Collision-Free Path Planning Applied Robotic Arms Using Homotopy Continuation Methods for Embedded Systems

2021 ◽  
Author(s):  
Gerardo C. Velez-Lopez ◽  
Luis Hernandez-Martinez ◽  
Hector Vazquez-Leal
Keyword(s):  
Embedded Systems ◽  
Path Planning ◽  
Free Path ◽  
Continuation Methods ◽  
Homotopy Continuation ◽  
Robotic Arms ◽  
Homotopy Continuation Methods

Exploring collision-free path planning by using homotopy continuation methods

2013 ◽  
Vol 219 (14) ◽  
pp. 7514-7532 ◽  
Author(s):  
H. Vazquez-Leal ◽  
A. Marin-Hernandez ◽  
Y. Khan ◽  
A. Yıldırım ◽  
U. Filobello-Nino ◽  
...  
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Continuation Methods ◽  
Homotopy Continuation ◽  
Homotopy Continuation Methods

A Novel Collision-Free Path Planning Modeling and Simulation Methodology for Robotical Arms Using Resistive Grids

Robotica ◽  
2019 ◽  
Vol 38 (7) ◽  
pp. 1176-1190
Author(s):  
Carlos Hernández-Mejía ◽  
Héctor Vázquez-Leal ◽  
Delia Torres-Muñoz
Keyword(s):  
Path Planning ◽  
Modeling And Simulation ◽  
Free Path ◽  
Configuration Space ◽  
Robotic Arms ◽  
Simulation Methodology ◽  
Time Modeling ◽  
Starting Point ◽  
Resistive Grids ◽  
Planning Methodology

SUMMARYPath planning represents planning collision-free strategies to move from starting point to ending point. These strategies can be carried out for known and unknown environments. Recently, a novel and reduced CPU-time modeling and simulation methodology for path planning in known environment based on resistive grids (RGs) has been introduced. In this work, a novel modified version of Resistive Grid Path Planning Methodology (RGPPM) methodology is presented with the purpose of exploring collision-free path planning for robotic arms. This extension of the methodology allows to numerically relate positions in the RG with angular values of the robotic systems. In addition, it is possible to include obstacles in the configuration space, and therefore collision detection can be established for RGs. Finally, the variation of links for robotic arms and obstacles for configuration space is explored by simulating different scenarios.

Numerical solution of multivariate polynomial systems by homotopy continuation methods

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 399-436 ◽  
Author(s):  
T. Y. Li
Keyword(s):  
Power Flow ◽  
Polynomial Systems ◽  
Continuation Methods ◽  
Homotopy Continuation ◽  
Multivariate Polynomial ◽  
Science And Engineering ◽  
Flow Problems ◽  
Homotopy Continuation Methods ◽  
Buchberger Algorithm ◽  
Image Position

Let P(x) = 0 be a system of n polynomial equations in n unknowns. Denoting P = (p1,…, pn), we want to find all isolated solutions offor x = (x1,…,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Gröbner bases, are the classical approach to solving (1.1), but their reliance on symbolic manipulation makes those methods seem somewhat unsuitable for all but small problems.

Sign in / Sign up

Export Citation Format

Share Document