Shift in Autonomous Remote Planetary Exploration of Mars and Beyond, Chapter 1 in Planet Mars Research Focus, Nova Science Publishers, Hauppauge, NY, 2008, ISBN 1-60021-826-1. [12] W. Fink, M.A. Tarbell, R. Furfaro, L. Powers, V.R. Baker, J.I. Lunine, Robotic test bed for autonomous surface exploration of Titan, Mars, and other planetary bodies, in: IEEE Aerospace Conference Proceedings, Big Sky, MT, 2011, paper #1770. [13] R. Furfaro, J.M. Dohm, W. Fink, Fuzzy logic expert system for tier-scalable planetary reconnaissance, in: 9th International Conference on Space Operations, AIAA, Rome, Italy, June 19–23, 2006. [14] R. Furfaro, J.M. Dohm, W. Fink, J.S. Kargel, D. Schulze-Makuch, A.G. Fairén, P.T. Ferré, A. Palmero-Rodriguez, V.R. Baker, T.M. Hare, M.A. Tarbell, H.H. Miyamoto, G. Komatsu, The search for life beyond earth through fuzzy expert systems, Planet. Space Sci. 56 (3–4) (2008) 448–472.

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