Abstract
We present a method of determining a solution of the inverse kinematics problem based on \({\mathbb G}_{3,1}\) for serial robot arm manipulators with an additional condition such as the prescribed gripper trajectory. The algorithm is based on geometrical understanding and \({\mathbb G}_{3,1}\) calculations. We propose an algorithm for determining the actuating rotations and, furthermore, we discuss different approaches to their segmentation in order to realize the appropriate motion optimally.
Similar content being viewed by others
References
Abłamowicz, R., Fauser, B.: CLIFFORD/Bigebra, A Maple Package for Clifford (Co)Algebra Computations. http://www.math.tntech.edu/rafal/ (2015). Accessed 1 Nov 2017
Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, 1st edn. Morgan Kaufmann, Burlington (2007)
Hestenes, D.: New Foundations for Classical Mechanics, 2nd edn. Kluwer Academic Publishers, Dordrecht (1999)
Hildenbrand, D.: Foundations of Geometric Algebra Computing. Springer, New York (2013)
Hrdina, J., Návrat, A.: Binocular computer vision based on conformal geometric algebra. Adv. Appl. Clifford Algebras 27(3), 1945–1959 (2017)
Hrdina, J., Vašík, P.: Notes on differential kinematics in conformal geometric algebra approach. Mendel 2015. Adv. Intell. Syst. Comput. 378, 363–374 (2015)
Hrdina, J., Návrat, A., Vašík, P.: Control of 3-link robotic snake based on conformal geometric algebra. Adv. Appl. Clifford Algebras 26(3), 1069–1080 (2016)
Hrdina, J., Návrat, A., Vašík, P., Matoušek, R.: CGA-based robotic snake control. Adv. Appl. Clifford Algebras 27(1), 633–645 (2016)
Hrdina, J., Matoušek, R., Návrat, A., Vašík, P.: Fisheye correction by CGA non-linear transformation. Math. Meth. Appl. Sci. 41(11), 4106–4116 (2018)
Liljebäck, P., Pettersen, K.Y., Stavdahl, Ø., Gravdahl, J.T.: Snake Robots. Modelling, Mechatronics and Control. Springer, Berlin (2013)
Lounesto, P.: Clifford Algebra and Spinors, vol. 2. Cambridge University Press, Cambridge (2006)
Perwass, Ch.: Geometric Algebra with Applications in Engineering. Springer, Berlin (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by a grant of the Czech Science Foundation (GAČR) number 17-21360S, “Advances in Snake-like Robot Control”.
This article is part of the Topical Collection on Proceedings ICCA 11, Ghent, 2017, edited by Hennie De Schepper, Fred Brackx, Joris van der Jeugt, Frank Sommen, and Hendrik De Bie.
Rights and permissions
About this article
Cite this article
Hrdina, J., Návrat, A. & Vašík, P. Notes on Planar Inverse Kinematics Based on Geometric Algebra. Adv. Appl. Clifford Algebras 28, 71 (2018). https://doi.org/10.1007/s00006-018-0890-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00006-018-0890-7