Robot grasping and regrasping kinematics using Lie algebra, the geodesic, and Riemann curvature tensor

• Autorzy: Sahin Haydar

Identyfikatory

DOI

10.24425/acs.2023.145111

• Języki publikacji: EN

Abstrakty

EN

Differential geometry is a strong and highly effective mathematical subject for robot gripper design when grasping within the predetermined trajectories of path planning. This study in grasping focuses on differential geometry analysis utilizing the Lie algebra, geodesic, and Riemann Curvature Tensors (RCT). The novelty of this article for 2RR robot mechanisms lies in the approach of the body coordinate with the geodesic and RCT. The importance of this research is significant especially in grasping and regrasping objects with varied shapes. In this article, the types of workspaces are clarified and classified for grasping and regrasping kinematics. The regrasp has not been sufficiently investigated of body coordinate systems in Lie algebra. The reason for this is the difficulty in understanding relative coordinates in Lie algebra via the body coordinate system. The complexity of the equations has not allowed many researchers to overcome this challenge. The symbolic mathematics toolbox in the Maxima, on the other hand, aided in the systematic formulation of the workspaces in Lie algebra with geodesic and RCT. The Lie algebra se(3) equations presented here have already been developed for robot kinematics from many references. These equations will be used to derive the following workspace types for grasping and regrasping. Body coordinate workspace, spatial coordinate workspace with constraints, body coordinate workspace with constraints, spatial coordinate workspace with constraints are the workspace types. The RCT and geodesic solutions exploit these four fundamental workspace equations derived using Lie algebra.

Słowa kluczowe

EN

body coordinate workspace; spatial coordinate workspace; regrasp planning; mechanism; differential geometry

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 1
• Strony: 5--23
• Opis fizyczny: Bibliogr. 10 poz., rys., tab., wzory

Twórcy

autor

Sahin Haydar

• Istanbul Gedik University, Engineering Faculty, Mechatronics Engineering Department, Istanbul, Türkiye

Bibliografia

• [1] M. Ali and J. Farrokh: Grasp synthesis of continuum robots. Mechanism and Machine Theory, 168 (2022), 1-31. DOI: 10.1016/j.mechmachtheory.2021.104575.
• [2] S. Haydar: The modular nonoverlapping grasp workspaces and dynamics for the grippers using the micro and macro C-manifold design. Journal of Scientific & Industrial Research. 80(9), (2021), 766-776. DOI: 10.56042/jsir.v80i09.47040.
• [3] S. Haydar: Algorithmic workspace programming of the collaborative multi-robots. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 5(1), (2022), 325-341. DOI: 10.47495/okufbed.1030575.
• [4] A. Müller: Screw and Lie group theory in multibody dynamics recursive algorithms and equations of motion of tree-topology systems. Multibody System Dynamics, 42 (2018), 219-248. DOI: 10.1007/s11044-017-9583-6.
• [5] A.S. Morgan, K. Hang, B. Wen, K. Bekris, and A.M. Dollar: Complex in-hand manipulation via compliance-enabled finger gaiting and multimodal planning. IEEE Robotics and Automation Letters, 7(2), (2022), 4821-4828. DOI: 10.1109/LRA.2022.3145961.
• [6] Z. Xian, P. Lertkultanon and Q.-C. Pham: Closed-chain manipulation of large objects by multi-arm robotic systems. IEEE Robotics and Automation Letters, 2(4), (2017), 1832-1839. DOI: 10.1109/LRA.2017.2708134.
• [7] J. Ma, W. Wan, K. Harada, Q. Zhu, and H. Liu: Regrasp planning using table object poses supported by complex structures. IEEE Transactions 10.1109/TCDS.2018.2868425.
• [8] A. Sintov, O. Tslil, and A. Shapiro: Robotic swing-up regrasping manipulation based on the impulse-momentum approach and cLQR control. IEEE Transactions on Robotics, 32(5), (2016), 1079-1090. DOI: 10.1109/TRO.2016.2593053.
• [9] Y. Zheng, F.F. Veiga, J. Peters, and V.J. Santos: Autonomous learning of page flipping movements via tactile feedback. IEEE Transactions on Robotics, Early Access, 1-16, (2022). DOI: 10.1109/TRO.2022.3168731.
• [10] A. Palleschi, G.J. Pollayil, M.J. Pollayil, M. Garabini, and L. Pallottino: High-level planning for object manipulation with multi heterogeneous robots in shared environments. IEEE Robotics and Automation Letters, 7(2), (2022), 3138-3145. DOI: 10.1109/LRA.2022.3145987.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)