American Institute of Mathematical Sciences

Advanced
February  2021, 1(1): 17-31. doi: 10.3934/steme.2021002

Redundancy understanding and theory for robotics teaching: Application on a human finger model

Med Amine Laribi 1,, and  Saïd Zeghloul 1,

1. 

Dept. GMSC, Prime Institute, CNRS - University of Poitiers - ENSMA - UPR 3346, Poitiers, France

* Correspondence: med.amine.laribi@univ-poitiers.fr; Tel: +5-49-496552

Academic Editor: Giuseppe Carbone

Received  October 2020 Revised  January 2021 Published  February 2021

This paper introduces the concept of redundancy in robotics to students in master degree based on a didactic approach. The definition as well as theoretical description related to redundancy are presented. The example of a human finger is considered to illustrate the redundancy with biomechanical point of view. At the same time, the finger is used to facilitate the comprehension and apply theoretical development to solve direct and inverse kinematics problems. Three different tasks are considered with different degree of redundancy. All developments are implemented under Matlab and validated in simulation on CAD software.

Keywords: robotics, redundancy, Matlab, human finger, direct kinematic problem, inverse kinematic problem.
Citation: Med Amine Laribi, Saïd Zeghloul. Redundancy understanding and theory for robotics teaching: Application on a human finger model. STEM Education, 2021, 1 (1) : 17-31. doi: 10.3934/steme.2021002
References:
[1]

Nof, S.Y. (ed.) (1985) Handbook of Industrial Robotics. John Wiley & Sons, New York. Google Scholar

[2]

Angeles, J. (2002) Fundamentals of Robotic Mechanical Systems (2nd ed.). Springer Verlag, New York. Google Scholar

[3]

Chiaverini S., Oriolo G., Maciejewski A.A. (2016) Redundant Robots. In: Siciliano B., Khatib O. (eds) Springer Handbook of Robotics. Springer Handbooks. Springer. Google Scholar

[4]

E.S. Conkur and R. Buckingham, Clarifying the definition of redundancy as used in robotics, Robotica, 15 (1997), 583-586.  doi: 10.1017/S0263574797000672.  Google Scholar

[5]

C.A. Nelson, M.A. Laribi and S. Zeghloul, Multi-robot system optimization based on redundant serial spherical mechanism for robotic minimally invasive surgery, Robotica, 37 (2019), 1202-1213.  doi: 10.1017/S0263574718000681.  Google Scholar

[6]

H. Saafi, M.A. Laribi and S. Zeghloul, Optimal torque distribution for a redundant 3-RRR spherical parallel manipulator used as a haptic medical device, Robotics and Autonomous Systems, 89 (2017), 40-50.   Google Scholar

[7]

de Wit, C.C., Siciliano, B., Bastin, G. (1996) Theory of Robot Control. Springer‐Verlag, London. Google Scholar

[8]

Angeles, J. (2006). Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (3rd ed.). Springer‐Verlag, New York. Google Scholar

[9]

M.L. Latash and V.M. Zatsiorsky, Multi-finger prehension: Control of a redundant mechanical system, Advances in Experimental Medicine and Biology, 629 (2009), 597-618.  doi: 10.1007/978-0-387-77064-2_32.  Google Scholar

[10]

Towell, C., Howard, M., Vijayakumar, S. (2010) Learning nullspace policies. The IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, pp. 241-248, doi: 10.1109/IROS.2010.5650663. Google Scholar

[11]

C. Mizera, M.A. Laribi, D. Degez, J.P. Gazeau, P. Vulliez and S. Zeghloul, Architecture choice of a robotic hand for deep-sea exploration based on the expert gestures movements analysis, Mechanisms and Machine Science, 72 (2019), 1-19.   Google Scholar

[12]

Hu, D., Ren, L., Howad, D., Zong, C. (2014) Biomechanical analysis of force distribution in human finger extensor mechanisms. BioMed Research International, 2014: Article ID 743460, https: //doi.org/10.1155/2014/743460. doi: 10.1155/2014/743460.  Google Scholar

show all references

References:
[1]

Nof, S.Y. (ed.) (1985) Handbook of Industrial Robotics. John Wiley & Sons, New York. Google Scholar

[2]

Angeles, J. (2002) Fundamentals of Robotic Mechanical Systems (2nd ed.). Springer Verlag, New York. Google Scholar

[3]

Chiaverini S., Oriolo G., Maciejewski A.A. (2016) Redundant Robots. In: Siciliano B., Khatib O. (eds) Springer Handbook of Robotics. Springer Handbooks. Springer. Google Scholar

[4]

E.S. Conkur and R. Buckingham, Clarifying the definition of redundancy as used in robotics, Robotica, 15 (1997), 583-586.  doi: 10.1017/S0263574797000672.  Google Scholar

[5]

C.A. Nelson, M.A. Laribi and S. Zeghloul, Multi-robot system optimization based on redundant serial spherical mechanism for robotic minimally invasive surgery, Robotica, 37 (2019), 1202-1213.  doi: 10.1017/S0263574718000681.  Google Scholar

[6]

H. Saafi, M.A. Laribi and S. Zeghloul, Optimal torque distribution for a redundant 3-RRR spherical parallel manipulator used as a haptic medical device, Robotics and Autonomous Systems, 89 (2017), 40-50.   Google Scholar

[7]

de Wit, C.C., Siciliano, B., Bastin, G. (1996) Theory of Robot Control. Springer‐Verlag, London. Google Scholar

[8]

Angeles, J. (2006). Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (3rd ed.). Springer‐Verlag, New York. Google Scholar

[9]

M.L. Latash and V.M. Zatsiorsky, Multi-finger prehension: Control of a redundant mechanical system, Advances in Experimental Medicine and Biology, 629 (2009), 597-618.  doi: 10.1007/978-0-387-77064-2_32.  Google Scholar

[10]

Towell, C., Howard, M., Vijayakumar, S. (2010) Learning nullspace policies. The IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, pp. 241-248, doi: 10.1109/IROS.2010.5650663. Google Scholar

[11]

C. Mizera, M.A. Laribi, D. Degez, J.P. Gazeau, P. Vulliez and S. Zeghloul, Architecture choice of a robotic hand for deep-sea exploration based on the expert gestures movements analysis, Mechanisms and Machine Science, 72 (2019), 1-19.   Google Scholar

[12]

Hu, D., Ren, L., Howad, D., Zong, C. (2014) Biomechanical analysis of force distribution in human finger extensor mechanisms. BioMed Research International, 2014: Article ID 743460, https: //doi.org/10.1155/2014/743460. doi: 10.1155/2014/743460.  Google Scholar

Figure 1.  Schematic representation of the hand
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Kinematic diagram of a single finger
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Task1 - Trajectory of the fingertip and corresponding joint angles.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Task2 - Trajectory of the fingertip and corresponding joint angles.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Task3 - Trajectory of the fingertip and corresponding joint angles.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  Task 1 - Numerical validation of the pseudo-inverse method: (a) Graphical finger construction (b) Trajectory of the fingertip (c) Computed joint angles of the finger.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7.  Task 1 - CAD simulation of the finger motion using the pseudo-inverse method.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 8.  Task 2 - Numerical validation of the pseudo-inverse method: (a) Graphical finger construction (b) Trajectory of the fingertip (c) Computed joint angles of the finger.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 9.  Task 2 - CAD simulation of the finger motion using the pseudo-inverse method.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 10.  Task 3 - Numerical validation of the pseudo-inverse method: (a) Graphical finger construction (b) Trajectory of the fingertip (c) Computed joint angles of the finger.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 11.  Numerical validation of the pseudo-inverse method with a criterion on the joint limits: (a) $ a = 1 $, $ b = 1 $ and $ c = 1 $ (b) $ a = 30 $, $ b = 1 $ and $ c = 1 $ (c) $ a = 100 $, $ b = 1 $ and $ c = 1 $.
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  The three tasks of the finger in the $ ({x}_{1}, {z}_{1}) $ plane.
Task Initial Configuration End-effector displacement
T1 $ {q}_{2}=45°, {q}_{3}=90°, {q}_{4}=30° $ 60 mm along $ {x}_{1} $
T2 $ {q}_{2}=45°, {q}_{3}=45°, {q}_{4}=45° $ 40 mm along $ {z}_{1} $
T3 $ {q}_{2}=0°, {q}_{3}=45°, {q}_{4}=45° $ 30 mm along $ {-x}_{1} $ et 20 mm along $ {z}_{1} $
Table Options

Download as excel

Task Initial Configuration End-effector displacement
T1 $ {q}_{2}=45°, {q}_{3}=90°, {q}_{4}=30° $ 60 mm along $ {x}_{1} $
T2 $ {q}_{2}=45°, {q}_{3}=45°, {q}_{4}=45° $ 40 mm along $ {z}_{1} $
T3 $ {q}_{2}=0°, {q}_{3}=45°, {q}_{4}=45° $ 30 mm along $ {-x}_{1} $ et 20 mm along $ {z}_{1} $
Table 2.  Degree of redundancy
Task Degree of redundancy $ (\mathit{n}-\mathit{m}) $
T1 2
T2 2
T3 1
Table Options

Download as excel

Task Degree of redundancy $ (\mathit{n}-\mathit{m}) $
T1 2
T2 2
T3 1
Table 3.  Solutions of the IKM with an additional constraint.
Joint variable Solution 1 Solution 2
$ \mathit{\boldsymbol{q}}_{2} $ $ {q}_{2}=atan2\left(\mathrm{sin}{q}_{2}, \mathrm{cos}{q}_{2}\right) $$ \mathrm{cos}{q}_{2}=\frac{-{\overline{x}}_{1}B-{\overline{z}}_{1}A}{{A}^{2}+{B}^{2}} $; $ \mathrm{sin}{q}_{2}=\frac{{\overline{z}}_{1}B-{\overline{x}}_{1}A}{{A}^{2}+{B}^{2}} $
$ \mathit{\boldsymbol{q}}_{3} $ $ {q}_{3}^{1}=arcos\left(\frac{{\overline{x}}^{2}+{\overline{z}}^{2}-\left({l}_{3}^{2}+{l}_{2}^{2}\right)}{2{l}_{2}{l}_{3}}\right) $ $ {q}_{3}^{2}=-{q}_{3}^{1} $
$ \mathit{\boldsymbol{q}}_{4} $ $ {q}_{4}=\alpha -{q}_{3}-{q}_{2} $
Table Options

Download as excel

Joint variable Solution 1 Solution 2
$ \mathit{\boldsymbol{q}}_{2} $ $ {q}_{2}=atan2\left(\mathrm{sin}{q}_{2}, \mathrm{cos}{q}_{2}\right) $$ \mathrm{cos}{q}_{2}=\frac{-{\overline{x}}_{1}B-{\overline{z}}_{1}A}{{A}^{2}+{B}^{2}} $; $ \mathrm{sin}{q}_{2}=\frac{{\overline{z}}_{1}B-{\overline{x}}_{1}A}{{A}^{2}+{B}^{2}} $
$ \mathit{\boldsymbol{q}}_{3} $ $ {q}_{3}^{1}=arcos\left(\frac{{\overline{x}}^{2}+{\overline{z}}^{2}-\left({l}_{3}^{2}+{l}_{2}^{2}\right)}{2{l}_{2}{l}_{3}}\right) $ $ {q}_{3}^{2}=-{q}_{3}^{1} $
$ \mathit{\boldsymbol{q}}_{4} $ $ {q}_{4}=\alpha -{q}_{3}-{q}_{2} $
Table 4.  The limit values of the joint angles.
Joint angle $ \mathit{\boldsymbol{q}}_{2} $ $ \mathit{\boldsymbol{q}}_{3} $ $ \mathit{\boldsymbol{q}}_{4} $
Maximum value $ 90° $ $ 120° $ $ 70° $
Minimum value $ 0° $ $ 0 $ $ 0 $
Table Options

Download as excel

Joint angle $ \mathit{\boldsymbol{q}}_{2} $ $ \mathit{\boldsymbol{q}}_{3} $ $ \mathit{\boldsymbol{q}}_{4} $
Maximum value $ 90° $ $ 120° $ $ 70° $
Minimum value $ 0° $ $ 0 $ $ 0 $
Table 5.  The phalangeal lengths of the finger.
$ \mathit{\boldsymbol{L}}_{1} $ $ \mathit{\boldsymbol{L}}_{2} $ $ \mathit{\boldsymbol{L}}_{3} $ $ \mathit{\boldsymbol{L}}_{4} $
Phalange length [mm] 152 45 35 32
Table Options

Download as excel

$ \mathit{\boldsymbol{L}}_{1} $ $ \mathit{\boldsymbol{L}}_{2} $ $ \mathit{\boldsymbol{L}}_{3} $ $ \mathit{\boldsymbol{L}}_{4} $
Phalange length [mm] 152 45 35 32
Table 6.  Orientations of the last phalange.
Task 1 Task 2 Task 3
$ \mathit{\boldsymbol{\alpha}}=\mathit{\boldsymbol{q}}_{2}+\mathit{\boldsymbol{q}}_{3}+\mathit{\boldsymbol{q}}_{4} $ 165° 135° 90°
Table Options

Download as excel

Task 1 Task 2 Task 3
$ \mathit{\boldsymbol{\alpha}}=\mathit{\boldsymbol{q}}_{2}+\mathit{\boldsymbol{q}}_{3}+\mathit{\boldsymbol{q}}_{4} $ 165° 135° 90°
[1]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021
[2]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271
[3]

Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022
[4]

Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463
[5]

Michel Chipot, Mingmin Zhang. On some model problem for the propagation of interacting species in a special environment. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020401
[6]

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151
[7]

Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261
[8]

Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulation of an adhesive contact problem with damage and long memory. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2781-2804. doi: 10.3934/dcdsb.2020205
[9]

Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1757-1778. doi: 10.3934/dcdss.2020453
[10]

Rongchang Liu, Jiangyuan Li, Duokui Yan. New periodic orbits in the planar equal-mass three-body problem. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2187-2206. doi: 10.3934/dcds.2018090
[11]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056
[12]

Namsu Ahn, Soochan Kim. Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021037
[13]

Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028
[14]

Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017

 Impact Factor: 

Tools

Article outline

Figures and Tables

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences