PRECISE LANDING OF VTOL UAVS USING A TETHER

Unmanned Aerial Vehicles (UAVs), also known as drones, are often considered the solution to complex robotics problems. The significant freedom to explore an environment is a major reason why UAVs are a popular choice for automated solutions. UAVs, however, have a very limited flight time due to the low capacity and weight ratio of current batteries. One way to extend the vehicles\u27 flight time is to use a tether to provide power from external batteries, generators on the ground, or another vehicle. Attaching a tether to a vehicle may constrain its navigation but it may also create some opportunities for improvement of some tasks, such as landing. A tethered UAV can still explore an environment, but with some additional limitations: the tether can become wrapped around or bent by an obstacle, stopping the drone from traveling further and requiring backtracking to undo; the tether can fall loose and get caught while dragging on the ground; or the base of the tether could be mobile and the UAV needs to have a way to return to it. Most issues, like those listed above, could be solved with a vision system and various kinds of markers, but this approach could not work in situations of low light, where cameras are no longer effective. In this project, a state machine was developed to land a tethered, vertical take-off and landing (VTOL) UAV using only angles taken from both ends of the tether, the tension in the tether, and the height of the UAV. The main scenarios focused on in this project were normal operation, obstacle interference, loose tether, and a moving base. Normal operation is essentially tether guidance using the tether as a direction back to the base. The obstacle case has to determine the best action for untangling the tether. The loose tether case has to handle the loss of information given by the angle sensors, as the tether direction is no longer available. This case is performed as a last-ditched effort to find the landing pad with only a moderate chance for success. Lastly, the moving base case uses the change in the angles over time to determine the speed needed to reach the base. The software was not the only focus of this project. Two hardware components of this project were a landing platform and a matching landing gear to support the landing process. These two components were designed to aid in the precision of the landed location and to ensure that the UAV was secured in position once landed. The landing platform was designed as a passive funnel-type positioning mechanism with a depression in the center that the landing gear was designed to match. The tension of the tether is used to further lock the UAV into place when in motion. While some of this project remained theoretical, particularly the moving base case, there was flight testing performed for validation of most states of the proposed state machine. The normal operation state was effective at guiding the UAV onto the landing pad. The loose tether case was also able to land within reasonable expectations. This case was not always successful at finding the landing pad. Particular methods of increasing the likelihood of success are discussed in Future Work. The Obstacle Case was also able to be detected, but the response action has yet to be tested in full. The prior testing of velocity following can be used as proof of concept due to its simplicity. In conclusion, this project successfully developed a state machine for precisely landing a tethered UAV with no environmental knowledge or localization. Further development is necessary to improve the likelihood of landing in problematic scenarios and more testing is necessary for the system as a whole. More landing scenarios could also be researched and added as cases to the state machine to increase the robustness of the landing process. However, each current subsystem achieved some level of validation and is to be improved with future developments

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

Reorganization of columnar architecture in the growing visual cortex

Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal circuits. Here, in acute and chronic experiments, we study the layout of ocular dominance (OD) columns in cat primary visual cortex (V1) during a period of substantial postnatal growth. We find that despite a considerable size increase of V1, the spacing between columns is largely preserved. In contrast, their spatial arrangement changes systematically over this period. While in young animals columns are more band-like, layouts become more isotropic in mature animals. We propose a novel mechanism of growth-induced reorganization that is based on the `zigzag instability', a dynamical instability observed in several inanimate pattern forming systems. We argue that this mechanism is inherent to a wide class of models for the activity-dependent formation of OD columns. Analyzing one member of this class, the Elastic Network model, we show that this mechanism can account for the preservation of column spacing and the specific mode of reorganization of OD columns that we observe. We conclude that neurons systematically shift their selectivities during normal development and that this reorganization is induced by the cortical expansion during growth. Our work suggests that cortical circuits remain plastic for an extended period in development in order to facilitate the modification of neuronal circuits to adjust for cortical growth.Comment: 8+13 pages, 4+8 figures, paper + supplementary materia

A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets

We give a sharpening of a recent result of Aschenbrenner and Pong about the maximal order type of the term ordering on the finite multisets over a wpo. Moreover we discuss an approach to compute maximal order types of well-partial orders which are related to tree embeddings

Argonaute2 regulates the pancreatic β-cell secretome

Argonaute2 (Ago2) is an established component of the microRNA-induced silencing complex. Similar to miR-375 loss-of-function studies, inhibition of Ago2 in the pancreatic beta-cell resulted in enhanced insulin release underlining the relationship between these two genes. Moreover, as the most abundant microRNA in pancreatic endocrine cells, miR-375 was also observed to be enriched in Ago2-associated complexes. Both Ago2 and miR-375 regulate the pancreatic beta-cell secretome and we identified using quantitative mass spectrometry the enhanced release of a set of proteins or secretion signature in response to a glucose stimulus using the murine beta-cell line, MIN6. In addition, loss of Ago2 resulted in the increased expression of miR-375 target genes, including gephyrin and ywhaz. These targets positively contribute to exocytosis indicating they may mediate the functional role of both miR-375 and Ago proteins in the pancreatic beta-cell by influencing the secretory pathway. This study specifically addresses the role of Ago2 in the systemic release of proteins from beta-cells and highlights the contribution of the microRNA pathway to the function of this cell type

An order-theoretic characterization of the Howard-Bachmann-hierarchy

In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π₁¹-comprehension

On Relating Theories: Proof-Theoretical Reduction

The notion of proof-theoretical or finitistic reduction of one theory to another has a long tradition. Feferman and Sieg (Buchholz et al., Iterated inductive definitions and subsystems of analysis. Springer, Berlin, 1981, Chap. 1) and Feferman in (J Symbol Logic 53:364–384, 1988) made first steps to delineate it in more formal terms. The first goal of this paper is to corroborate their view that this notion has the greatest explanatory reach and is superior to others, especially in the context of foundational theories, i.e., theories devised for the purpose of formalizing and presenting various chunks of mathematics. A second goal is to address a certain puzzlement that was expressed in Feferman’s title of his Clermont-Ferrand lectures at the Logic Colloquium 1994: “How is it that finitary proof theory became infinitary?” Hilbert’s aim was to use proof theory as a tool in his finitary consistency program to eliminate the actual infinite in mathematics from proofs of real statements. Beginning in the 1950s, however, proof theory began to employ infinitary methods. Infinitary rules and concepts, such as ordinals, entered the stage. In general, the more that such infinitary methods were employed, the farther did proof theory depart from its initial aims and methods, and the closer did it come instead to ongoing developments in recursion theory, particularly as generalized to admissible sets; in both one makes use of analogues of regular cardinals, as well as “large” cardinals (inaccessible, Mahlo, etc.). (Feferman 1994). The current paper aims to explain how these infinitary tools, despite appearances to the contrary, can be formalized in an intuitionistic theory that is finitistically reducible to (actually Π02 -conservative over) intuitionistic first order arithmetic, also known as Heyting arithmetic. Thus we have a beautiful example of Hilbert’s program at work, exemplifying the Hilbertian goal of moving from the ideal to the real by eliminating ideal elements

The tomato Prf complex is a molecular trap for bacterial effectors based on Pto transphosphorylation

The bacteria Pseudomonas syringae is a pathogen of many crop species and one of the model pathogens for studying plant and bacterial arms race coevolution. In the current model, plants perceive bacteria pathogens via plasma membrane receptors, and recognition leads to the activation of general defenses. In turn, bacteria inject proteins called effectors into the plant cell to prevent the activation of immune responses. AvrPto and AvrPtoB are two such proteins that inhibit multiple plant kinases. The tomato plant has reacted to these effectors by the evolution of a cytoplasmic resistance complex. This complex is compromised of two proteins, Prf and Pto kinase, and is capable of recognizing the effector proteins. How the Pto kinase is able to avoid inhibition by the effector proteins is currently unknown. Our data shows how the tomato plant utilizes dimerization of resistance proteins to gain advantage over the faster evolving bacterial pathogen. Here we illustrate that oligomerisation of Prf brings into proximity two Pto kinases allowing them to avoid inhibition by the effectors by transphosphorylation and to activate immune responses