High-Dimensional Design Evaluations For Self-Aligning Geometries

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Doctor of Philosophy (PhD)
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Mechanical Engineering & Applied Mechanics
Applied Mathematics
Mechanical Engineering
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Eckenstein, Nicholas Edward

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 'pre-partitioning' 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.

Mark H. Yim
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