Topology (electrical circuits)
Related papers: 20
About
Topology, in the context of robotics and AI, refers to the mathematical study of spatial properties and structural relationships that remain invariant under continuous deformation — concerned with connectivity, boundaries, and shape rather than precise distances or coordinates. In robotics, topological concepts appear across multiple domains: mobile robots use topological maps to represent environments as networks of nodes and edges rather than metric grids, enabling navigation and simultaneous localization and mapping (SLAM) without exact geometric precision. Topological methods also characterize the configuration spaces of manipulators and mobile platforms, identifying singularities, reachable regions, and motion planning complexity. In multi-robot systems, graph-theoretic (topological) descriptions of communication and sensing networks underpin formation control, consensus protocols, and connectivity maintenance algorithms. Neural network architecture design similarly leverages topological thinking when evolving network structures. Topology matters because it captures the essential "shape" of a problem — revealing fundamental constraints on motion planning, quantifying task complexity independent of specific geometries, and enabling robust, lightweight representations that scale well to large environments and systems.
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Top Institutes
Top Cited Papers
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Structural properties and classification of kinematic and dynamic models of wheeled mobile robots
G. Campion, Georges Bastin, Brigitte d’Andréa-Novel
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Jonathan Lawton, Randal W. Beard, Bobbi Young
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Learning metric-topological maps for indoor mobile robot navigation
Sebastian Thrun
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The Spatial Semantic Hierarchy
Benjamin Kuipers
Citations: 722 • 2000
A robot exploration and mapping strategy based on a semantic hierarchy of spatial representations
Benjamin Kuipers, Yung-Tai Byun
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Topological simultaneous localization and mapping (SLAM): toward exact localization without explicit localization
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Statics and Dynamics of Continuum Robots With General Tendon Routing and External Loading
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A motion planner for nonholonomic mobile robots
Jean‐Paul Laumond, P. Jacobs, Michel Taïx, Richard M. Murray
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Robot navigation functions on manifolds with boundary
Daniel E. Koditschek, Elon Rimon
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Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments
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Singular Configurations of Parallel Manipulators and Grassmann Geometry
Jean‐Pierre Merlet
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Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems
Soon‐Jo Chung, Jean-Jacques Slotine
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Laura Krick, Mireille E. Broucke, Bruce A. Francis
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New lower bound techniques for robot motion planning problems
John Canny, John H. Reif
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Singular configurations of parallel manipulators and grassmann geometry
Jean‐Pierre Merlet
Citations: 499 • 1989
Analyzing proteome topology and function by automated multidimensional fluorescence microscopy
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