Optimal trajectory planning for redundant manipulators based on minimum jerk

Jingzhou Yang, Joo Kim, Esteban Pena Pitarch, Karim Abdel-Malek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. the objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.

Original languageEnglish (US)
Title of host publication2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008
Pages1141-1150
Number of pages10
Volume2
EditionPART B
DOIs
StatePublished - 2009
EventASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2008 - Brooklyn, NY, United States
Duration: Aug 3 2008Aug 6 2008

Other

OtherASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2008
CountryUnited States
CityBrooklyn, NY
Period8/3/088/6/08

Fingerprint

Redundant manipulators
Trajectories
Planning
Splines
Manipulators
Derivatives
Inverse kinematics
Degrees of freedom (mechanics)
End effectors
Robotics
Robots

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Industrial and Manufacturing Engineering
  • Mechanical Engineering

Cite this

Yang, J., Kim, J., Pitarch, E. P., & Abdel-Malek, K. (2009). Optimal trajectory planning for redundant manipulators based on minimum jerk. In 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008 (PART B ed., Vol. 2, pp. 1141-1150) https://doi.org/10.1115/DETC2008-49268

Optimal trajectory planning for redundant manipulators based on minimum jerk. / Yang, Jingzhou; Kim, Joo; Pitarch, Esteban Pena; Abdel-Malek, Karim.

2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. Vol. 2 PART B. ed. 2009. p. 1141-1150.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yang, J, Kim, J, Pitarch, EP & Abdel-Malek, K 2009, Optimal trajectory planning for redundant manipulators based on minimum jerk. in 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. PART B edn, vol. 2, pp. 1141-1150, ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2008, Brooklyn, NY, United States, 8/3/08. https://doi.org/10.1115/DETC2008-49268
Yang J, Kim J, Pitarch EP, Abdel-Malek K. Optimal trajectory planning for redundant manipulators based on minimum jerk. In 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. PART B ed. Vol. 2. 2009. p. 1141-1150 https://doi.org/10.1115/DETC2008-49268
Yang, Jingzhou ; Kim, Joo ; Pitarch, Esteban Pena ; Abdel-Malek, Karim. / Optimal trajectory planning for redundant manipulators based on minimum jerk. 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008. Vol. 2 PART B. ed. 2009. pp. 1141-1150
@inproceedings{dce794404fe94e03a4847a6b6f91ec13,
title = "Optimal trajectory planning for redundant manipulators based on minimum jerk",
abstract = "This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. the objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.",
author = "Jingzhou Yang and Joo Kim and Pitarch, {Esteban Pena} and Karim Abdel-Malek",
year = "2009",
doi = "10.1115/DETC2008-49268",
language = "English (US)",
isbn = "9780791843253",
volume = "2",
pages = "1141--1150",
booktitle = "2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008",
edition = "PART B",

}

TY - GEN

T1 - Optimal trajectory planning for redundant manipulators based on minimum jerk

AU - Yang, Jingzhou

AU - Kim, Joo

AU - Pitarch, Esteban Pena

AU - Abdel-Malek, Karim

PY - 2009

Y1 - 2009

N2 - This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. the objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.

AB - This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. the objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.

UR - http://www.scopus.com/inward/record.url?scp=70049117045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70049117045&partnerID=8YFLogxK

U2 - 10.1115/DETC2008-49268

DO - 10.1115/DETC2008-49268

M3 - Conference contribution

AN - SCOPUS:81155138169

SN - 9780791843253

SN - 9780791843260

VL - 2

SP - 1141

EP - 1150

BT - 2008 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC 2008

ER -