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.

Top Cited Papers

Singularity analysis of closed-loop kinematic chains

Clément Gosselin, Jorge Angeles

Citations: 1719 • 1990

Distributed multi‐vehicle coordinated control<i>via</i>local information exchange

Wei Ren, Ella Atkins

Citations: 1478 • 2006

Structural properties and classification of kinematic and dynamic models of wheeled mobile robots

G. Campion, Georges Bastin, Brigitte d’Andréa-Novel

Citations: 1162 • 1996

A decentralized approach to formation maneuvers

Jonathan Lawton, Randal W. Beard, Bobbi Young

Citations: 1050 • 2003

Learning metric-topological maps for indoor mobile robot navigation

Sebastian Thrun

Citations: 1049 • 1998

Elastic bands: connecting path planning and control

Sean Quinlan, Oussama Khatib

Citations: 797 • 2002

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

Citations: 707 • 1991

Topological simultaneous localization and mapping (SLAM): toward exact localization without explicit localization

Howie Choset, Keiji Nagatani

Citations: 619 • 2001

Statics and Dynamics of Continuum Robots With General Tendon Routing and External Loading

D. Caleb Rucker, Robert J. Webster

Citations: 616 • 2011

A modal approach to hyper-redundant manipulator kinematics

Gregory S. Chirikjian, Joel W. Burdick

Citations: 584 • 1994

A motion planner for nonholonomic mobile robots

Jean‐Paul Laumond, P. Jacobs, Michel Taïx, Richard M. Murray

Citations: 582 • 1994

Robot navigation functions on manifolds with boundary

Daniel E. Koditschek, Elon Rimon

Citations: 565 • 1990

Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments

Yongcan Cao, Daniel Stuart, Wei Ren, Ziyang Meng

Citations: 560 • 2010

Singular Configurations of Parallel Manipulators and Grassmann Geometry

Jean‐Pierre Merlet

Citations: 554 • 1989

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Soon‐Jo Chung, Jean-Jacques Slotine

Citations: 551 • 2009

Stabilisation of infinitesimally rigid formations of multi-robot networks

Laura Krick, Mireille E. Broucke, Bruce A. Francis

Citations: 547 • 2008

New lower bound techniques for robot motion planning problems

John Canny, John H. Reif

Citations: 544 • 1987

Singular configurations of parallel manipulators and grassmann geometry

Jean‐Pierre Merlet

Citations: 499 • 1989

Analyzing proteome topology and function by automated multidimensional fluorescence microscopy

Walter Schubert, Bernd Bonnekoh, Ansgar J. Pommer, Lars Philipsen, Raik Böckelmann, Yanina N. Malykh, Harald Gollnick, Manuela Friedenberger, Marcus Bode, Andreas Dress

Citations: 495 • 2006