Identification of cryovolcanism on Titan using fuzzy cognitive maps

ARTICLE IN PRESS Planetary and Space Science 58 (2010) 761–779

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Identification of cryovolcanism on Titan using fuzzy cognitive maps Roberto Furfaro a,n, Jeffrey S. Kargel b, Jonathan I. Lunine c, Wolfgang Fink d,e, Michael P. Bishop f a

Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA Department of Hydrology and Water Resource, University of Arizona, Tucson, AZ 85721, USA Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA d Visual and Autonomous Exploration Systems Research Laboratory, Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA e Departments of Electrical & Computer Engineering and Biomedical Engineering, University of Arizona, Tucson, AZ 85721, USA f Department of Geography and Geology, University of Nebraska at Omaha, NE 68182, USA b c

a r t i c l e in fo

abstract

Article history: Received 25 May 2009 Received in revised form 15 November 2009 Accepted 16 December 2009 Available online 6 January 2010

Future planetary exploration of Titan will require higher degrees of on-board automation, including autonomous determination of sites where the probability of significant scientific findings is the highest. In this paper, a novel Artificial Intelligence (AI) method for the identification and interpretation of sites that yield the highest potential of cryovolcanic activity is presented. We introduce the theory of fuzzy cognitive maps (FCM) as a tool for the analysis of remotely collected data in planetary exploration. A cognitive model embedded in a fuzzy logic framework is constructed via the synergistic interaction of planetary scientists and AI experts. As an application example, we show how FCM can be employed to solve the challenging problem of recognizing cryovolcanism from Synthetic Aperture Radar (SAR) Cassini data. The fuzzy cognitive map is constructed using what is currently known about cryovolcanism on Titan and relies on geological mapping performed by planetary scientists to interpret different locales as cryovolcanic in nature. The system is not conceived to replace the human scientific interpretation, but to enhance the scientists’ ability to deal with large amounts of data, and it is a first step in designing AI systems that will be able, in the future, to autonomously make decisions in situations where human analysis and interpretation is not readily available or could not be sufficiently timely. The proposed FCM is tested on Cassini radar data to show the effectiveness of the system in reaching conclusions put forward by human experts and published in the literature. Four tests are performed using the Ta SAR image (October 2004 fly-by). Two regions (i.e. Ganesa Macula and the lobate high backscattering region East of Ganesa) are interpreted by the designed FCM as exhibiting cryovolcanism in agreement with the initial interpretation of the regions by Stofan et al. (2006). Importantly, the proposed FCM is shown to be flexible and adaptive as new data and knowledge are acquired during the course of exploration. Subsequently, the FCM has been modified to include topographic information derived from SAR stereo data. With this additional information, the map concludes that Ganesa Macula is not a cryovolcanic region. In conclusion, the FCM methodology is shown to be a critical and powerful component of future autonomous robotic spacecraft (e.g., orbiter(s), balloon(s), surface/lake lander(s), rover(s)) that will be deployed for the exploration of Titan. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Autonomous systems Titan Cryovolcanism Artificial Intelligence Fuzzy cognitive maps Planetary exploration

1. Introduction Autonomy will be a critical factor in enabling future sciencedriven and less constrained planetary reconnaissance of remote bodies (e.g., Titan and Europa). Indeed, the exploration of the outer planets of the Solar System and their moons has the potential to yield a large wealth of geological and possibly exobiological information. Lately, these planetary bodies received a great deal of attention from NASA, ESA, and other space agencies around the world. Established by NASA in 2004, the Outer Planet

n

Corresponding author. E-mail address: [email protected] (R. Furfaro).

0032-0633/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2009.12.003

Assessment Group (OPAG) identified scientific priorities and pathways for the exploration of the outer Solar System including advocating flagship missions. The goal is to increase our understanding of the outer portion of the Solar System. Flagship mission architectures may be comprised of single or multiple agents (e.g., orbiter(s), balloon(s), lander(s), rover(s)) and may be deployed following a tier-scalable reconnaissance architecture (Fink et al., 2005). The agent deployment requires the design, implementation, and integration of an intelligent reconnaissance system (Furfaro et al., 2006, 2007, 2008a,b; Fink et al., 2008). Such system should (1) include software packages that enable fully automated and comprehensive identification, characterization, and quantification of feature information within an operational region, including anomaly detection, with subsequent target

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prioritization and selection for close-up reexamination (e.g., Automated Global Feature Analyzer, AGFA, Fink et al., 2008; Fink, 2006) and (2) integrate existing information with acquired, ‘‘in transit’’ spatial and temporal sensor data to automatically perform intelligent planetary reconnaissance, which includes identification of sites with the highest potential to yield significant geological and astrobiological information (Furfaro et al., 2008a). Balloon-borne Titan exploration especially needs a high degree of autonomous operation and interpretation, because a wellinstrumented balloon without a well-designed intelligent system may overfly and pass up areas of highest scientific interest before Earth-based observers are even aware of the interesting encounter, as discussed below. To address such challenges, expertise from the field of Artificial Intelligence (AI) must be integrated with expert knowledge residing within the planetary science community. Novel tools must be developed (a) that may be implemented on on-board processors of the respective agents to autonomously identify geological features and (b) that may provide autonomous interpretation of the geologic and exobiologic content exhibited by the observed locale. Various AI methods and techniques are available to tackle such a challenging problem. Generally speaking, designing an intelligent system that reasons over data mimicking the planetary scientist approach requires two fundamental ingredients: knowledge and inference representation. Planetary science knowledge can be represented by rules or methods from which it is possible to perform plausible reasoning to obtain new facts and hypotheses. Knowledge must be coupled with an inference mechanism, defined as the process of matching data and knowledge to infer new information. The way knowledge and inference are integrated into AI algorithms marks the difference between the various approaches. For example, symbolic AI, fuzzy logic-based and neural networks-based schemes provide different frameworks that can generate intelligent systems for planetary exploration. Neural networks fall under the category of connectionist systems. In such cases, knowledge is distributed among various nodes. Indeed, neural networks are constructed in such a way that knowledge is unstructured as they learn by examples, by doing or by analogy. Moreover, they are capable of good generalization and adaptation. Conversely, symbolic AI and fuzzy systems are conceived and designed to represent structured knowledge, i.e. knowledge is captured via rules that are defined either symbolically or that are directly derived from the human language. Whereas inference is exact in symbolic AI, it is approximate in fuzzy-based and neural network systems. Symbolic AI systems do not deal very well with missing, corrupted, and inexact data. Fuzzy logic has been recently considered as premiere AI technique to mimic human reasoning over planetary science data (Furfaro et al., 2008a,b). For example, Furfaro et al. (2008b) have tackled the problem of designing and implementing intelligent systems capable of autonomous reasoning while performing science-driven reconnaissance of Titan and Enceladus. Previous work showed that fuzzy logic can be an attractive and effective framework to implement expert knowledge while looking for life (Furfaro et al., 2008a) or following the water (Furfaro et al., 2006). Fuzzy cognitive maps (FCMs) are an attractive knowledge-based Artificial Intelligence (AI) methodology that merges fuzzy logic and neural network properties (Stylios and Groumpos, 2000). FCMs employ a soft computing technique (Kosko, 1986; Stylios and Groumpos, 2004) that was conceived to deal with uncertain and fuzzy concept description using similar procedures employed by human reasoning (Papageorgiou et al., 2004) on the basis of knowledge and experience derived from a particular field of study. The required knowledge is structured using an array of

concepts and a web of relationships between them. Such techniques have been employed in a large variety of fields including biomedical and other engineering areas. For example, FCMs have been successfully used in modeling supervisory control systems for industrial applications (Stylios and Groumpos, 2004), causal inference (Miao and Liu, 2000), in modeling and analyzing radiotherapy processes (Papageorgiou et al., 2003), in modeling the process of selecting brain tumors (Papageorgiou et al., 2008), and in managing nuclear power plants (EspinosaParedes et al., 2008). In this paper, we develop FCMs as an intelligent system capable of identifying cryovolcanism on Titan. The fuzzy-based scheme is designed to reason over the Cassini Synthetic Aperture Radar (SAR) image data (Elachi et al., 2005) and determine if cryovolcanism is present in the observed region. The system employs concepts and a web of causal connections to mimic the inference process executed by planetary scientists to interpret/ identify the geological processes shaping Titan’s surface. Some interesting features of FCMs that we wish to exploit are their flexibility in modeling and design, their ability to abstractly represent the behavior of complex systems, and their ability to change an interpretation when newly added data direct the FCM to a different assessment of probability. Cryovolcanism has been hypothesized to occur on the largest saturnian satellite based on radar data (Stofan et al., 2006; Lopes et al., 2007), but it is unknown to what extent this process has shaped Titan’s surface. It is our goal to introduce cognitive models into the planetary science community to show how human-like reasoning may be effectively implemented to perform intelligent planetary reconnaissance. Importantly, although based on a similar AI framework, FCMs represent an alternative to fuzzybased expert systems that have been designed to perform similar human-like reasoning (Furfaro et al., 2008a,b). Fuzzy expert systems capture field knowledge using rules coded in a linguistic fashion and employ the methods of fuzzy logic to perform inference. Designing such systems requires that AI experts work with planetary scientists to define the proper IF-THEN rules that capture the understanding of a specific process. Ultimately, a knowledge-base is defined as a collection of linguistic rules that capture what is known about the problem. Conversely, as discussed above, FCMs capture knowledge using concepts spread across a map linked by a web of causal connections that defines what is understood about the specific process that is modeled. At this stage, we believe that both approaches are valid. Here, our goal is to show how FCMs can be designed to reason over cryovolcanism and we highlight the effectiveness of such methodology. This work may stimulate research on defining other AI approaches that may be critical for planetary exploration. The paper is organized as follows. In Section 2, a theoretical background is provided. Cryovolcanism on Titan is described and a brief introduction to the concept of FCMs is provided. After discussing the need for cognitive models for the exploration of Titan, the process of constructing, implementing, and testing a FCM for autonomous identification of cryovolcanism on Titan is described in Section 3. Section 4 reports on four case studies where the designed FCM is tested against Cassini SAR images to show that the proposed system reasons like planetary scientists by correctly reproducing human interpretations of the examined areas as cryovolcanic, according to the planetary science literature (e.g., Lopes et al., 2007). Section 5 shows how FCMs can be modified to account for new knowledge and effectively can produce a change of interpretation or a reinforcement of a prior interpretation as new data and new concepts are added. Section 6 reports discussion and conclusions.

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2. Theoretical background 2.1. Cryovolcanism on Titan Since Cassini-Huygens entered the planned orbit around Saturn (July 2004), its instrument suite has been constantly observing Titan and returning a wealth of data about its surface morphology and atmospheric composition. Individual and combined observations performed by the Cassini SAR (Elachi et al., 2005), the Visual Infrared Mapping Spectrometer (VIMS, Brown et al., 2004), the Imaging Surface Subsystem (ISS, Porco et al., 2004), and the Huygens-mounted Descent Imager Spectral Radiometer (DISR ,Tomasko et al., 2005; Soderblom et al., 2007) revealed that Titan is an extremely geologically complex planetary body. One of the geological processes that may have contributed to shape Titan’s surface is cryovolcanism (Lopes et al., 2007). Proposed to occur on Titan long before the Cassini mission (Lorenz (1996)), cryovolcanism may occur on several outer planet satellites of the solar system (Kargel, 1995). As new data have been acquired through a succession of missions from Voyager to Galileo and Cassini, old interpretations of cryovolcanism on icy satellites have been left untouched or been reinforced (e.g., Croft et al., 1995), spectacular new findings of cryovolcanism have been revealed (Porco et al., 2006), some old interpretations have fallen under the weight of new data (e.g., Collins et al., 1998) or have found both new support, new doubts, or have taken new twists and turns (e.g., Pappalardo et al., 1997, Fagents et al., 2000, Schenk et al., 2001). As we develop below, FCMs are able to mimic aspects of human interpretations of cryovolcanism on Titan and also mimic evolution of thought as new data are obtained. Cryovolcanism manifests itself through eruptions of icy-cold aqueous or non-polar solutions or partly crystallized slurries, derived by partial melting of ice-bearing materials (Kargel, 1991, 1992, 1995; Kargel et al., 1991). Theoretical models show that cryovolcanism is possible on Saturn’s satellites, including Titan. Nebula condensation and satellite accretion processes in the Saturnian Nebula would have produced satellites composed of complex mixtures of materials, including water ice and many other volatiles, such as ammonia hydrates (Lewis, 1972; Fegley and Lewis, 1980; Prinn and Fegley, 1988). No consensus exists on details of the subsequent evolution of any icy satellite. However, the physical and chemical properties of the volatile mixtures are such that the volatiles likely partially melted inside Titan and possibly inside some other Saturnian satellites. As such they might have formed subsurface aqueous oceans and partly melted zones, and possibly could have caused cryovolcanism; furthermore, subsurface liquids may still exist and cryovolcanism could still be active at Titan (Ellsworth and Schubert, 1983; Consolmagno, 1985; Kargel, 1992; Grasset and Sotin, 1996; Sotin and Tobie, 2008; Tobie et al., 2005, 2006, 2009). Mitri et al. (2008), for example, showed that thermal convection can occur in a stagnant-lid regime of Ice I, Titan’s shell floating on a subsurface water–ammonia ocean. Such thermal regime may generate eruptions of water–ammonia mixtures through Titan’s ice shell leading to cryovolcanism. The proposed model envisions cryovolcanic eruptions to be related to crevasses forming at the bottom of the ice shell coupled with transport of water–ammonia pockets at the base of the stagnant lid via ice convection and refreezing water–ammonia chambers. Cryovolcanism can be identified by detecting cryovolcanic features that indicate the occurrence of the abovementioned processes. On Titan, cryovolcanism should exhibit features that are different when compared with cryovolcanic features observed on other outer solar system bodies having either no atmosphere or tenuous ones. Triton, with a surface pressure of just tens of microbars, has a wide array of compelling cryovolcanic landforms,

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many produced by explosive gas-driven eruptions (Kargel and Strom, 1990; Croft et al., 1995). According to Lorenz (1996), Titan’s cryovolcanic eruptions are more likely to be diffusive than explosive. Indeed, the presence of a dense atmosphere (with high atmospheric pressure) suppresses vesiculation (gas exsolution and bubble formation) in cryomagmas, and thus suppresses opportunities for explosive eruptions. Moreover, since cryomagmas may be comprised of mainly water or a mixture of water and ammonia with a limited ( o1%) amount of methane, (Kargel et al., 1991; Kargel, 1995), the relatively volatile-poor magma composition strongly favors the hypothesis of diffusive eruptions. During the four Titan fly-bys, executed between October 2004 and October 2005 (Ta, T3, T7, T8; Elachi et al., 2005), the Cassini SAR imaged the satellite surface allowing the identification of many features that have been linked to cryovolcanism. For example, the Ta SAR image shows regions associated with cryovolcanic eruptions including a volcanic dome and extensive flow features. A particular feature called Ganesa Macula is thought to be a volcanic edifice, i.e., a dome or a shield volcano (Lopes et al., 2007). The construct shows evidence of a caldera as well as channels and ridges, which are interpreted as cryolava channels running at the flanks of the volcano. Very recently, this interpretation has been questioned as new topographic information, acquired via SAR stereogrammetric techniques, shows very low elevation (Kirk et al., 2009), opening the way to alternative interpretations (e.g., erosional features carved by liquid methane). Stereo radar imagery of an area known as Hotei Arcus shows features that might be solidified cryovolcanic flows (Wall et al., 2009), and the area appears to have fluctuated in brightness as seen in Cassini near-infrared data (Nelson et al., 2009). In summary, cryovolcanism is a reasonable hypothesis to explain some features seen on Titan, but data beyond Cassini-Huygens may be needed to establish whether indeed it has taken place or is taking place. One critical step toward a fully autonomous interpretation of the detected features, requires the implementation of a suitable scheme that mimic human-like reasoning to provide proper inference of the cryovolcanic processes occurring on Titan. The framework of fuzzy cognitive maps, as introduced in the next section, is an effective and powerful methodology implemented to provide the proper geological context as derived from planetary scientist expertise. Clearly, a comprehensive FCM scheme should take advantage of all available data. While SAR images are probably the most useful tool currently available for the detection and interpretation of cryovolcanic features, VIMS has recently shown to be functional in identifying regions exhibiting potential for cryovolcanic activity (LeCorre et al., 2009; Nelson et al., 2009). In the present work, we illustrate how to construct AI systems based on fuzzy logic and cognitive maps using exclusively SAR data. Since, to our knowledge, this is the first attempt to define an AI system that reasons on cryovolcanism, we focus mainly on the methodology as applied to a single set of data, i.e. we focus on illustrating how to implement the artificial reasoning process that mimics the reasoning approach performed by planetary scientists while examining SAR data. The latter should help understanding how to construct such algorithms and show the path to future design of FCMs that integrate multiple data sets.

2.2. Introduction to fuzzy cognitive maps Fuzzy cognitive maps are modeling techniques that follow an approach similar to both human reasoning and human decisionmaking processes. In its basic formulation, FCMs are digraphs designed to capture the system-inherent cause/effect relationships. Two basic elements form the backbone of the maps: nodes

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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 represent the causal relationships between concepts with a degree of causality. Cognitive maps (CM) were originally introduced by Axelrod (1976) in the context of political science. Using two elements, i.e., concepts and causes, CM can be designed to express/model a system of believes. Kosko (1986) extended the CM notion to the fuzzy realm by introducing the causal algebra operating in the range between  1 and 1. FCM models incorporate the available knowledge and expertise by selecting appropriate concepts and causal connection between them. Concepts abstractly represent key-factors of the modeled system. The interconnections between FCM concepts represent the cause and effect relationships exhibited by the concepts employed to model the system behavior. Fig. 1 shows a schematic representation of a simple FCM. Generally, a FCM model is described as a one-layer network. The nodes are assigned with concept meaning and the arcs represent the interconnection between concepts. The weighted interconnections are defined to show both the direction and the degree of influence between concepts. The weight Wji between two concepts Ci and Cj has a numerical value ranging between  1 and 1. The weight sign indicates if the relationship between two concepts is direct or inverse. Here, a positive sign indicates a direct causal relationship (e.g. if the concept Ci increases, then the concept Cj increases as well), whereas a negative sign indicates an inverse causal relationship (i.e. if the concept Ci increases, then the concept Cj decreases). Independently of the system to be modeled, the methodology for developing FCMs is based on knowledge and opinions of a group of experts. Such experts are asked to (a) define the concepts involved in the model and (b) describe the relationships (i.e., connections) among concepts. The experts describe each interconnection using a fuzzy rule, i.e., the use of a linguistic variable to determine the grade of causality between the two concepts. Two approaches are possible. In one case, a group of experts are individually asked to formulate their opinion about the map (Papageorgiou et al., 2008). The rules coming from the experts are

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Fig. 1. Example fuzzy cognitive map (FCM) architecture. In this example, the map is comprised of four nodes and a web of causal connections between nodes. The latter are representative of concepts involved in the problem to be modeled. The weighted arcs are generally established by the human experts that define positive, null or negative connections as well as the strength of the connection (ranging between 0 and 1). Importantly, a positive sign indicates a direct causal relationship (i.e., if the concept Ci increases, then the concept Cj increases as well), whereas a negative sign indicates an inverse causal relationship (i.e., if the concept Ci increases, then the concept Cj decreases).

aggregated and de-fuzzified (e.g., using the centroid method (Ross, 2004) and the resulting value is placed as the weight between the two concepts. The other approach simply implies the use of one linguistic fuzzy rule which defines a-priori agreement between experts. The latter is more convenient when the group of experts agrees to use just one linguistic rule. If different opinions arise, the first method is resumed. The value Ai (Eq. (1)) of the concept Ci is computed by accounting for all possible influences derived from interconnected concepts. An iterative process is generally required to update the concept values and can be summarized in the following formula: 1 0 C B C B X C B C A ðkÞ þ A ðkÞW Ai ðk þ1Þ ¼ f B ji C j B i C B i ¼ 1; N A @ ia j

ð1Þ

Here, A(k)={Ai, i= 1, y, N} is a 1  N (row) vector that represent the value of the concept at iteration k, W= {Wji, j,i= 1, y, N} is the N  N matrix of the causal interconnection and f(  ) is a threshold function. FCMs concepts are initialized using either measurements coming from real data or fuzzy values coming from qualitative expert description of the data. Importantly, real data must be fuzzified and mapped onto the interval [0–1]. Either way, the initial concept values are used to initialize the iterative process that is generated by free interaction between the map concepts. The modeled FCM is therefore a dynamical system that exhibits the typical behavior of non-linear systems, such as Hopfield attractor-networks (Hopfield, 1982). This includes (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. The numerical stability of the map is an important aspect of the FCM design process. 2.2.1. Methods for constructing fuzzy cognitive maps The methodology employed to design and implement FCMs is a critical factor to guarantee sufficient model fidelity. The behavior of the proposed FCM strongly depends on the understanding of the process under consideration by an expert or group of experts. In the case of planetary reconnaissance and space exploration, planetary scientists possess knowledge and understanding of the processes occurring on remote planetary bodies. The proposed FCM for Titan’s cryovolcanism must be designed to extract knowledge from the experts and to exploit their experience accumulated over years of studying and data analysis. Expertise residing within our group is utilized in determining the number and typology of concepts comprising the proposed FCM. The overall expert goals are (a) to identify the concepts important for modeling the hypothesized cryovolcanic processes occurring on Titan’s surface, (b) to define the indicators that can be extracted from remotely sensed data, and (c) to transform the scientific knowledge in a weighted, interconnected dynamic graph. In the case of cryovolcanism, planetary scientists define the elements of the system (i.e., concepts) and the way such elements influence each other. Indeed, 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. As mentioned in the previous section, each expert opinion can be accounted individually via independent linguistic rules that are subsequently aggregated and de-fuzzified. Our group agreed on

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Fig. 2. Membership functions employed to determine the strength of the connection between the concepts. Our team experts determined if the connection is direct (positive) or inverse (negative) as well as the strength of the connection. The latter is defined using linguistic variables. Five membership functions are considered to represent the strength of the connection, i.e., Very Low (VL), Low (L), Medium (M), High (H), and Very High (VH). The centroid method is used to defuzzify the membership function and assign a numerical value (which can be either positive or negative) to the established web of connections.

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). We define the influence between two concepts to be either ‘‘positive’’ or ‘‘negative’’. The fuzzy causal connection is determined using the appropriate linguistic fuzzy variable (Papageorgiou et al., 2003, 2008). Five possible variables are currently employed, i.e., 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. 2. 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 subsequently determined using the centroid method (Ross, 2004). Clearly, FCM topology and degree of causality depend on both the problem under consideration and the expert opinion. Given a specified problem, different groups of experts might have different opinions and consequently might generate different maps. Hence, we believe that the best FCM constructed to model a specified process is determined after an open discussion between a diverse group of experts.

2.3. The need for fuzzy cognitive models for the exploration of Titan Optimal deployment of future orbiters and hot-air balloons for intelligent and science-driven reconnaissance of Titan requires the implementation of novel AI algorithms capable of autonomously assessing the potential exhibited by the observed locale to yield scientific information (Furfaro et al., 2008c). Two major questions may be raised by the scientific community regarding (a) the general need for autonomous systems and (b) the specific need of fuzzy cognitive maps algorithms as the AI premiere choice for planetary reconnaissance. The next sections address both questions.

2.3.1. Why do we need autonomous systems for the exploration of Titan? Clearly, for a given mission design, the requirement of having on-board AI systems for autonomous real-time decisions increases with the distance from the explored body (e.g., communication/commanding time-lag). Two major factors should be considered, i.e., (a) the ability of the spacecraft command and data handling subsystem to store data and (b) the distance of the observed planet from Earth and the related issues of communications and decision-making time. In the Titan exploration case, Cassini is downlinking to Earth a great deal of information originating from its 12 instruments deployed for remote data collection. Science data are stored in the solid-state recorder (SSR) capable of retaining as much as 3 gigabits of information (Porco et al., 2004). If the acquired data exceeds the storage system capability, information must be erased. Consequently, blind (i.e., non-intelligent) acquisition of remote data is not optimal and can be improved by an on-board autonomous system that is capable of real-time data analysis to decide which acquired data should be stored for future relay to Earth. As far as distance is concerned, Cassini is located between 8.2 and 10.2 astronomical units (AU). It currently takes between 68 and 84 min to communicate/relay information back to the ground station on Earth (i.e., one-way). Real-time communication is impossible and as a matter of fact, a minimum of 3 h (round-trip) is estimated for Cassini to receive the commands produced by the Earth-based operation system reacting to any on-board problem and/or sudden discovery. The absence of robust software capable of autonomous decisionmaking and control jeopardizes the ability of Cassini to perform optimal reconnaissance (e.g., following up on transient events (Fink et al., 2007) such as a cloud on Titan, a water plume on Enceladus or cryovolcanism on Titan). Such limitations might be overcome with a new generation of autonomous systems and exploration architectures (Fink et al., 2005, 2007) that efficiently and intelligently address the problem.

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If properly designed, AI systems may perform on-board, real-time data interpretation (Fink et al., 2008; Furfaro et al., 2006, 2008a,c), may make autonomous decision on the best sequence of observations (Fink, 2006; Fink et al., 2008; Furfaro et al., 2006, 2008a,c), may schedule additional observations and furthermore issue a sequence of control actions to maintain the system within the observed region (i.e., station-keeping of a balloon). For example, local guidance and control schemes have been proposed for the autonomous navigation of Titan’s atmosphere with hot-air balloons (Furfaro et al., 2008c). The controller architecture relies on a fuzzy-based expert system capable of providing indications regarding the scientific importance of a region (e.g., cryovolcanism is identified; potential for life habitability is high). Based on such information, the balloon guidance system autonomously schedules a station-keeping maneuver to acquire more information or issues a lower-the-altitude command to provide a close-up view of the observed area. If the information is assessed to be not useful, the intelligent system may decide to discard it or store it with the lowest level of priority (i.e., temporary storage with possible deletion if more interesting data are acquired). The latter might be transmitted to Earth depending if the system is capable of holding low-priority information until the next communication opportunity with the ground station (i.e., Earth). Autonomous systems may be implemented on orbiting platforms as well. Indeed, orbiters may be part of tier-scalable reconnaissance mission architectures (Fink et al., 2005, 2007) where the spaceborne and airborne (orbiter(s) and balloon(s)) tiers are coordinated to optimize planetary reconnaissance. The orbiter may acquire data and perform autonomous assessment of the observed region and thus provide a global context for the subsequent, more regionally or even locally focused balloon exploration. Indeed, the orbiter may command the balloon to explore regions where the potential for a scientific discovery is higher. The above discussion makes apparent that in the context of Titan exploration, autonomous systems are a critical component of future mission architectures. Importantly, autonomous robotic explorers (including spacecrafts, balloons, and rovers) will require highly modular AI software platforms comprising AGFA-like algorithm (Fink et al., 2008) and fuzzy-based systems (e.g. FCMs, fuzzy experts, Furfaro et al., 2008a,b,c). However, the need for autonomy heavily impacts the overall robotic explorer system requirements which may force a shift in the architectural design philosophy and implement a less conservative, less risk-adverse solution for planetary reconnaissance. While implementing novel paradigms for autonomous, science-driven planetary exploration implies the need to change the approach to space system architecture design, we believe that ultimately, high-scientific pay-off will justify such shift to more autonomous reconnaissance mission architectures and robotic explorers.

2.3.2. The case for fuzzy logic: why FCM algorithms? Planetary exploration is about understanding the history of celestial bodies (including processes and feedback mechanisms that determine the evolution of planets and their surfaces) through remote and/or in-situ data collection. Newly acquired data are employed to test working hypotheses as well as to formulate new hypotheses. Furfaro et al. (2006, 2007, 2008a,b) made the case for using fuzzy logic as one premiere framework for implementing planetary expertise in the form of an autonomous computing algorithm. Indeed, the fuzzy logic semantic provides an ideal framework to deal with multiple layers of information of varying degrees of confidence such as elevated methane content, low numbers of channels and ridges, and medium number of valley networks. Generally, fuzzy logic provides a powerful

framework that can be exploited to design expert systems to be embedded in any kind of reconnaissance mission architecture for planetary exploration. FCMs are closely related to fuzzy expert systems although the implementation is conceptually different. Fuzzy experts are systems where structured knowledge is directly implemented by intuitive, easy-to-devise, fuzzy rules comprising the knowledge-base as defined by planetary scientists. FCMs are able to represent structured knowledge via a web of causal interconnections where concepts are interrelated according to a set of links defined by planetary scientists. Importantly, the basis for fuzzy logic, which is shared by both fuzzy experts and FCMs, is the basis of human communication. While observing Titan’s surface (and possibly subsurface), both systems (i.e., fuzzy experts and FCMs) should be able not only to make autonomous decisions but also to provide sound explanations allowing scientists to evaluate/judge if the implemented algorithm is reasoning correctly. Importantly, planetary scientists are required to provide their knowledge, which is implemented in the fuzzy experts/FCMs architecture, i.e., scientists are an integral part of the design. Scientists and AI experts are required to find a common ground for sharing information and a deep mutual understanding of the respective fields. While fuzzy expert systems have been designed and simulated for various scenarios (Furfaro et al., 2006, 2007, 2008a,b), FCMs have never been designed and implemented for autonomous reasoning over planetary data. Some of the advantages of using FCMs are embedded in the capability of the system to describe causal relationships between qualitative concepts (as derived from data) and its ability to show how the concept values are changing in an iterative fashion (until the map stability is reached). Knowledge is readily available as described by the map for a deeper understanding and explanation of why the system reached the presented conclusion. FCMs may also be trained for fine-tuning the maps against expert conclusions (Papageorgiou et al., 2004). The implementation of a full FCM system might incorporate real-time assessment of eolian, tectonic, and other types of features, as well as real-time assessment of geochemical and other data, etc. We envisage that for cryovolcanism, knowledge gained from volcanic terrains and landforms on Venus, Earth, the Moon, Mars and on several icy satellites would be incorporated in a modular FCM. The system would have the ability to discern cinder cones, cryolava tubes, cryoclastic deposits, and all sorts of volcanic landforms, as well as the other mentioned types of landforms and landscapes. In our example used to illustrate the approach, we took a very simplified case of one particular data set covering one cryovolcanic landscape and attempted to reproduce the human interpretive process to the degree necessary for a FCM- and AGFA-equipped system to recognize a similar landscape if it encountered one.

3. Fuzzy cognitive map model for autonomous identification of cryovolcanism on Titan 3.1. FCM concepts and attributes The first step toward designing and constructing a FCM capable of implementing human-like reasoning to identify cryovolcanism on Titan is to define the concepts that are part of the map topology. The latter is subsequently constructed to represent the modeled relationship between concepts. The concepts describe a set of qualitative attributes defined by the domain experts. They are intimately connected to the data available for analysis since some of the information extracted from available remote sensing data can be naturally employed as initial data for the dynamic evolution of the FCM. To define a

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strategy for FCM design and construction, we focused on what is currently known about cryovolcanism on Titan. During the Ta Cassini fly-by (October 2005) the SAR images showed two regions interpreted to be cryovolcanic in nature. More generally, the radar strip was thoroughly analyzed and the relevant geological units were mapped and interpreted. Fig. 3 shows the corresponding Ta SAR image and the mapped geological units as interpreted by Stofan et al. (2006). Table 1 (also derived from Stofan et al., 2006) reports the various units, their basic characteristics and their geological interpretation. Each unit is characterized by few distinct indicators that provide a clear way to discriminate between different geological units and surficial processes. For example, the Ganesa Macula region clearly shows a circular feature with dark material inside as well as few possible fluviallike patterns. Outside the circular feature, there is an area of intermediate to high backscatter material, which is identified as the Ganesa Macula mottled unit. Such observed features are both linked to the presence of a caldera (also indentified in the image) and presence of cryovolcanic flow. Both factors are evidence of cryovolcanism operating on the observed region. A lobate-shaped, high backscattering area is identified on the east side of the strip and it is linked to cryovolcanic flow. Other parts of the Ta SAR image regions are identified as distinct units with fluvial and tectonic characteristics. For example, a dark material, patchy area is interpreted as an area featuring possible ponds of liquid hydrocarbons. The geological interpretation performed by Stofan et al. (2006) is the basis for the

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definition of the concepts involved in the FCM construction. Twelve concepts have been identified by the experts in connection with the scientist interpretation of the Ta SAR image. Table 2 reports the concepts and their qualitative assessment as revealed by the Ta SAR image: C1 is the potential for cryovolcanism, which also represents the FCM output; C2 is the potential for cryovolcanic geomorphology; C3 is the potential for cryovolcanic flow; C4 and C5 are the potential for the presence of domes and calderas, respectively; C6 is the potential for craters; C7–C12 are associated with observation of the SAR images and are related to features that can be identified from the image, i.e., they can be readily extracted by analyzing the image both quantitatively and qualitatively. Importantly, some of the concepts (i.e., C9 and C10) can be both observed and derived during the FCM reasoning process. Indeed, some of the concepts, although observed, may be changing due to the influence of other concepts embedded in the map’s architecture. Generally, observed concepts are kept constant during the iteration process. However, the FCM behavior is analyzed for various scenarios including situations where some of the observed concepts that are left free to evolve (see Sections 4.2 and 4.3).

3.2. FCM topology and weight matrix After identifying the concepts of the desired FCM, the causal relationship between concepts must be clearly outlined. This step

Fig. 3. Ta synthetic aperture radar image and the mapped geological units as interpreted by Stofan et al. (2006).

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Table 1 Geological mapping and interpretation of the Ta SAR image (derived from Stofan et al., 2006). Unit name

Symbol

Description

Interpretation

Homogeneous Unit Mottled Unit Bright Mottled Unit Dark Mottled Unit Bright Lobate Unit Bright Lineated Unit Ganesa Dark Material Ganesa Mottled Material

HU MU BMU DMU BLU BLNU GDM GMM

Relatively featureless with low to intermediate backscatter Variable low to intermediate backscatter at scales of 10’s–100’s km Intermediate to high backscatter unit variable at scales of 10’s–100’s km Patchy, low backscatter unit which. sometimes forms crescent-shaped patches Relatively high backscatter unit with lobate boundaries Relatively high backscatter unit with distinct lineations Dark, relatively featureless unit associated with Ganesa Macula Intermediate to high backscatter materials associated with Ganesa Macula

Plains unit composed dominantly of water ice Plains unit composed of fractured ice Plains unit composed of rough, fractured ice Possible liquid hydrocarbon ponds Cryovolcanic flows Possible tectonically deformed materials Cryovolcanic flows Cryovolcanic flows

Table 2 Concepts comprising the proposed FCM and their qualitative description. ID

Concept

Qualitative description

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Potential for cryovolcanism Potential for cryovolcanic geomorphology Potential for cryovolcanic flow Potential for domes Potential for calderas Potential for craters Large circular features Small, radar-bright, circular features Potential for channels near calderas Mottled terrains outside circular features Lobate (flow-like) features Bright material inside lobate regions

Absent, Absent, Absent, Absent, Absent, Absent, Absent, Absent, Absent, Absent, Absent, Absent,

yields the web of interconnections between concepts as required for the full FCM design and implementation. Fig. 4 shows the FCM topology as conceived by our team. The FCM architecture follows a logic that aims at capturing the current interpretation of SAR data. For example, the potential for calderas and domes are critically connected to the potential for cryovolcanic geomorphology which positively influences the overall potential for cryovolcanism. Observed features such as large circular features and bright small circular features are connected to the presence of craters, domes, and calderas. The potential for craters tends to reduce the potential for cryovolcanism while identification of calderas has a negative influence on craters and increase the potential for cryovolcanic geomorphology. Potential for calderas generally increases the potential for channels near the construct (parameter that can be observed). Lobate, flow-like areas with high radar backscattering, increase the potential for cryovolcanic flow. Importantly, cryovolcanic flow increases the potential for a caldera-like structure even though it might not be directly observed. The web of connections has been designed to account for the likely interactions between concepts during the dynamical evolution of the map toward equilibrium. The connections can be defined as direct (plus (+ ) sign) or inverse (minus (  ) sign) and the feedback between concepts is indicative of the non-linear nature of the proposed FCM. Following the reasoning behind the causal connection between concepts is relatively straightforward. For example, positive changes in both the potential for cryovolcanic constructs (C2) and the potential for cryovolcanic flow (C3) increase the potential for cryovolcanism; conversely, positive changes in the potential for craters (C6) reduce the potential for cryovolcanic processes. The relationships between concepts are established via IFTHEN rules (Mamdani, 1977). Such rules are used to linguistically infer the weight representing the cause and effect relationship between every pair of concepts. The general structure of the rules is the following (Papageorgiou et al., 2008):

uncertain, very uncertain, very uncertain, very uncertain, very uncertain ,very uncertain ,very uncertain, very uncertain, very uncertain, very uncertain, very uncertain, very uncertain, very

low, low, low, low, low, low, low, low, low, low, low, low,

low, low, low, low, low, low, low, low, low, low, low, low,

medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium, medium,

high, high, high, high, high, high, high, high, high, high, high, high,

very very very very very very very very very very very very

high high high high high high high high high high high high

IF the value concept of Ci is X AND the value of the concept Cj is Y THEN the weight connecting Ci and Cj is Z. Here X, Y, and Z are linguistic variable that can take any of the five available sets, i.e., {VL, L, M, H, VH} (see Section 2.2.1). Our experts use only one rule to identify the linguistic weight defining the fuzzy causal link. Other approaches are possible: as shown in Section 2.2.1, many experts can be consulted, their opinion recorded in a fuzzy IFTHEN statement and the resulting rule-output aggregated before defuzzification. In our case, we use only one rule for inference because of the agreement among our team experts. Table 3 shows the weight matrix expressed in linguistic statements. To illustrate the meaning of such a matrix we provide two examples. First, consider the connection between concept C5 (i.e., potential for calderas) and C2 (i.e., potential for cryovolcanic geomorphology). The corresponding mark on the weight matrix table reads ‘‘PH’’. The P stands for ‘‘plus ( +)’’, which is indicative of the direct connection between the two concepts. H stands for ‘‘high’’. The IF-THEN rule employed to derive this linguistic weight is expressed as follows: IF a high change occurs in the value of concept C5 (potential for calderas) THEN a high change in the value of concept C2 (potential for cryovolcanic constructs) is caused. Clearly, the connection between the two concepts is described by the fuzzy membership function positive H, which generates, after de-fuzzification, a fuzzy causal value of +0.75. The latter expresses numerically the notional fact that there is a high causal connection between the presence of calderas and potential for cryovolcanic geomorphology, thus reflecting actual planetary expert knowledge of this relationship. As a second example, consider the connection between concept C6 (i.e., potential for craters) and concept C2 (i.e., potential for cryovolcanic constructs). The corresponding mark on the weight matrix table reads ‘‘NH’’. The N stands for ‘‘negative ( )’’, which is indicative of the inverse connection between the two concepts. H stands for ‘‘high’’. The IF-THEN rule employed to derive this linguistic weight is expressed as follows:

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Fig. 4. FCM architecture for autonomous cryovolcanism identification. The proposed FCM is comprised of 12 concepts connected by a web of causal relationships. Some of the concepts are linked to features that can be directly extracted from the SAR image (e.g., large circular features, lobate (flow-like) regions). Others are concepts that are inferred during the FCM iterative process (e.g., potential for cryvolcanic geomorphology). The concept C1 (potential for cryovolcanism) is the output of the FCM.

Table 3 Weight matrix expressed in linguistic terms. Causes

Effects C1

C1 C2 C3 C\4 C5 C6 C7 C8 C9 C10 C11 C12

C2

C3

PH PVH

NH

C4

C5

PM

PH

PH PH NH

C6

NH PH

C7

C8

C9

C10

C11

C12

PM

PH PVH

PL PH PVH PH

PM

Legend: P= Positive; N= negative; VL= Very Low; L = Low; M = Medium, H=High; VH =Very High. For example, PH means ‘‘Positive (plus) High’’.

IF a high change occurs in the value of concept C6 (potential for craters) THEN a negative high change in the value of concept C1 (potential for cryovolcanic geomorphology) is caused. Clearly, the connection between the two concepts is described by the fuzzy membership function negative H, which generates,

after de-fuzzification, a fuzzy causal value of  0.75. The latter expresses numerically the notional fact that there is a high but inverse causal connection between the presence of craters and cryovolcanic constructs, i.e., increasing the potential for craters decreases the potential for geological structures that are

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associated with cryovolcanism. Indeed, this is connected to the observation that a circular feature can be interpreted either as a dome or as a crater. If the circular feature is a crater, no cryovolcanism is likely to be observed. Thus, the numerical weight matrix becomes the following: 2

0 6 6 0:75 6 6 0:9 6 6 6 0 6 6 0 6 6 6 0:75 W ¼ fWji g ¼ 6 6 0 6 6 6 0 6 6 0 6 6 6 0 6 6 0 4 0

0

0

0

0

0

0

0

0

0

0

0 0

0 0

0 0:5

0 0:75

0 0

0 0

0 0

0 0

0 0

0 0

0:75

0

0

0

0

0

0

0

0

0

0:75

0

0

0

0:75

0

0

0:5

0

0

0:75 0

0 0

0 0:75

0 0

0 0:75

0 0

0 0

0 0

0 0

0 0

0

0

0

0:9

0

0

0

0

0

0

0 0

0:25 0:75

0 0

0 0

0 0

0 0

0 0

0 0

0:5 0

0 0

0

0:9

0

0

0

0

0

0

0

0

0

0:75

0

0

0

0

0

0

0

0

0

3

7 07 7 07 7 7 07 7 07 7 7 07 7 7 07 7 07 7 07 7 7 07 7 07 5 0

ð2Þ

if negative. As explained in Section 2.2, it is conceivable that the FCM might act chaotically, oscillate, or even converge to undesired regions. Various remedies are available to mitigate the problem. For example, FCMs can be trained using active Hebbian learning (AHL, Papageorgiou et al., 2004) in which the concepts are activated asynchronously and the weights are updated according to a modification of the Hebbian rule (Hebb, 1949). Hebbian learning is commonly employed in the unsupervised training of artificial neural networks. In our case, we did not experience any of the abovementioned maladies and therefore no weight-update rule was implemented, i.e., the weight matrix was kept constant during the FCM iterations (i.e., synchronous activation). The FCM algorithm has been implemented using the MATLAB Fuzzy Logic Toolbox and run on a mobile workstation equipped with an Intel Core 2 Duo processor (2.8 GHz clock speed and 2 GB, DDR2-800 SDRAM). The FCM is shown to converge in less than a second for all analyzed scenarios. Next we analyze the individual results of the FCM as applied to the selected Ta SAR regions.

4. Case studies 4.1. Region 1&2: no cryovolcanism detected Portions of the Ta SAR Cassini image are considered for case studies to show that the constructed FCM indeed performs as desired, i.e., it effectively mimics the interpretation process of planetary scientists. It is expected that the FCM reaches the same conclusion as the domain expert by correctly interpreting areas that have been identified as cryovolcanic. The FCM is initialized by setting the initial values of the concepts comprising the map. Four areas of the Ta SAR images are identified as test cases. Fig. 5 shows close-up SAR images of the analyzed regions. For each of the considered cases, the experts are asked to examine the area and to provide a qualitative assessment of the concepts that are ‘‘observable’’, i.e. concepts that can be associated with geomorphological features directly observed on the images. Such concepts, which act as inputs, are directly connected to quantitative data as they can be readily extracted from a visual inspection of the radar image. The qualitative assessment of the FCM initial values is executed by (a) visually inspecting the Ta SAR and (b) selecting the linguistic variables that best represent the observable concepts. For example, region 4 shows a lobate, flow-like region and a bright material (high backscattering) inside the lobate area. Consequently, the input concepts C11 and C12 are assessed to be ‘‘Very High’’. Conversely, for the same region, since no circular features are observed, the values of C7 and C8 are assessed to be ‘‘absent’’ (corresponding to an initial value of 1). Generally, all the other concepts are initialized as ‘‘uncertain’’ (corresponding to an initial value of 0). Importantly, concepts that are observable but influenced by other concepts on the map (i.e., channels near calderas and mottled terrain near circular features) are generally initialized as ‘‘absent’’ if all of the observable concepts are absent, and uncertain if any of the observable concepts is present. The linguistic values are subsequently fuzzified using the membership functions associated with the linguistic values (Fig. 6). The initial values of the concepts are subsequently propagated according to Eq. (1). The tangent-sigmoid function is selected as the threshold function. As illustrated in Fig. 7, the function is positive or negative depending on whether the input argument is positive or negative. The constructed FCM undergoes an iterative process (Eq. (1)) which generally converges to a final value for each of the concepts comprising the map (either positive or negative). The convergence is shown to occur within a maximum number of 115 iterations for all analyzed cases. For the FCM output (potential for cryovolcanism) the converged value is indicative of cryovolcanism if positive and indicates its absence

The first regions to be analyzed are shown in the top-row of Fig. 5. Region 1 (top-left corner) has been mapped as a dark mottled unit (Stofan et al., 2006) and contains many oxbow and irregular patches that could be ponds of liquid hydrocarbons (Elachi et al., 2005; Lorenz et al., 2005). Region 2 (top-right corner, Fig. 5) has been mapped as a bright mottled unit (Stofan et al., 2006) and it is interpreted to be a region mainly comprised of plains with rough fractured ice. The region also exhibits patches of featureless homogeneous plains mainly containing water ice. The regions are therefore not interpreted to be cryovolcanic in nature since they do not show any of the features that could potentially link them to cryovolcanism. The constructed FCM should reach the same conclusion. We initialize the map by selecting the initial values of the input concepts (C1–C12) in a linguistic fashion. Table 4 (first and second column) shows the initial linguistic values selected for the FCM concepts. Since none of the observable concepts are identified, their values are linguistically labeled as ‘‘absent’’ which is equivalent to an initial numerical value of  1. The remaining concepts values (C1–C6) are initialized by setting them to the linguistic attribute of ‘‘uncertain’’. The initial concept value vector (1  N) is therefore: AIn Region12 ¼ ½0; 0; 0; 0; 0; 0; 1; 1; 1; 1; 1; 1

ð3Þ

The FCM iterates according to Eq. (1) and the concept values are updated until the map converges. The convergence criterion is based on computing the Euclidian norm of the difference between vectors at iteration k and k+ 1. The iteration process is stopped when the norm of the error is less than 0.001 (i.e., user-defined tolerance), i.e.: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX 2 ð4Þ ðAi ðk þ1ÞAi ðkÞÞ o tol ¼ 0:001 :Aðkþ 1ÞAðkÞ:2 ¼ t i¼1

The map converged after 35 iterations to an output value of the potential for cryovolcanism equal to  0.98. The negative value indicates that the proposed FCM reaches the conclusion that no cryovolcanic processes are detected. FCM correctly mimics the interpretation of the planetary experts. 4.2. Region 3: Bright lobate unit with cryovolcanic flow The third region under investigation is shown in the bottomright corner of Fig. 5. The region has been mapped as a bright

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771

Plains

Fractured Ice

Ponds of Liquid Hydrocarbons Region 1

Region 2 Bright Lobate Unit (possible cryoflow)

Caldera

Shield/Dome

Mottled Terrain

Region 4

Region 3

Fig. 5. Four test-regions are extracted from the Ta SAR data (see Fig. 3). Each region is visually inspected to extract the features that form initial values for the concepts comprising level-1 of the proposed FCM. Following the interpretation by Stofan et al. (2006), regions 1 and 2 do not show signs of cryovolcanism: region 1 has been mapped as a dark mottled unit and contains many dark patches that could be ponds of liquid hydrocarbons, whereas region 2 has been mapped as a bright mottled unit and interpreted as a region comprised of plains and rough fractured ice. Conversely, regions 3 and 4 show clear signs of cryovolcanism: region 3 has been mapped as a bright lobate unit showing probable cryovolcanic flow extending from a small hill, whereas region 4 (Ganesa Macula region) has been interpreted as a cryovolcanic construct—either a dome or a shield.

lobate unit (Stofan et al., 2006). The region exhibits a high backscattering region with lobate boundaries. The bright lobate unit is evidence for cryovolcanism (Elachi et al., 2005; Lopes et al., 2007). The cryovolcanic flow seems to extend from a small hill (absent in the SAR image). Importantly, the cryovolcanic flow is surrounded by homogeneous units, which delineate its boundaries. The constructed FCM is expected to reach similar conclusions. As before, the map is initialized by selecting the initial values of the input concepts C1–C12 in a linguistic fashion. Table 4 (third column) shows the initial linguistic values selected for the FCM. In this case, no circular features are observed (‘‘absent’’) while lobate, flow-like areas (‘‘Very High’’) with high backscattering (‘‘High’’) are identified. The other concepts are initially set to be ‘‘uncertain’’ and shall be determined by the FCM dynamics. The fuzzy membership functions reported in Fig. 6 are employed to obtain a crisp value of the initial concepts via defuzzification. The initial concept value vector (1  N) is therefore the following: AIn Region3 ¼ ½0; 0; 0; 0; 0; 0; 1; 1; 0; 0; 0:75; 0:9

ð5Þ

Two possible simulations are considered. In the first simulation, we run the FCM until convergence assuming that the initial values for the observed concepts (A7, A8, A11, A12) do not change during the FCM evolution. The idea is to simulate the FCM dynamics keeping the observed parameters at a fixed value

corresponding to what it is observed. The FCM is iterated according to Eq. (1) and the concept values are updated until the map converges. The convergence criterion is based on computing the Euclidian norm of the difference between vectors at iteration k and k +1. The iteration is stopped when the norm of the error is less than 0.001. The map converged after 16 iterations. The overall evolution of the concept values during the FCM iterative process is reported in Fig. 8. Table 5 (first row) reports the final (converged) values of the FCM concepts. The FCM reaches the conclusion that potential for cryovolcanism is very high on the observed region (0.92). It also infers that the potential for cryovolcanic geomorphology is negative (  0.86), i.e., negative potential for calderas and domes (  0.76 and  0.80, respectively). Therefore cryovolcanism is likely due to the high potential for cryovolcanic flow (0.88). Negative potentials for craters ( 0.71), for channels near calderas (  0.83), and for mottled terrains (  0.85) indicate that the FCM reasons that those processes/ features are unlikely to occur. Clearly, keeping the observable initial concepts constant forces the map to reason only on the available data, i.e., flow-like features are directly used to infer cryovolcanic flow which increases the overall potential for cryovolcanism. Other features/processes that are likely to occur but are not present in the data set are not inferred. In the second simulation, we run the FCM until convergence without keeping the values of the observed concepts constant, i.e.,

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Very Low

Low

Medium

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

0.7

0.8

0.9

1

nitial concept value C1-C12 (or C1-C14 for the upgraded FCM) Fig. 6. Membership functions employed to qualitatively describe the initial value of the concepts observed in the SAR image. Crisp values are obtained via de-fuzzification using the centroid method.

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -5

-4

-3

-2

-1

0

1

2

3

4

5

Fig. 7. Tangent-sigmoid transfer function implemented in the proposed FCM.

A7, A8, A11, A12 are allowed to change during the FCM evolution. In this case, the map converges in 114 iterations. The overall evolution of the concept values during the FCM iterative process is reported in Fig. 9. Table 5 (second row) shows the final (converged) values of the map. Importantly, the FCM reaches the same conclusion as before converging to a very high value of potential for cryovolcanism (0.99). Interestingly, in this case, the map is able to reason about other cryovolcanic processes most likely occurring and connected to cryovolcanic flow but not directly observed. The map infers a high value of potential for cryovolcanic geomorphology (0.99) due to high potentials of

calderas (0.91) and domes (0.84). The potential for craters is negative (  0.93) and a high potential for cryovolcanic flow (0.96) is determined. The latter are inferred by the observed concepts.

4.3. Region 4: Ganesa Macula as cryovolcanic region The forth region under investigation is shown in the bottomleft corner of Fig. 5. The Ganesa Macula region has been interpreted as composed of two units, i.e., a dark material unit and a bright mottled unit (Stofan et al., 2006). There are two

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circular features, one demarcating the dark material unit and another delineating a possible caldera. Outside the circular region, the mottled region seems connected to cryovolcanic flow. Ganesa Macula has been interpreted as a cryovolcanic construct, either a dome or a shield. Moreover, several other features in the region have been interpreted as cryovolcanic in origin (Lopes et al.,

2007). FCM is expected to autonomously identify the region as cryovolcanic. As usual, the map is initialized by selecting the initial values of the input concepts C1–C12 in a linguistic fashion. Table 4 (forth column) shows the initial linguistic values selected for the FCM concepts. In this case, a large circular feature is clearly observed (‘‘Very High’’) together with a small, bright circular feature, most likely identified as a caldera (‘‘Very High’’). Mottled units outside the large circular feature are detected (‘‘High’’). Few channels that might be possibly connected to cryovolcanic flow are also observed. However, the initial value set for this concept is set to be ‘‘Low’’ because it is uncertain if these channels are fluvial or cryovolcanic in origin. Flow-like, lobate regions are not observed (‘‘absent’). All other concepts are set to ‘‘uncertain’’ and will be determined by the dynamic evolution of the FCM. The initial concept value vector (1  N) is therefore the following:

Table 4 Initial values of the FCM for the four case studies. Concepts initial value (linguistic)

Region 1

Region 2

Region 3

Region 4

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Absent Absent Absent Absent Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Absent Absent Absent Absent Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Absent Uncertain Uncertain High Very High

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Very High Very High Low High Absent Absent

773

AIn Region4 ¼ ½0; 0; 0; 0; 0; 0; 0:9; 0:9; 0:2; 0:75; 1; 1

ð6Þ

In this simulation, we run the FCM until convergence assuming that the initial observed concepts are free to change according to the rules established by the map architecture. The map converged after 115 iterations. The overall evolution of the concept values during the FCM iterative process is reported in Fig. 10. Table 5 (third row) reports the final (converged) values of the FCM concepts. The FCM reaches the conclusion that potential for cryovolcanism is very high on the observed region (0.99). It infers that the cryovolcanic processes are possible because of the high potential for cryovolcanic geomorphology (0.99). Indeed, the

The initial values are expressed in linguistic form. De-fuzzification is applied by using the corresponding membership function for VL, L, M, H, VH (see Fig. 6). ‘‘Uncertain’’ corresponds to the crisp value of zero and ‘‘Absent’’ corresponds to the crisp value of  1.

0 A1

-0.1

A2

A3

A4

A5

A6

A7

A8

A9

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A12

-0.2

Concept Values (Ai)

-0.3 -0.4 0.5 -0.6 0.7 -0.8 -0.9 -1 0

5

10

15 20 Number of Iterations

25

30

35

Fig. 8. Evolution of the concept values during the FCM simulation over region 1. Some of the concepts are kept constant during the iterative process to force the map to reason over the observed data. In this case the map converges after 35 iterations exhibiting a final value of the potential for cryovolcanism equal to  0.98. Consistently, no cryovolcanic activity is observed.

Table 5 Final (converged) values of the FCM for the respective regions of interest.

Region Region Region Region

3 (a) 3 (b) 4 4 Rev

A1

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

0.92 0.99 0.99  0.99

 0.86 0.99 0.99  0.98

0.88 0.96 0.92  0.96

 0.80 0.84 0.89  0.35

 0.76 0.91 0.93  0.94

 0.71  0.93  0.91 0.93

1  0.11 0.11 0.10

1  0.11 0.11 0.11

 0.83 0.86 0.87  0.87

 0.85 0.86 0.86  0.86

0.75 0.11  0.11  0.10

0.9 0.11  0.11  0.10

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1 0.8

Concept Values (Ai)

0.6 0.4 A1

0.2

A2

A3

A4

A5

A6

A7

A8

A9

A10

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A12

0 -0.2 -0.4 -0.6 -0.8 -1 2

4

6

8 10 Number of Iterations

12

14

16

1 0.8

Concept Values (Ai)

0.6 0.4 0.2 0 -0.2 -0.4 A1

-0.6

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

-0.8 -1 0

20

40

60 Number of Iterations

80

100

Fig. 9. (A) Evolution of the concept values during the first FCM simulation over the lobate region. Some of the concepts are kept constant during the iterative process to force the map to reason only on the observed data. In this case, the FCM converges after 16 iterations. (B) Evolution of the concept values during the second FCM simulation over the lobate region. In this case, all concepts are allowed to freely change during the iterative process. The FCM converges after 114 iterations to a final value of the potential for cryovolcanism equal to 0.99. The FCM interprets the region as highly cryovolcanic.

potentials for domes and calderas are very high (0.89 and 0.93, respectively). Cryovolcanic flow is likely to occur (0.92), mainly due to channels activity near the caldera (0.86) which results in an increased high value for mottled units outside the circular feature (0.87). Again, the FCM reasons accordingly, identifying cryovolcanism as predicted by domain experts (i.e., planetary scientists). Additional FCM simulations that kept the observed concepts constant during the FCM iterations have yielded similar results. 4.4. FCM sensitivity analysis A sensitivity analysis for the proposed FCM has been conducted to study the robustness of the map under input

uncertainties. The FCM has been designed and implemented as means to provide autonomous reasoning that is consistent with the way planetary scientists approach the data interpretation problem. Since the system is not completely autonomous, i.e. input data are provided by humans that extract the observable concepts by assigning them qualitative attributes, a properly designed system should show robustness to small input perturbations. FCMs are non-linear dynamical systems (Section 2.2) whose behaviors are not easy to study. Since no general theoretical framework exists that predicts short and long term system behavior, the stability and convergence of the FCM is not guaranteed. Nevertheless, good map’s behavior implies that slight changes in the qualitative input values do not alter the convergence of the map. One of the major issues is the subjective

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775

1 0.8

Concept Values (Ai)

0.6 0.4 0.2 0 -0.2 -04 A1

-0.6

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

-0.8 -1 0

20

40

60 Number of Iterations

80

100

Fig. 10. Evolution of the concept values during FCM simulation over the Ganesa Macula region. In this case, all concepts are allowed to freely change during the iterative process. The FCM converges after 115 iterations. The FCM output value (potential for cryovolcanism) is 0.99. Consequently, Ganesa Macula is interpreted as a region exhibiting high potential for cryovolcanism.

assessment of the observed parameters. The fuzzy logic framework is ideally suited to deal with uncertainties naturally found during the course of space exploration (Furfaro et al., 2008a,c). Indeed, qualitative statements such as ‘‘High’’, ‘‘Medium’’, ‘‘Low’’, are functional in describing the observable parameters without requiring higher level of precision. Yet, some degree of disagreement between different scientists examining the same SAR image is expected, although it is assumed to be reasonably small. For example, it is conceived that while examining the Ganesa Macula region, one field expert describes the observable concept C10 (mottled terrain outside the circular feature) to be ‘‘High’’, whereas another field expert may describe it as ‘‘Very High’’. To understand the consequences of slightly different choices for the input parameters, we considered region 1 (not cryovolcanic) and region 4 (cryovolcanic). For both baseline cases, we perturbed the qualitative inputs and run the designed FCM for three alternative scenarios. The qualitative inputs and the outcome of the FCM for both cases are reported in Tables 6 and 7. In all cases, the map converged to values that are very close to those obtained for the baseline scenarios. The latter indicates that the proposed FCM is robust under input uncertainties, i.e. small changes in the input values cause small changes in the FCM output. The map correctly indicates that for the perturbed data, region 1 is not cryovolcanic in nature and that region 4 exhibits cryovolcanism. The latter is consistent with the results obtained in Sections 4.1 and 4.3.

5. Adapting FCMs to new knowledge and data: Ganesa Macula revisited The FCM proposed for cryovolcanism identification has been designed to implement knowledge derived from available remote sensing data (i.e., SAR images). More specifically, the FCM architecture reflects an understanding of the observed processes that has been extracted by planetary experts from thorough analysis of available SAR data. New data coming from different sensors might yield a better understanding of the processes

Table 6 Concepts initial value (linguistic)

Region 1a

Region 1b

Region 1c

Region 1d

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Absent Absent Absent Absent Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Very low Absent Absent Low Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Absent Low Very Low Absent Absent Low

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Very low Absent Absent Very low Low Absent

FCM output

 0.98

 0.98

 0.96

 0.96

Concepts initial value (linguistic)

Region 4a

Region 4b

Region 4c

Region 4d

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Very high Very high Low High Absent Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain High Very high Very Low Very high Absent Very Low

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Very high High Medium Medium Very low Absent

Uncertain Uncertain Uncertain Uncertain Uncertain Uncertain Very high Very high Very low Very high Very low Low

FCM output

0.99

0.96

0.98

0.99

Table 7

occurring in the regions, proving or disproving phenomena that seemed to be likely from currently available information. FCMs are knowledge-driven as they reason by mimicking the human

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inference process. Clearly, FCMs have the same limitations that humans have in interpreting data: if new knowledge or data are available, the FCMs must be modified to reflect the new understanding of the processes occurring in the observed regions. Recently, Kirk et al. (2009) performed a stereoanalysis of Cassini SAR data to extract information about topography of the observed regions. Since 1–2% of Titan’s surface includes overlapping coverage, stereogrammetric techniques can be applied to obtain topographic information, such as elevation. Such techniques require availability of SAR pairs of the same region. Clearly, additional topographic information may help clarify if certain features are exactly what they seemed to be from the original SAR data examination. The proposed FCM has been constructed to reflect what was inferred by planetary scientist without the help of stereo data. Indeed, circular features were causally connected to calderas, domes or impact craters. However, stereo images may yield different conclusions. In this respect, the case of Ganesa Macula is instructive. Kirk et al. (2009) reported a SAR stereo image illustrating the topographic structure of Ganesa Macula. Surprisingly, the SAR topographic profile does not show a region that is consistently elevated. Thus, little or no expression of a dome (or a shield) is observed as originally indicated. Overall, Ganesa is tilted, low along its western edge and non-uniformly

elevated in the east. In light of this new information, the cryovolcanic interpretation appears to be weak as the region may have been extensively modified by tectonic processes and fluvial erosion. Indeed, no cryovolcanism at all may have occurred there, contrary to earlier interpretations that did not have the benefit of the stereo topographic data. What appeared to be flows could be fluvial deposits, such as overbank flood deposits, or alluvial fans. The evidence for the caldera appears to have been undermined as new data have come in (or else it is a caldera but it has partly collapsed—a fairly unattractive caveat). FCM can be modified to account for newly observed data. Here we show how to upgrade the map to process the new available information. Fig. 11 shows the modified FCM. Two new concepts (observables) have been included, i.e., the Relief Parameter (C13) and the Caldera Steepness Parameter (C14). The relief parameter is connected to the topographic height. In this case, the relationship with topographic height is set to be inverse, i.e., high elevation sets the relief parameter to be low. Despite the latter being somewhat counterintuitive, this is a choice made by the FCM designers who set a negative (high) causal relationship between relief parameter and the potential for domes. Clearly, if the relief parameter increases, the potential for domes decreases. The relief parameter is also connected to the potential for calderas. Here, the relationship is described as

Fig. 11. Updated FCM, modified to incorporate new data and/or knowledge. Two new concepts (C13: relief parameter and C14: calderas steepness parameter, both in red) have been included in the map. Such concepts negatively influence (inverse connection) both the potential for calderas and the potential for domes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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inverse (negative), i.e. increasing the relief parameter decreases the potential for calderas. The caldera steepness parameter is directly connected to the steepness of the observed circular feature. Clearly, if the circular feature shows high steepness, it is not likely to be interpreted as a caldera. Thus there is a negative (very high) causal connection between the caldera steepness parameter and the potential for calderas, i.e., increase in steepness decreases the potential for calderas. The weight matrix has been upgraded to include the connections C13–C4 (NH), C13–C5 (NH), and C14–C5 (NVH). The so updated FCM is run using inputs that characterize the Ganesa Macula region, including new data coming from the SAR stereo images. As usual, the map is initialized by selecting the initial values of the input concepts C1–C14 in a linguistic fashion. The initial concepts C1–C12 are set to be equal to the ones reported in the previous simulation (see Section 4.4). The relief parameter is set to be ‘‘Very High’’ (i.e., very low elevation) and the caldera steepness relief is set to ‘‘High’’. The initial concept value vector (1  N) is therefore the following: AIn Region4 ¼ ½0; 0; 0; 0; 0; 0; 0:9; 0:9; 0:2; 0:75; 1; 1; 0:9; 0:75

ð7Þ

In this simulation, we run the FCM until convergence assuming that the initial observed concepts are free to change according to the rules established by the map architecture. The map converged after 139 iterations. The overall evolution of the concept values during the FCM iterative process is reported in Fig. 12. Table 7 (forth row) reports the final (converged) values of the FCM concepts. The upgraded FCM reaches the conclusion that Ganesa Macula is not cryovolcanic (potential for cryovolcanism is 0.99). This conclusion is consistent with the new interpretation provided by Kirk et al. (2009). Importantly, this example shows that (a) FCMs are able to effectively mimic the planetary scientist inference process and (b) FCMs can be adapted to account for new data, i.e., as new data are introduced, the interpretation may evolve accordingly as new concepts are introduced to deal with the new data. Hence, FCMs should be required to have a capability to evolve, just as human thinking evolves.

777

6. Discussion and conclusions As shown in the previous section, the proposed FCM reaches the same conclusions as planetary scientists (i.e., using information available in the literature) by correctly identifying locales that have been interpreted as cryovolcanic. Moreover, the proposed FCM correctly interprets regions where no cryovolcanic processes are likely to occur. Importantly, FCM can be modified to account for new interpretations of the observed regions. Therefore, the FCM design appears effective and reasoning is autonomously performed in agreement with the implemented structured knowledge. Importantly, the proposed FCM is the first attempt to introduce cognitive maps coupled with fuzzy reasoning ideas to the planetary community. The proposed FCM is a proof-of-concept design that shows how the methodology can be extended to tackle the difficult problem of determining if cryovolcanism is operating/has operated on Titan. While the proposed system is self-contained, it does not show full-scale autonomy. Rather, it shows autonomous reasoning and interpretation provided that SAR data are preprocessed to extract the appropriate input concepts. Indeed, the FCM inputs have been derived by using qualitative human understanding of the SAR images. The latter helped our team to focus on the critical issue of designing a system that reasons like a scientist. Our team believes that this is only the first step towards a comprehensive approach to on-board autonomous science performed by intelligent planetary reconnaissance systems, such as tier-scalable reconnaissance mission architectures (Fink et al., 2005). Importantly, even in the case of cryovolcanism on Titan, the map could have been designed differently. Different teams may have decided to construct an alternative map to embed alternative reasoning. The latter may stimulate research in the area of how to apply FCMs for planetary exploration. It is conceivable that different/alternative views may yield completely new webs of causal connections between concepts as well as different choices of concepts. It is even conceivable that interpretation results may result from committee decisions of various FCM implementations for the same application (e.g., identification of cryovolcanism),

1 0.8 A1

0.6

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

A13

A14

Concept Values (Ai)

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0

20

40

60 80 Number of Iterations

100

120

140

Fig. 12. Evolution of the concept values during upgrade FCM simulation over the Ganesa Macula region. In this case, all concepts are allowed to freely change during the iterative process. The FCM converges after 139 iterations. The FCM potential for cryovolcanism is shown to be  0.99. Ganesa Macula is interpreted by the updated FCM as a region with very low potential for cryovolcanism.

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thereby reflecting the different prevailing scientific opinions amongst the planetary community. Clearly, careful analysis must be devoted to select concepts that can be described qualitatively but have a quantitative root. In this work, the FCM input data, required to initialize the map, have been provided directly by field experts looking at the SAR images. The initial value for the concepts have been qualitatively described by the field experts and transformed via fuzzy membership functions into a numerical value between  1 and 1. From a qualitative as well as quantitative point of view, FCM can be connected with image processing algorithms, data analysis, and anomaly detection drivers (e.g., Automated Global Feature Analyzer, AGFA, Fink et al., 2008). Such algorithms are generally able to extract numerical values for features detected from the image data. Subsequently, the processed values may be fuzzified to initialize the map. The connection between AGFA-like algorithms and FCMs represents a critical step toward designing fully autonomous systems. Indeed, future work will include implementing and testing an integrated platform to provide a sequence of autonomous algorithms that provide a closed link between observations and data interpretation. While integration and testing is planned for the integrated software using planetary data (e.g. SAR images), we are also envisioning its implementation in a tier-scalable architecture. A demonstrative two-layer test-bed (ground/rovers–aerial/blimps) is currently under development (Fink and Tarbell, 2007, 2008, 2009a,b). The ultimate goal will be to deploy and test the hardware–software autonomous tierscalable system in terrestrial environments to demonstrate its autonomous operational capabilities, and test the autonomous interpretation of real-time data streaming. The framework of FCMs is appealing because of the way structured knowledge is implemented. As in the case for fuzzy expert systems, the basis for implementing such maps is human communication and reasoning. To design such algorithms, the planetary community is required to play a critical role to ensure an effective and efficient implementation. FCMs are not merely data analysis tools where feature identifications and decisions are based purely on data crunching. FCMs put the observed data into a geological context where anomalies and identified features play a role according to the scientist understanding of the geological process at hand. Future work will include the extension of FCM to multiple scenarios such as identification of fluvial, eolian, and tectonic processes. Moreover, the design of a fuzzy expert system capable of reasoning over the same problem (i.e., autonomous assessment of cryovolcanism) is underway. As explained before, we think that both FCM and fuzzy expert systems are excellent schemes for autonomous human-like reasoning. Comparing and contrasting various techniques will deepen our understanding on how the choice of a particular scheme, employed to solve a specific problem, depends on the problem itself. In conclusion, we look to FCMs simply to help scientists and spacecraft to handle deluges of data and to help spacecraft make improved observations even under time-of-light-travel-constrained but data-rich conditions. We believe we are at the beginning of a journey that may yield innovative human-like agents capable of autonomously exploring remote planetary bodies and closely collaborating with humans. Importantly, such a process will be planetary scientist-centered, thus allowing human expertise to be implemented in linguistic form for effective communication between man and machine during the course of planetary exploration. Whereas geologists will not be able to make real-time decisions due to the delay of data streaming to and from the remote agent(s), their expertise will nevertheless be implemented to enable remote systems to reason like geologists, and even like specific human geologists and communities of geologists. Data streamed back can be evaluated and new knowledge can be acquired, allowing for the modifica-

tion of existing FCMs or the generation of new FCMs, both with upgraded reasoning capabilities.

Acknowledgments The authors wish to thank Sebastien Rodriguez for his thoughtful review comments that helped improve the manuscript.

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