Geometry
Related papers: 20
About
Geometry, in the context of robotics and AI, is the mathematical study of shapes, spatial relationships, distances, and transformations that forms the foundational language for describing and reasoning about physical systems. It encompasses both classical geometry and its computational extensions, including the representation of points, curves, surfaces, and rigid bodies in two- and three-dimensional space. In robotics, geometry is applied across a vast range of tasks: computing robot kinematics and workspace boundaries, planning collision-free motion paths, registering point clouds for perception, calibrating sensors relative to manipulators, and modeling the structure of continuum and parallel robots. Computational geometry provides the algorithms needed to efficiently solve these problems, such as distance computation between objects, convex optimization over geometric constraints, and coordinate frame transformations using quaternions or rotation matrices. Geometry matters because nearly every robotic capability — grasping, navigation, manipulation, and scene understanding — ultimately depends on correctly representing and reasoning about spatial structure, making geometric methods indispensable to both the theory and practice of modern robotics and AI.
Top Researchers
Top Cited Papers
Computational Geometry: Algorithms and Applications
Mark de Berg, Otfried Cheong, Marc van Kreveld, Mark Overmars
Citations: 4506 • 1997
Closed-form solution of absolute orientation using unit quaternions
Berthold K. P. Horn
Citations: 4109 • 1987
The university of Florida sparse matrix collection
Timothy A. Davis, Yifan Hu
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Applications of second-order cone programming
Miguel Sousa Lobo, Lieven Vandenberghe, Stephen Boyd, Hervé Lebret
Citations: 2415 • 1998
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
Robert J. Webster, Bryan A. Jones
Citations: 2213 • 2010
On-Line Computational Scheme for Mechanical Manipulators
J.Y.S. Luh, Michael Walker, Richard P. Paul
Citations: 1574 • 1980
A fast procedure for computing the distance between complex objects in three-dimensional space
Éric Gilbert, Daniel Johnson, S. Sathiya Keerthi
Citations: 1470 • 1988
Soft Robotics for Chemists
Filip Ilievski, Aaron D. Mazzeo, Robert F. Shepherd, Xin Chen, George M. Whitesides
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A new technique for fully autonomous and efficient 3D robotics hand/eye calibration
R. Tsai, R. Lenz
Citations: 1343 • 1989
Handbook of Discrete and Computational Geometry, Second Edition
Citations: 1229 • 2004
Computational Geometry in C
Joseph O’Rourke, A. John Mallinckrodt
Citations: 1207 • 1995
Closed-form solution of absolute orientation using orthonormal matrices
Berthold K. P. Horn, Hugh M. Hilden, S. Negahdaripour
Citations: 1147 • 1988
Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control
Yoshihiko Nakamura, Hideo Hanafusa
Citations: 1064 • 1986
Deep Closest Point: Learning Representations for Point Cloud Registration
Yue Wang, Justin Solomon
Citations: 1008 • 2019
Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles
Zhihua Qu, Jing Wang, R Hull
Citations: 1005 • 2009
Biomechanical Consequences of a Tear of the Posterior Root of the Medial Meniscus
Robert Allaire, Muturi Muriuki, Lars G. Gilbertson, Christopher D. Harner
Citations: 1002 • 2008
Minimum-time control of robotic manipulators with geometric path constraints
Kang G. Shin, Neil David McKay
Citations: 992 • 1985
PCN: Point Completion Network
Wentao Yuan, Tejas Khot, David Held, Christoph Mertz, Martial Hebert
Citations: 955 • 2018
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
Clément Gosselin, Jorge Angeles
Citations: 948 • 1991
Kinematics for multisection continuum robots
Cliff B. Jones, Ian D. Walker
Citations: 937 • 2006