Multi-robot team formation control in the GUARDIANS project

Purpose The GUARDIANS multi-robot team is to be deployed in a large warehouse in smoke. The team is to assist firefighters search the warehouse in the event or danger of a fire. The large dimensions of the environment together with development of smoke which drastically reduces visibility, represent major challenges for search and rescue operations. The GUARDIANS robots guide and accompany the firefighters on site whilst indicating possible obstacles and the locations of danger and maintaining communications links. Design/methodology/approach In order to fulfill the aforementioned tasks the robots need to exhibit certain behaviours. Among the basic behaviours are capabilities to stay together as a group, that is, generate a formation and navigate while keeping this formation. The control model used to generate these behaviours is based on the so-called social potential field framework, which we adapt to the specific tasks required for the GUARDIANS scenario. All tasks can be achieved without central control, and some of the behaviours can be performed without explicit communication between the robots. Findings The GUARDIANS environment requires flexible formations of the robot team: the formation has to adapt itself to the circumstances. Thus the application has forced us to redefine the concept of a formation. Using the graph-theoretic terminology, we can say that a formation may be stretched out as a path or be compact as a star or wheel. We have implemented the developed behaviours in simulation environments as well as on real ERA-MOBI robots commonly referred to as Erratics. We discuss advantages and shortcomings of our model, based on the simulations as well as on the implementation with a team of Erratics.</p

Overcoming the Newtonian Paradigm: The Unfinished Project of Theoretical Biology from a Schellingian Perspective

Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that has always had to give ground, it is shown that many of the most important advances in mathematics and physics over the last two centuries have followed from Schelling’s demand for a new physics that could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but progressive tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico echemical morphology research program, the biosemiotics movement, and the relational biology of Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Some open problems on permutation patterns

This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns in Permutations and words}. I first survey recent developments on the enumeration and asymptotics of the pattern 1324, the last pattern of length 4 whose asymptotic growth is unknown, and related issues such as upper bounds for the number of avoiders of any pattern of length $k$ for any given $k$. Other subjects treated are the M\"obius function, topological properties and other algebraic aspects of the poset of permutations, ordered by containment, and also the study of growth rates of permutation classes, which are containment closed subsets of this poset.Comment: 20 pages. Related to upcoming talk at the British Combinatorial Conference 2013. To appear in London Mathematical Society Lecture Note Serie

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman's functionals and related entropic values are used for deriving relativistic geometric evolution flow equations. For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. We analyze possible connections between relativistic models of nonholonomic Ricci flows and emergent modified gravity theories. We prove that corresponding systems of nonlinear partial differential equations, PDEs, for entropic flows and modified gravity possess certain general decoupling and integration properties. There are constructed new classes of exact and parametric solutions for nonstationary configurations and locally anisotropic cosmological metrics in modified gravity theories and general relativity. Such solutions describe scenarios of nonlinear geometric evolution and gravitational and matter field dynamics with pattern-forming and quasiperiodic structure and various space quasicrystal and deformed spacetime crystal models. We analyze new classes of generic off-diagonal solutions for entropic gravity theories and show how such solutions can be used for explaining structure formation in modern cosmology. Finally, we speculate why the approaches with Perelman-Lyapunov type functionals are more general or complementary to the constructions elaborated using the concept of Bekenstein-Hawking entropy.Comment: accepted to EPJC; latex2e 11pt, 35 pages with a table of contents; v3 is substantially modified with a new title and a new co-autho

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties

We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the Bialynicki-Birula stratification of a variety with an action of the multiplicative group. The resulting categorical cell decomposition provides an algebro-geometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K-theory and Hochschild homology of module categories of interest in geometric representation theory.Comment: Version 2. A number of minor edits and corrections. Comments welcom

Control structure for a car-like robot using artificial neural networks and genetic algorithms

The idea of improving human’s life quality by making life more comfortable and easy is nowadays possible using current technologies and techniques to solve complex daily problems. The presented idea in this work proposes a control strategy for autonomous robotic systems, specifically car-like robots. The main objective of this work is the development of a reactive navigation controller by means of obstacles avoidance and position control to reach a desired position in an unknown environment. This research goal was achieved by the integration of potential fields and neuroevolution controllers. The neuro-evolutionary controller was designed using the (NEAT) algorithm “Neuroevolution of Augmented Topologies” and trained using a designed training environment. The methodology used allowed the vehicle to reach a certain level of autonomy, obtaining a stable controller that includes kinematic and dynamic considerations. The obtained results showed significant improvements compared to the comparison workCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQNão te