A New Quantum-computing-based Algorithm for Robotic Arms ‎and Rigid Bodies’ Orientation

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Université du Québec à Trois-Rivières & Institut de Recherche sur l’Hydrogène, 3351 Boulevard des Forges,‎ Trois-Rivières, QC G8Z 4M3, Canada

2 Laboratoire RECITS, Université de la Science et de la Technologie Houari Boumediene, BP 32 Bab Ezzouar, 16111, Algiers, Algeria

3 Département Hydraulique Urbaine, École Nationale Supérieure d’Hydraulique Arbaoui Abdallah, 29 Route de Soumaâ, Blida, Algeria ‎

4 Projet Véo, Université de Sherbrooke, 2500 Boulevard de l'Université, Sherbrooke, QC J1K 2R1, Canada

5 Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, Algiers, Algeria

6 Faculty of Engineering and Science, Western Norway University of Applied Sciences Bergen, 5063, Norway

Abstract

Quantum computing model of robotic arm orientation is presented. Spherical and vector coordinates, a homogenous rotation matrix, Pauli gates and quantum rotation operators are used to formulate the orientation model and establish a new algorithm. The quantum algorithm uses a single qubit to compute orientation and has the advantage of operation reversibility. This was validated for a SCARA robot and a five-joints articulated robotic arm. The obtained results show the effectiveness of the proposed methodology.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Berry, D.W., High-Order Quantum Algorithm for Solving Linear Differential Equations, Journal of Physics A: Mathematical and Theoretical, 47(10), 2014, 105301.
[2] Cao, Y., Daskin, S., Frankel, S., Kais, S., Quantum Circuit Design for Solving Linear Systems of Equations, Molecular Physics, 110(1), 2012, 1675-1680.
[3] Cai, X.D., Weedbrook, C., Su, Z.E., Chen, M., Cu, M.J., Zhu, L., Li, N.L., Liu, C.Y., Lu, J.W.P., Experimental Quantum Computing to Solve Systems of Linear Equations, Physical Review Letters, 110, 2013, 230501.
[4] Nagata, K., Nakamura, T., Quantum Algorithm for the Root-Finding Problem, Chapman University, Springer, 2018.
[5] Leyton, S.K., Osborne, T.J., A Quantum Algorithm to Solve Nonlinear Differential Equations, arXiv: 0812.4423v1, 2008.
[6] Xin, T., Wei, S., Cui, J., Xiao, J., Arrazola, I., Lamata. L., Kong, X., Lu, D., Solano, E., Long, G., A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment, Physical Review A, 101(1), 2018, 032307.
[7] Terno, D.R., Nonlinear Operations in Quantum-Information Theory, Physical Review A, 59(5), 1999, 3320.
[8] Daoud, E.A., Quantum Computing for Solving a System of Nonlinear Equations over GF(q), The International Arab Journal of Information Technology, 4(3), 2007, 201-205.
[9] Grover, L.K.,  A Fast Quantum Mechanical Algorithm for Database Search in STOC '96, Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing, 1996.
[10] Singhal, A., Chatterjee, A., Grover's Algorithm, 2018.
[11] Pimentel, D.R.M., Castro, A.S., A Laplace Transform Approach to the Quantum Harmonic Oscillator, European Journal of Physics, 34(1), 2013, 199.
[12] Sarikaya, M.Z., Alp, N., q-Laplace Transform on Quantum Integral, Kragujevac Journal of Mathematics, 47, 2023, 153–164.
[13] Jorrand, P., Transformée de Fourier Quantique - Algorithmes, Notes de cours - Module Informatique Quantique, UJF Grenoble, 2006.
[14] Quantum Fourier Transform, Qiskit, [Online]. Available: https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html. [Accessed 10 05 2021].
[15] Wossnig, L., Zhao, Z., Prakash, A., A Quantum Linear System Algorithm for Dense Matrices, Physical Review Letters, 120, 2017, 050502.
[16] Kyriienko, O., Quantum Inverse Iteration Algorithm for Programmable Quantum Simulators, npj Quantum Information, 6, 2020, 7.
[17] Schilling, R.J., Fundamentals of Robotics: analysis and control, Simon & Schuster Trade, 1996.
[18] Khalil, E.D.W., Modélisation, Identification et commande des Robots, Hermès Science, 1999.
[19] Siciliano, B., Sciavico, L., Villani, L., Oriolo, G., Robotics: Modelling, Planning and Control, Springer Science & Business Media, 2010.
[20] Sciavico, L., Siciliano, B. Modelling and Control of Robot Manipulators, Springer Science & Business Media, 2012.
[21] Forstner, W.B.P.W., Photogrammetric computer vision: statistics, geometry, orientation and reconstruction, Springer, 2016.
[22] Mittal, I.N.R., Robotics and control, Tata McGraw-Hill, 2003.
[23] Blösch, M., An Introduction to 3D Orientations and Quaternions, ETH Zurich, Zurich, 2015.
[24] Adorno, B.V., Robot Kinematic Modeling and Control Based on Dual Quaternion Algebra - Part I: Fundamentals, Department of Electrical Engineering, Federal University of Minas Gerais, Brazil, 2017.
[25] Al Attar, A., Kormushev, P., Kinematic-Model-Free Orientation Control for Robot Manipulation Using Locally Weighted Dual Quaternions, Robotics, 9(4), 2020, 76.
[26] Barbic, J., Quaternions and Rotations in CSCI 420, Computer Graphics, 2020.
[27] Chen, L., Zielinska, T., Wang, J., Ge, W., Solution of an Inverse Kinematics Problem Using Dual Quaternions, International Journal of Applied Mathematics and Computer Science, 30(2), 2020, 351–361.
[28] Valverde, A., Tsiotras, P., Spacecraft Robot Kinematics Using Dual Quaternions, Robotics, 7(4), 2018, 64.
[29] Griffiths, R.B., Consistent Quantum Theory, Cambridge University Press, 2002.
[30] McMahon, D., Quantum Computing Explained, Wiley - IEEE, 2007.
[31] Abhijith, J., Adedoyin, A., Ambrosiano, j., Anisimov, P., Bärtschi, A., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., Gunter, D., Karra, S., Lemons, N., Lin, S., Malyzhenkov, A., Quantum Algorithm Implementations for Beginners, ArXiv, 2018.
[32] Chikh, N.Z.L., Design, realization and control of a SCARA robot, National Polytechnic School (ENP), Algiers, Algeria, 2006.
[33] Zioui, N., Mahmoudi, A., Mahmoudi, Y., Rezgui, A., A Comparative Study of Performances between the Sliding Modes and the Trust Control Strategies for an Articulated Robotic Arm Position Control, International Journal of Mechatronics and Mechanical Engineering, 21(1), 2021, 64-72.