121 research outputs found
High-Dimensional Design Evaluations For Self-Aligning Geometries
Physical connectors with self-aligning geometry aid in the docking process for many robotic and automatic control systems such as robotic self-reconfiguration and air-to-air refueling. This self-aligning geometry provides a wider range of acceptable error tolerance in relative pose between the two rigid objects, increasing successful docking chances. In a broader context, mechanical alignment properties are also useful for other cases such as foot placement and stability, grasping or manipulation. Previously, computational limitations and costly algorithms prevented high-dimensional analysis. The algorithms presented in this dissertation will show a reduced computational time and improved resolution for this kind of problem.
This dissertation reviews multiple methods for evaluating modular robot connector geometries as a case study in determining alignment properties. Several metrics are introduced in terms of the robustness of the alignment to errors across the full dimensional range of possible offsets. Algorithms for quantifying error robustness will be introduced and compared in terms of accuracy, reliability, and computational cost. Connector robustness is then compared across multiple design parameters to find trends in alignment behavior. Methods developed and compared include direct simulation and contact space analysis algorithms (geometric by a \u27pre-partitioning\u27 method, and discrete by flooding). Experimental verification for certain subsets is also performed to confirm the results. By evaluating connectors using these algorithms we obtain concrete metric values. We then quantitatively compare their alignment capabilities in either SE(2) or SE(3) under a pseudo-static assumption
Local topological moves determine global diffusion properties of hyperbolic higher-order networks
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, represents nowadays still a challenge and is the object of intense research. Here we introduce two non-equilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the interwined appearance of small-world behavior, -hyperbolicity and community structure. We show that different topological moves determining the non-equilibrium growth of the higher-order hyperbolic network models induce tunable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the areavolume ratio, the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the areavolume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics
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