Details
| Original language | English |
|---|---|
| Title of host publication | Advances in Robot Kinematics 2022 |
| Editors | Oscar Altuzarra, Andrés Kecskeméthy |
| Pages | 399-408 |
| Number of pages | 10 |
| ISBN (electronic) | 978-3-031-08140-8 |
| Publication status | Published - 18 Jun 2022 |
| Event | International Symposium on Advances in Robot Kinematics 2022 - Bilbao, Spain Duration: 26 Jun 2022 → 30 Jun 2022 |
Publication series
| Name | Springer Proceedings in Advanced Robotics |
|---|---|
| Volume | 24 SPAR |
| ISSN (Print) | 2511-1256 |
| ISSN (electronic) | 2511-1264 |
Abstract
Geometric formulations for the inverse kinematics problem (IKP) in robotics are often set up in the full Cartesian space of three translational and three rotational coordinates (3T3R). When transferring this to tasks with spatial rotation like 3T2R, 2T3R or 2T2R, the result is usually not defined in a minimal set of independent coordinates. Removing the excluded operational space coordinates completely from the expressions is interesting from a theoretical point of view and simplifies further calculations. This can be achieved by formulating a 2R residual using the Z- Y ′ - X ′ ′ Tait-Bryan angles and a 2T residual derived by the projection of the pointing direction on a plane. In this paper, the minimal-coordinate IKP is derived for 2T2R and 2T3R tasks on position level with application to a gradient-projection scheme. Limitations of the redundant coordinate are considered within the nullspace.
Keywords
- 2T2R, 2T3R, Coordinate inequality constraint, Functional redundancy, Geometric model, Inverse kinematics, Nullspace projection, Serial-link robot
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Engineering (miscellaneous)
- Computer Science(all)
- Artificial Intelligence
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
Advances in Robot Kinematics 2022. ed. / Oscar Altuzarra; Andrés Kecskeméthy. 2022. p. 399-408 (Springer Proceedings in Advanced Robotics; Vol. 24 SPAR).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Geometric Model for Serial-Chain Robot Inverse Kinematics in Case of Two Translational DoF, Spatial Rotation and Functional Redundancy
AU - Schappler, Moritz
AU - Blum, Tobias
AU - Job, Tim-David
N1 - Funding Information: The authors acknowledge the support by the Deutsche Forschungsgemeinschaft (DFG) under grant number 341489206. Matlab code to reproduce the results is available at GitHub under free license at github.com/SchapplM/ robotics-paper ark2022 2T2R.
PY - 2022/6/18
Y1 - 2022/6/18
N2 - Geometric formulations for the inverse kinematics problem (IKP) in robotics are often set up in the full Cartesian space of three translational and three rotational coordinates (3T3R). When transferring this to tasks with spatial rotation like 3T2R, 2T3R or 2T2R, the result is usually not defined in a minimal set of independent coordinates. Removing the excluded operational space coordinates completely from the expressions is interesting from a theoretical point of view and simplifies further calculations. This can be achieved by formulating a 2R residual using the Z- Y ′ - X ′ ′ Tait-Bryan angles and a 2T residual derived by the projection of the pointing direction on a plane. In this paper, the minimal-coordinate IKP is derived for 2T2R and 2T3R tasks on position level with application to a gradient-projection scheme. Limitations of the redundant coordinate are considered within the nullspace.
AB - Geometric formulations for the inverse kinematics problem (IKP) in robotics are often set up in the full Cartesian space of three translational and three rotational coordinates (3T3R). When transferring this to tasks with spatial rotation like 3T2R, 2T3R or 2T2R, the result is usually not defined in a minimal set of independent coordinates. Removing the excluded operational space coordinates completely from the expressions is interesting from a theoretical point of view and simplifies further calculations. This can be achieved by formulating a 2R residual using the Z- Y ′ - X ′ ′ Tait-Bryan angles and a 2T residual derived by the projection of the pointing direction on a plane. In this paper, the minimal-coordinate IKP is derived for 2T2R and 2T3R tasks on position level with application to a gradient-projection scheme. Limitations of the redundant coordinate are considered within the nullspace.
KW - 2T2R
KW - 2T3R
KW - Coordinate inequality constraint
KW - Functional redundancy
KW - Geometric model
KW - Inverse kinematics
KW - Nullspace projection
KW - Serial-link robot
UR - http://www.scopus.com/inward/record.url?scp=85133245220&partnerID=8YFLogxK
U2 - 10.15488/12465
DO - 10.15488/12465
M3 - Conference contribution
SN - 9783031081392
T3 - Springer Proceedings in Advanced Robotics
SP - 399
EP - 408
BT - Advances in Robot Kinematics 2022
A2 - Altuzarra, Oscar
A2 - Kecskeméthy, Andrés
T2 - International Symposium on Advances in Robot Kinematics 2022
Y2 - 26 June 2022 through 30 June 2022
ER -