Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T12:03:26.123Z Has data issue: false hasContentIssue false
  • English
  • Français

Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator

Published online by Cambridge University Press:  06 August 2013

Hayder F. N. Al-Shuka ,
B. Corves  and
Wen-Hong Zhu
Hayder F. N. Al-Shuka*
Affiliation:
Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany
B. Corves
Affiliation:
Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany
Wen-Hong Zhu
Affiliation:
Canadian Space Agency, Canada
*
*Corresponding author. E-mail: al-shuka@igm.rwth-aachen.de
Get access Rights & Permissions [Opens in a new window]

Summary

The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamics-based control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e.g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.

Keywords

Virtual decomposition controlAdaptive controlFunction approximation techniqueComputational complexityBiped robotOrthogonal functions
Type
Articles
Information
Robotica , Volume 32 , Issue 3 , May 2014 , pp. 375 - 399
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Luh, J. Y. S., Walker, M. W. and Paul, R. P. C., “On-line computational scheme for mechanical manipulator,” Trans. ASME J. Dyn. Syst. Meas. Control 102 (2), 69–76 (1980).CrossRefGoogle Scholar
2.Hollerbach, J. M., “A recursive Lagrangian formulation of manipulator dynamics and comparative study of dynamics formulation complexity,” IEEE. Trans. Syst. Man Cybern. SMC- 10 (11), 730–736 (1980).Google Scholar
3.Walker, M. W. and Orin, D. E., “Efficient dynamic computer simulation of robotic mechanisms,” Trans. ASME J. Dyn. Syst. Meas. Control 104 (3), 205–211 (1982).CrossRefGoogle Scholar
4.Balafoutis, C. A. and Patel, R. V., “Efficient computation of manipulator, inertia matrices and the direct dynamics problem,” IEEE Trans. Syst. Man Cybern. 19 (4), 1313–1321 (1989).Google Scholar
5.Angeles, J., Ma, O. and Rojas, A., “An algorithm for the inverse dynamics of n-axis general manipulator using Kane's formulation of dynamical equations,” Comput. Math. Appl. 17 (12), 1545–1561 (1998).Google Scholar
6.Saha, S. K., “Dynamics of serial multibody systems using the decoupled natural orthogonal complement matrices,” ASME J. Appl. Mech. 66, 986–996 (1999).Google Scholar
7.Featherstone, R., “The calculation of robot dynamics using articulated-body inertias”, Int. J. Robot. Res. 2 (1), 13–30 (1983).Google Scholar
8.Brandle, H., Johanni, R. and Otter, M., “A Very Efficient Algorithm for the Simulation of Robots and Similar Multibody Systems without Inversion of the Mass Matrix,” In: Proceedings of IFAC/IFIP/IMACS International Symposium on Theory of Robots, Vienna, Austria (Dec. 1986), pp. 95–100.Google Scholar
9.Mohan, A. and Saha, S. K., “A recursive, numerically stable and efficient simulation algorithm for serial robots,” Int. J. Multibody Syst. Dyn. 17 (4), 291–319 (2007).Google Scholar
10.Lee, K. and Chirikjian, G. S., “A New Perspective on O(n) Mass-Matrix Inversion for Serial Revolute Manipulators,” In: Proceeding of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005), pp. 4722–4726.Google Scholar
11.Featherstone, R. and Orin, D., “Robot Dynamics: Equations and Algorithms,” In: Proceedings of the IEEE International Conference on Robotics and Automation, ICRA'00, San Francisco, CA, USA (Apr. 2000), vol. 1, pp. 826–834.Google Scholar
12.Saha, S. K., “Recursive Dynamics Algorithms for Serial, Parallel and Closed-Chain Multibody Systems,” Indo-US Workshop on Protein Kinematics and Protein Conformations, IISC, Bangalore (Dec. 2007).Google Scholar
13.Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., Robotics: Control, Sensing, Vision, and Intelligence (McGraw-Hill, New York, USA, 1987).Google Scholar
14.Sandell, N. R., Varaiya, J. R. P., Athans, M. and Safonov, M. G., “Survey of decentralized control methods for large scale systems”, IEEE Trans. Autom. Control AC- 23 (2), 108–128 (1978).Google Scholar
15.Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control (John Wiley & Sons, New York, USA, 1989).Google Scholar
16.Boha, J., Belda, K. and Valasue, M., “Decentralized control of redundant parallel robot construction,” In: Proceeding of the 10th Mediterranean Conference on Control and Automation, Libson, Portugal (Jul. 2002), pp. 9–12.Google Scholar
17.Ohri, J., Dewan, L. and Soni, M. K., “Tracking Control of Robots Using Decentralized Robust PID Control for Friction and Uncertainty Compensation,” In: Proceedings of the World Congress on Engineering and Computer Science, San Francisco, CA, USA (Oct. 2007).Google Scholar
18.Xu, K., Integrating Centralized and Decentralized Approaches for Multi-Robot Coordination Ph.D. Thesis (Mechanical and Aerospace Engineering, New Brunswick, New Jersey, USA, 2010).Google Scholar
19.Leena, G. and Ray, G., “A set of decentralized PID controller for an n-link robot manipulator,” Indian Acad. Sci. 37, 405–423 (2012).Google Scholar
20.Zhu, W.-H., Virtual Decomposition Control: Toward Hyper Degrees of Freedom Robots (Springer-Verlag, Berlin, Heidelberg, 2010).Google Scholar
21.Dallali, H., Medrano-Corda, G. A. and Brown, M., “A Comparison of Multivariable and Decentralized Control Strategies for Robust Humanoid Walking,” In: Proceedings of UKACC International Conference on Control, Coventry, UK (Sept. 2010).Google Scholar
22.Zhu, W.-H., Xi, Y. G. and Zhang, Z. J., “Coordinative Control of Two Space Robots Based on Virtual Decomposition,” In: Proceedings of the 3rd IEEE Conference on Control Application, Glasgow, Scotland (1994) pp. 327–332.Google Scholar
23.Zhu, W.-H., Xi, Y. G., Zhang, Z. J., Bien, Z. and De Schutter, J., “Virtual decomposition based control for generalized high dimensional robotic systems with complicated structure,” IEEE Trans. Robot. Autom. 13 (3), 411–436 (1997).Google Scholar
24.Zhu, W.-H., Bien, Z. and De Schutter, J., “Adaptive motion/force control of coordinated multiple manipulators with joint flexibility based on virtual decomposition,” IEEE Trans. Autom. Control 43 (1), 46–60 (1998).Google Scholar
25.Zhu, W.-H. and Schutter, J. De, “Adaptive control of mixed rigid/flexible joint robot manipulators based on virtual decomposition,” IEEE Trans. Robot. Autom. 15 (2), 310–317 (1999).Google Scholar
26.Zhu, W. H. and De Schutter, J., “Adaptive control of electrically driven space robots based on virtual decomposition,” AIAA J. Guid. Control Dyn. 22 (2), 329–339 (1999).Google Scholar
27.Zhu, W.-H. and Schutter, J. De, “Experimental verifications of virtual decomposition based motion/force control,” IEEE Trans. Robot. Autom. 18 (3), 379–386 (2002).Google Scholar
28.Zhu, W.-H. and Schutter, J. De, “Virtual Decomposition Based Motion/Force Control of an Industrial Manipulator KUKA361,” In: Preprint of 15th IFAC World Congress, Barcelona, Spain (2002), pp. 1902–1907.Google Scholar
29.Zhu, W.-H., Lange, C. and Callot, M., “Virtual Decomposition Control of a Planar Flexible-Link Robot,” In: Preprint of 17th IFAC World Congress, Seoul, Korea (2008) pp. 1697–1702.Google Scholar
30.Antonelli, G., Caccavale, F. and Chiaverini, S., “A Virtual-Decomposition Based Approach to Adaptive Control of Underwater Vehicle-Manipulator Systems,” In: The 9th Mediterranean Conference on Control and Automation, Dubrovnik, Croatia (2001).Google Scholar
31.Song, Y. D., “Adaptive Motion Tracking Control of Robot Manipulators-Non-Regressor Based Approach,” In: Proceeding of the IEEE International Conference on Robotics and Automation, San Diego, CA, USA (May 1994), vol. 4, pp. 3008–3013.Google Scholar
32.Sadegh, N. and Horowitz, R., “Stability and robustness analysis of a class of adaptive controller for robotic manipulators,” Int. J. Robot. Res. 9 (3), 74–92 (1990).Google Scholar
33.Lu, W. S. and Meng, Q. H., “Recursive Computation of Manipulator Regressor and Its Application to Adaptive Motion Control of Robots,” In: Proceedings of the IEEE Conference on Communication, Computation and Signal Processing, Victoria, BC, USA (May 1991) pp. 170–173.Google Scholar
34.Kawasaki, H., Bito, T. and Kanzaki, K., “An efficient algorithm for model-based adaptive controller of robot manipulators,” IEEE Trans. Robot. Autom. 12 (3), 496–501 (1996).Google Scholar
35.Yang, J. H., “Adaptive Tracking Control for Manipulators with Only Position Feedback,” In: Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering, Alberta, Canada (May 1999) vol. 3, pp. 1740–1745.Google Scholar
36.Qu, Z. and Dorsey, J., “Robust tracking control of robots by a linear feedback law,” IEEE Trans. Autom. Control 36 (9), 1081–1084 (1991).Google Scholar
37.Park, J. S., Jiang, Y. A., Hesketh, T. and Clements, D. J., “Trajectory Control of Manipulators Using Adaptive Sliding Mode Control,” In: Proceedings of the IEEE, Southeastcon'94, Miami, FL, USA (Apr. 1994) pp. 142–146.Google Scholar
38.Yuan, J. and Stepanenko, Y., “Adaptive PD Control of Flexible Joint Robots without Using the High-Order Regressor,” In: Proceedings of the 36th Midwest Symposium on Circuits and Systems, Detroit, MI, USA (Aug. 1993), vol. 1, pp. 389–393.Google Scholar
39.Su, C. Y. and Stepanenko, Y., “Adaptive Control for Constrained Robots without Using Regressor,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, USA (Apr. 1996), vol. 1, pp. 264–269.Google Scholar
40.Huang, A.-C. and Chien, M.-C., Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach (World Scientific, Singapore/USA, 2010).Google Scholar
41.Cong, S., Liang, Y. and Shang, W., “Function approximation-based sliding mode adaptive control for time-varying uncertain nonlinear systems,” Nonlinear Dyn. 54 (5), 223–230 (2008).Google Scholar
42.Liang, J.-W., Chen, H.-Y. and Tsu, Y.-T., “FAT-based Adaptive Sliding Mode Control for a Piezoelectric-Actuated System,” In: Proceedings of the IEEE International Conference on Control and Automation, Christchurch, New Zealand (Dec. 2009) pp. 848–853.Google Scholar
43.Fossen, T., Guidance and Control of Ocean Vehicles (John Wiley & Sons, Chicheste, UK, 1994).Google Scholar
44.Craig, J. J., Introduction to Robotics: Mechanics and Control, 3rd ed. (Pearson, New Jersey, USA, 2005).Google Scholar
45.Slotine, J.-J. E. and Li, W., Applied Nonlinear Control (Prentice-Hall, New Jersey, USA, 1991).Google Scholar
46.Farrell, A. and Polycarpou, M. M., Adaptive Approximation Based: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches (John Wiley & Sons, New York, USA, 2006).Google Scholar
47.Faires, J. D. and Burden, R. L., Numerical Methods, 3rd ed. (Brooks Cole, Pacific Grove, CA, USA, 2002).Google Scholar
48.Chaoui, H., Sicard, P. and Gueaieb, W., “ANN-based adaptive control of robotic manipulators with friction and joint elasticity,” IEEE Trans. Ind. Electron. 56 (8), 3174–3187 (2009).Google Scholar
49.Chen, C., Cheng, M. H., Yang, C. and Chen, J., “Robust Adaptive Control for Robot Manipulators with Friction,” In: Proceedings of the IEEE 3rd International Conference on Innovative Computing Information and Control (ICICIC'08), Dalian, Liaoning, China (Jun. 2008) p. 422.Google Scholar
50.Hunger, R., Floating Point Operations in Matrix–Vector Calculus, Technical Report (Associate Institute for Signal Processing, Technische Universitäte Mümchen, 2007).Google Scholar
51.Kajita, S., Morisawa, M., Miura, K., Nakaoka, S., Harada, K., Kaneko, K., Kanehiro, F. and Yokoi, K., “Biped Walking Stabilization Based on Inverted Pendulum Tracking,” In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Taiwan (2010) pp. 4489–4496.Google Scholar
52.Roussel, L., Canudas-de-Wit, C. and Goswami, A., “Generation of Energy Optimal Complete Gait Cycles for Biped Robots,” In: Proceedings of the IEEE Conference on Robotics and Automations, Leuven, Belgium (May 1998) vol. 3, pp. 2036–2041.Google Scholar
53.Azevedo, C., Poignet, P. and Esspiau, B., “On Line Optimal Control for Biped Robots,” In: IFAC, 15th Triennial World Congress, Barcelona, Spain (2002).Google Scholar
54.Tzafestas, S., Raibert, M. and Tzafestas, C., “Robust sliding–mode control applied to a 5-link biped robot,” J. Intell. Robot. Syst. 15, 76–133 (1996).Google Scholar
55.Mu, X. and Wu, Q., “Dynamic Modeling and Sliding Mode Control of a Five-Link Biped Robot during the Double Support Phase,” In: Proceeding of the 2004 American Control Conference, Boston, MA, USA (2004) pp. 2609–2614.Google Scholar
56.Al-Shuka, H. F. N. and Corves, B., “On the walking pattern generators of biped robot,” J. Autom. Control 1 (2), 149–155 (2013).Google Scholar