Tree (set theory)
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A tree, in set theory and computer science, is a hierarchical data structure consisting of nodes connected by edges, where one node serves as the root and every other node has exactly one parent, forming branching pathways without cycles. In robotics and AI, trees appear pervasively across diverse applications: Rapidly-exploring Random Trees (RRTs) sample configuration space to solve high-dimensional motion planning problems for robots and autonomous vehicles; Behavior Trees organize decision-making logic for autonomous agents by structuring task switching in a modular, readable hierarchy; skill trees decompose complex manipulation sequences learned from demonstration; and junction trees support probabilistic inference in SLAM systems. Trees also underlie hierarchical mixture-of-experts learning architectures, spanning-tree coverage planners, and decomposition-based grasp planners. Their importance stems from several key properties: they efficiently represent branching possibilities while avoiding redundant loops, support incremental construction and anytime refinement, scale gracefully to high-dimensional spaces, and naturally encode sequential or conditional relationships. This versatility makes trees one of the most foundational mathematical structures in robotics algorithms, from perception and planning to control and learning.
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Hierarchical Mixtures of Experts and the EM Algorithm
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Neural RRT*: Learning-Based Optimal Path Planning
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Behavior Trees in Robotics and AI
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Natural terrain classification using three‐dimensional ladar data for ground robot mobility
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A new geometric notation for open and closed-loop robots
Wisama Khalil, J. Kleinfinger
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Spanning-tree based coverage of continuous areas by a mobile robot
Yoav Gabriely, Elon Rimon
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The Marathon 2: A Navigation System
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ImageRover: a content-based image browser for the World Wide Web
Stan Sclaroff, Leonid Taycher, Marco La Cascia
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Robot learning from demonstration by constructing skill trees
George Konidaris, Scott Kuindersma, Roderic A. Grupen, Andrew G. Barto
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An Efficient Sampling-Based Method for Online Informative Path Planning in Unknown Environments
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Learning contact-rich manipulation skills with guided policy search
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The Parti-game Algorithm for Variable Resolution Reinforcement Learning in Multidimensional State-spaces
Andrew Moore, Christopher G. Atkeson
Citations: 262 • 1995
Receding horizon path planning for 3D exploration and surface inspection
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Matteo Iovino, Edvards Scukins, Jonathan Styrud, Petter Ögren, Christian Smith
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Anytime RRTs
Dave Ferguson, Anthony Stentz
Citations: 235 • 2006