Frenet–Serret formulas

Real-time robot motion planning using rasterizing computer graphics hardware

Jed Lengyel, Mark Reichert, Bruce R. Donald, Donald P. Greenberg

Citations: 219 • 1990

Path planning for deformable linear objects

Mark Moll, Lydia E. Kavraki

Citations: 204 • 2006

3D Shape Sensing With Multicore Optical Fibers: Transformation Matrices Versus Frenet-Serret Equations for Real-Time Application

Davide Paloschi, Kirill Bronnikov, Sanzhar Korganbayev, Alexey A. Wolf, А. В. Достовалов, Paola Saccomandi

Citations: 54 • 2020

Parsimonious Evaluation of Concentric-Tube Continuum Robot Equilibrium Conformation

Robert J. Webster, Daniel Rücker

Citations: 43 • 2009

Rational rotation-minimizing frames on polynomial space curves of arbitrary degree

Rida T. Farouki, Takis Sakkalis

Citations: 39 • 2010

Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves

Rida T. Farouki

Citations: 36 • 2002

Different Kinematic Path Following Controllers for a Wheeled Mobile Robot of (2,0) Type

J. Płaskonka

Citations: 27 • 2013

Model-Based Planar Contour Following in the Presence of Pose and Model Errors

Sabine Demey, Herman Bruyninckx, Joris De Schutter

Citations: 17 • 1997

Feedback-linearization-based 3D needle steering in a Frenet-Serret frame using a reduced order bicycle model

Mohsen Khadem, Carlos Rossa, Nawaid Usmani, Ron S. Sloboda, Mahdi Tavakoli

Citations: 16 • 2017

Geometry of the motion of robot manipulators

Adolf Karger

Citations: 16 • 1988

The path following control of a unicycle based on the chained form of a kinematic model derived with respect to the Serret-Frenet frame

J. Płaskonka

Citations: 15 • 2012

Characterisation of Frenet–Serret and Bishop motions with applications to needle steering

J. M. Selig

Citations: 15 • 2013

Velocity Distribution Profile for Robot Arm Motion Using Rational Frenet–Serret Curves

Reza Ravani, Ali Meghdari

Citations: 12 • 2006

Differential geometry modeling and application of roller pose and trajectory of robot roller hemming for complex curved surface-curved edge panels

Shunchao Wang, Wenfeng Zhu, Mozhi Li

Citations: 11 • 2023

Chained formulation of 3D path following for nonholonomic autonomous robots in a Serret-Frenet frame

Ali Oulmas, Nicolas Andreff, Stéphane Régnier

Citations: 11 • 2016

Kinematic Analysis of Novel Soft Robotic Arm Based on Virtual Work Principle

Zhiyuan Zhang, Xueqian Wang, Houde Liu, Bin Liang, Songtao Wang

Citations: 9 • 2018

Introducing Radius of Torsure and Cylindroid of Torsure

David B. Dooner

Citations: 7 • 2003

Spatial rational motions based on rational frenet-serret curves

Reza Ravani, Ali Meghdari

Citations: 7 • 2005

Industrial Robot Contouring Control Based on Non-Uniform Rational B-Spline Curve

Guirong Wang, Jiahao Chen, Kun Zhou, Zhihui Pang

Citations: 6 • 2022

Reconstruction method with twisting measurement and compensation for shape sensing of flexible robots

Xiangyan Chen, Tingting Shen, Jinwu Qian, Yingjie Yu, Zhonghua Miao

Citations: 5 • 2024