Tree (set theory)

Related papers: 20

About

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.

Top Cited Papers

Hierarchical Mixtures of Experts and the EM Algorithm

Michael I. Jordan, Robert A. Jacobs

Citations: 2632 • 1994

Motion Planning in Dynamic Environments Using Velocity Obstacles

Paolo Fiorini, Zvi Shiller

Citations: 1930 • 1998

Anytime Motion Planning using the RRT*

Sertaç Karaman, Matthew R. Walter, Alejandro Pérez, Emilio Frazzoli, Seth Teller

Citations: 871 • 2011

Receding Horizon "Next-Best-View" Planner for 3D Exploration

Andreas Bircher, Mina Kamel, Kostas Alexis, Helen Oleynikova, Roland Siegwart

Citations: 601 • 2016

A Real-Time Apple Targets Detection Method for Picking Robot Based on Improved YOLOv5

Bin Yan, Pan Fan, Xiaoyan Lei, Zhijie Liu, Fuzeng Yang

Citations: 564 • 2021

Sensors and systems for fruit detection and localization: A review

Aleana Gongal, Suraj Amatya, Manoj Karkee, Q. Zhang, K.M. Lewis

Citations: 557 • 2015

Neural RRT*: Learning-Based Optimal Path Planning

Jiankun Wang, Wenzheng Chi, Chenming Li, Chaoqun Wang, Max Q.‐H. Meng

Citations: 533 • 2020

Behavior Trees in Robotics and AI

Michele Colledanchise, Petter Ögren

Citations: 465 • 2018

Natural terrain classification using three‐dimensional ladar data for ground robot mobility

Jean‐François Lalonde, Nicolas Vandapel, Daniel F. Huber, Martial Hebert

Citations: 461 • 2006

A new geometric notation for open and closed-loop robots

Wisama Khalil, J. Kleinfinger

Citations: 392 • 1986

Spanning-tree based coverage of continuous areas by a mobile robot

Yoav Gabriely, Elon Rimon

Citations: 380 • 2001

The Marathon 2: A Navigation System

Steve Macenski, Francisco Martí­n, Ruffin White, Jonatan Ginés

Citations: 329 • 2020

ImageRover: a content-based image browser for the World Wide Web

Stan Sclaroff, Leonid Taycher, Marco La Cascia

Citations: 301 • 1997

Robot learning from demonstration by constructing skill trees

George Konidaris, Scott Kuindersma, Roderic A. Grupen, Andrew G. Barto

Citations: 300 • 2011

An Efficient Sampling-Based Method for Online Informative Path Planning in Unknown Environments

Lukas Schmid, Michael Pantic, Raghav Khanna, Lionel Ott, Roland Siegwart, Juan Nieto

Citations: 297 • 2020

Learning contact-rich manipulation skills with guided policy search

Sergey Levine, Nolan Wagener, Pieter Abbeel

Citations: 280 • 2015

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

Andreas Bircher, Mina Kamel, Kostas Alexis, Helen Oleynikova, Roland Siegwart

Citations: 257 • 2016

A survey of Behavior Trees in robotics and AI

Matteo Iovino, Edvards Scukins, Jonathan Styrud, Petter Ögren, Christian Smith

Citations: 250 • 2022

Anytime RRTs

Dave Ferguson, Anthony Stentz

Citations: 235 • 2006