Citation: Velez-Lopez, G.C.,
Vazquez-Leal, H.;
Hernandez-Martinez, L.;
Sarmiento-Reyes, A.; Diaz-Arango,
G.; Huerta-Chua, J.; Rico-Aniles,
H.D.; Jimenez-Fernandez, V.M. A
Novel Collision-Free Homotopy Path
Planning for Planar Robotic Arms.
Sensors 2022, 22, 4022. https://
doi.org/10.3390/s22114022
Academic Editors: Yuansong Qiao
and Seamus Gordon
Received: 6 April 2022
Accepted: 18 May 2022
Published: 26 May 2022
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Article
A Novel Collision-Free Homotopy Path Planning for Planar
Robotic Arms
Gerardo C. Velez-Lopez
1
, Hector Vazquez-Leal
2,3,
* , Luis Hernandez-Martinez
1
, Arturo Sarmiento-Reyes
1
,
Gerardo Diaz-Arango
4
, Jesus Huerta-Chua
4
, Hector D. Rico-Aniles
5
and Victor M. Jimenez-Fernandez
2
1
Electronics Department, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1,
Santa María Tonantzintla, Cholula 72840, Puebla, Mexico; gcvelez@inaoep.mx (G.C.V.-L.);
luish@inaoep.mx (L.H.-M.); jarocho@inaoep.mx (A.S.-R.)
2
Facultad de Instrumentacion Electronica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltran S/N,
Xalapa 91000, Veracruz, Mexico; vicjimenez@uv.mx
3
Consejo Veracruzano de Investigacion Cientifica y Desarrollo Tecnologico (COVEICYDET),
Av. Rafael Murillo Vidal No. 1735, Xalapa 91069, Veracruz, Mexico
4
Instituto Tecnologico Superior de Poza Rica, Tecnologico Nacional de Mexico,
Luis Donaldo Colosio Murrieta S/N, Poza Rica 93230, Veracruz, Mexico;
gerardo.diaz@itspozarica.edu.mx (G.D.-A.); chua@itspozarica.edu.mx (J.H.-C.)
5
Electrical Engineering Department, North Central College, 30 N. Brainard St., Naperville, IL 60540, USA;
hdricoaniles@noctrl.edu
* Correspondence: hvazquez@uv.mx
Abstract:
Achieving the smart motion of any autonomous or semi-autonomous robot requires an
efficient algorithm to determine a feasible collision-free path. In this paper, a novel collision-free path
homotopy-based path-planning algorithm applied to planar robotic arms is presented. The algorithm
utilizes homotopy continuation methods (HCMs) to solve the non-linear algebraic equations system
(NAES) that models the robot’s workspace. The method was validated with three case studies with
robotic arms in different configurations. For the first case, a robot arm with three links must enter
a narrow corridor with two obstacles. For the second case, a six-link robot arm with a gripper is
required to take an object inside a narrow corridor with two obstacles. For the third case, a twenty-link
arm must take an object inside a maze-like environment. These case studies validated, by simulation,
the versatility and capacity of the proposed path-planning algorithm. The results show that the CPU
time is dozens of milliseconds with a memory consumption less than 4.5 kB for the first two cases.
For the third case, the CPU time is around 2.7 s and the memory consumption around 18 kB. Finally,
the method’s performance was further validated using the industrial robot arm CRS CataLyst-5 by
Thermo Electron.
Keywords:
collision-free path planning; autonomous robot; robot arm; homotopy continuation
methods
1. Introduction
Significant advances have been made in robotics with more powerful and versatile
robots being developed. Currently, robots exhibit enhanced capabilities for performing
autonomous and semi-autonomous tasks with a high degree of human interaction. Their
applications have been expanded from the traditional ones used in industry and research
environments to areas such as clinical surgery and rehabilitation therapy [
1
–
3
]. More-
over, the robotics field offer support functions such as automated navigation, warehouse
management, and household management [2,4–9].
The design of robotic arms has been part of the robotics evolution by incorporating not
only new materials and mechanical structures, but also novel application-specific models.
An example of this evolution is hyper-redundant robots; these have a mechanical structure
capable of deforming continuously according to their degrees of freedom (DoF) to adapt to
Sensors 2022, 22, 4022. https://doi.org/10.3390/s22114022 https://www.mdpi.com/journal/sensors
