On Advanced Mobility Concepts for Intelligent Planetary Surface Exploration

Surface exploration by wheeled rovers on Earth's Moon (the two Lunokhods) and Mars (Nasa's Sojourner and the two MERs) have been followed since many years already very suc-cessfully, specifically concerning operations over long time. However, despite of this success, the explored surface area was very small, having in mind a total driving distance of about 8 km (Spirit) and 21 km (Opportunity) over 6 years of operation. Moreover, ESA will send its ExoMars rover in 2018 to Mars, and NASA its MSL rover probably this year. However, all these rovers are lacking sufficient on-board intelligence in order to overcome longer dis-tances, driving much faster and deciding autonomously on path planning for the best trajec-tory to follow. In order to increase the scientific output of a rover mission it seems very nec-essary to explore much larger surface areas reliably in much less time. This is the main driver for a robotics institute to combine mechatronics functionalities to develop an intelligent mo-bile wheeled rover with four or six wheels, and having specific kinematics and locomotion suspension depending on the operational terrain of the rover to operate. DLR's Robotics and Mechatronics Center has a long tradition in developing advanced components in the field of light-weight motion actuation, intelligent and soft manipulation and skilled hands and tools, perception and cognition, and in increasing the autonomy of any kind of mechatronic systems. The whole design is supported and is based upon detailed modeling, optimization, and simula-tion tasks. We have developed efficient software tools to simulate the rover driveability per-formance on various terrain characteristics such as soft sandy and hard rocky terrains as well as on inclined planes, where wheel and grouser geometry plays a dominant role. Moreover, rover optimization is performed to support the best engineering intuitions, that will optimize structural and geometric parameters, compare various kinematics suspension concepts, and make use of realistic cost functions like mass and consumed energy minimization, static sta-bility, and more. For self-localization and safe navigation through unknown terrain we make use of fast 3D stereo algorithms that were successfully used e.g. in unmanned air vehicle ap-plications and on terrestrial mobile systems. The advanced rover design approach is applica-ble for lunar as well as Martian surface exploration purposes. A first mobility concept ap-proach for a lunar vehicle will be presented

A systematic literature review of soft set theory

[EN] Soft set theory, initially introduced through the seminal article ‘‘Soft set theory—First results’’ in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is notably absent in the existing literature. We aim to bridge this gap. This survey delves into the basic elements of the theory, including the notion of a soft set, the operations on soft sets, and their semantic interpretations. It describes various generalizations and modifications of soft set theory, such as N-soft sets, fuzzy soft sets, and bipolar soft sets, highlighting their specific characteristics. Furthermore, this work outlines the fundamentals of various extensions of mathematical structures from the perspective of soft set theory. Particularly, we present basic results of soft topology and other algebraic structures such as soft algebras and sigma-algebras. This article examines a selection of notable applications of soft set theory in different fields, including medicine and economics, underscoring its versatile nature. The survey concludes with a discussion on the challenges and future directions in soft set theory, emphasizing the need for further research to enhance its theoretical foundations and broaden its practical applications. Overall, this survey of soft set theory serves as a valuable resource for practitioners, researchers, and students interested in understanding and utilizing this flexible mathematical framework for tackling uncertainty in decision-making processes

Cluster soft sets and cluster soft topologies

The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental properties of cluster soft sets are demonstrated. Moreover, the concept of a cluster soft topology on a universal set is introduced with regard to the cluster soft sets. The cluster soft topology is derived from a soft topology with an associated soft ideal, but it is finer than the original soft topology. On the other hand, if we start constructing the cluster soft topology from another cluster soft topology, we will end up with the first cluster soft topology we started with. The implication of cluster soft topologies is highlighted using some examples. Eventually, we represent the cluster soft closed sets in terms of several forms of soft sets

Softarisons: theory and practice

[EN] This paper introduces the concept of softarison. Softarisons merge soft set theory with the theory of binary relations. Their purpose is the comparison of alternatives in a parameterized environment. We develop the basic theory and interpretations of softarisons. Then, the normative idea of ‘optimal’ alternatives is discussed in this context. We argue that the meaning of ‘optimality’ can be adjusted to fit in with the structure of each problem. A sufficient condition for the existence of an optimal alternative for unrestricted sets of alternatives is proven. This result means a counterpart of Weierstrass extreme value theorem for softarisons; thus, it links soft topology with the act of choice. We also provide a decision-making procedure—the minimax algorithm—when the alternatives are compared through a softarison. A case-study in the context of group interviews illustrates both the application of softarisons as an evaluation tool, and the computation of minimax solutions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL