Application of Mathematical Analysis and Theory to Robotics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 2974

Special Issue Editors


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Guest Editor
Mechanical Engineering Department, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Interests: kinematics; dynamics; robotics; screw theory; Lie algebra; Euclidean group
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Interests: kinematics; robotics; mechanical design; material science

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics focuses on the Application of Mathematical Analysis and Theory to Robotics, with the aim of solving emerging problems in a creative, novel, and efficient way, as well as optimizing solutions to existing robotics problems. With the exponential growth of new areas of robotics, such as reconfigurable manipulators, walking machines, rehabilitation robots, grasping robots, collaborative robots, hyper-redundant manipulators, and so on, in addition to conventional robots such as parallel and serial manipulators, mathematical methods have been challenged to progress in relatively short periods of time. The benefits of efficient mathematical methods in line with new robot manipulators are reflected, for example, in faster, more accurate, and environmentally friendly robots. The purpose of this Special Issue is to selectively collect new results related to the application of known and new mathematical methods for solving emerging problems in robotics, in addition to improving existing ones. Thus, this is an open invitation to academics to share research work in this area.

Prof. Dr. Jaime Gallardo-Alvarado
Prof. Dr. L. A. Alcaraz-Caracheo
Guest Editors

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Keywords

  • higher-order kinematics
  • Lie algebra
  • screw theory
  • Euclidean group
  • polynomial equation reduction
  • elimination methods in kinematics
  • path planning trajectory
  • symbolic computation
  • closed-form solutions
  • topology optimization
  • software development
  • robot stability
  • computational geometry in robotics
  • robot singularities
  • parametrization
  • synthesis
  • Monte Carlo methods

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Published Papers (1 paper)

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Research

24 pages, 2101 KiB  
Article
Symbolic Computation of the Lie Algebra se(3) of the Euclidean Group SE(3): An Application to the Infinitesimal Kinematics of Robot Manipulators
by Jaime Gallardo-Alvarado, Mario A. Garcia-Murillo, Juan Manuel Tabares-Martinez and X. Yamile Sandoval-Castro
Mathematics 2024, 12(16), 2538; https://doi.org/10.3390/math12162538 - 16 Aug 2024
Viewed by 1677
Abstract
This paper reports an application of the Lie algebra se(3) of the Euclidean group SE(3), which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic [...] Read more.
This paper reports an application of the Lie algebra se(3) of the Euclidean group SE(3), which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration characteristics of the end effector in serial manipulators in order to allow the compact and efficient modeling of velocity and acceleration analyses of both parallel and serial robotic manipulators. Unlike other algebras, these procedures can be extended without significant effort to higher-order analyses such as the jerk and jounce. Full article
(This article belongs to the Special Issue Application of Mathematical Analysis and Theory to Robotics)
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