Graph
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A graph is a mathematical structure composed of nodes (vertices) and edges (connections between nodes), forming a flexible framework for representing relationships, spatial layouts, and sequential decisions. In robotics and AI, graphs appear across an exceptionally broad range of applications: motion planning algorithms build roadmaps or search trees through configuration spaces to find collision-free paths; SLAM systems represent robot poses and sensor constraints as factor or pose graphs, enabling efficient map optimization; multi-robot coordination uses graph-theoretic tools to model communication topology and formation structure; and activity recognition or trajectory prediction leverages graph neural networks to capture spatial-temporal relationships between agents. Algorithms such as A*, D*, and probabilistic roadmaps fundamentally operate by constructing and searching graphs. The versatility of graph representations makes them indispensable throughout robotics—they unify geometric, probabilistic, and relational information into a single abstraction, enabling scalable and principled solutions to planning, perception, mapping, and coordination problems that would otherwise be computationally intractable or difficult to formalize.
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Lydia E. Kavraki, P. Švestka, J.-C. Latombe, M.H. Overmars
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Robot Motion Planning
Jean‐Claude Latombe
Citations: 5429 • 1991
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A Tutorial on Graph-Based SLAM
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Modeling and control of formations of nonholonomic mobile robots
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Robot Motion Planning: A Distributed Representation Approach
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Numerical potential field techniques for robot path planning
Jérôme Barraquand, B. Langlois, J.-C. Latombe
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The focussed D* algorithm for real-time replanning
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Landmarks in graphs
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Toward Efficient Trajectory Planning: The Path-Velocity Decomposition
Kamal Kant, Steven W. Zucker
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AND/OR Graph Representation of Assembly Plans
Luiz S. Homem de Mello
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Introduction to Algorithms
Peter Grossman
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STGAT: Modeling Spatial-Temporal Interactions for Human Trajectory Prediction
Ying-Fan Huang, Huikun Bi, Zhaoxin Li, Tianlu Mao, Zhaoqi Wang
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Path planning techniques for mobile robots: Review and prospect
Lixing Liu, Xu Wang, Hongjie Liu, Jianping Li, Pengfei Wang
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Integration of representation into goal-driven behavior-based robots
Maja J. Matarić
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Stabilisation of infinitesimally rigid formations of multi-robot networks
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Anytime dynamic A*: an anytime, replanning algorithm
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Factor Graphs and GTSAM: A Hands-on Introduction
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Unstructured human activity detection from RGBD images
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