Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-10T12:09:14.496Z Has data issue: false hasContentIssue false
  • English
  • Français

On Motion Planning and Control for Partially Differentially Flat Systems

Published online by Cambridge University Press:  16 July 2020

Yang Bai Open the ORCID record for Yang Bai [Opens in a new window] ,
Mikhail Svinin Open the ORCID record for Mikhail Svinin [Opens in a new window] ,
Evgeni Magid Open the ORCID record for Evgeni Magid [Opens in a new window]  and
Yujie Wang Open the ORCID record for Yujie Wang [Opens in a new window]
Yang Bai*
Affiliation:
Information Science and Engineering Department, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan. E-mail: svinin@fc.ritsumei.ac.jp
Mikhail Svinin
Affiliation:
Information Science and Engineering Department, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan. E-mail: svinin@fc.ritsumei.ac.jp
Evgeni Magid
Affiliation:
Department of Intelligent Robotics, Kazan Federal University, Kremlyovskaya str. 35, Kazan 420008, Russian Federation. E-mail: magid@it.kfu.ru
Yujie Wang
Affiliation:
Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana-Champaign, IL, USA. E-mail: yujiew4@illinois.edu
*
*Corresponding author. E-mail: yangbai@fc.ritsumei.ac.jp
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper deals with motion planning and control problems for a class of partially differentially flat systems. They possess a feature that the derivative of the fiber variable can be represented purely by the base variable and its derivatives. Based on this feature, a Beta function-based motion planning algorithm is proposed with less computational cost compared with the optimal control formulation while providing similar system performance. Then, an adaptive controller is constructed through a function approximation technique-based approach. Finally, the feasibility of the proposed motion planning and control algorithms is verified by simulations.

Keywords

Motion planning and controlUnderactuated systemsPartial differential flatness

Information

Type
Articles
Information
Robotica , Volume 39 , Issue 4 , April 2021 , pp. 718 - 734
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

References

Bai, Y., Svinin, M. and Yamamoto, M., “Motion Planning for a Hoop-Pendulum Type of Underactuated Systems,” Proceedings of the IEEE International Conference on Robotics and Automation (2016) pp. 2739–2744.Google Scholar
Bai, Y., Svinin, M. and Yamamoto, M., “Adaptive Trajectory Tracking Control for the Ball-Pendulum System with Time-Varying Uncertainties,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (2017) pp. 2083–2090.Google Scholar
Bai, Y., Svinin, M. and Yamamoto, M., “Function approximation based control for non-square systems,” SICE J. Control Measure. Syst. Integr. 11(6), 477–485 (2018).CrossRefGoogle Scholar
Bullo, F., Leonard, N. E. and Lewis, A. D., “Controllability and motion algorithms for underactuated Lagrangian systems on lie groups,” IEEE Trans. Autom. Control 45(8), 1437–1454 (2000).CrossRefGoogle Scholar
Bullo, F. and Lynch, K. M., “Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems.” IEEE Trans. Robot. Autom. 17(4), 402–412 (2001).CrossRefGoogle Scholar
Chien, M. and Huang, A., “Adaptive control for flexible-joint electrically driven robot with time-varying uncertainties,” IEEE Trans. Ind. Electron. 54(2), 1032–1038 (2007)CrossRefGoogle Scholar
Gao, B., Zhang, X., Chen, H. and Zhao, J.. “Energy-Based Control Design of an Underactuated 2-Dimensional Tora System,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (2009) pp. 1296–1301.Google Scholar
Huang, J., Guan, Z. H., Matsuno, T., Fukuda, T. and Sekiyama, K., “Sliding-mode velocity control of mobile-wheeled inverted-pendulum systems,” IEEE Trans. Robot. 26(4), 750–758 (2010).CrossRefGoogle Scholar
Kelly, S. and Murray, R., “Geometric phases and robotic locomotion,” J. Robot. Syst. 12(6), 417–431 (1995).CrossRefGoogle Scholar
Liang, Y., Cong, S. and Shang, W., “Function approximation-based sliding mode adaptive control,” Nonlinear Dyn. 54(3), 223–230 (2008).CrossRefGoogle Scholar
Fantoni, I. and Lozano, R., Non-Linear Control for Underactuated Mechanical Systems (Springer-Verlag, New York, NY, USA, 2002).CrossRefGoogle Scholar
Martinez, S., Cortes, J. and Bullo, F., “Analysis and design of oscillatory control systems,” IEEE Trans. Autom. Control 48(7), 1164–1177 (2003).CrossRefGoogle Scholar
McNinch, L. C. and Ashrafiuon, H., “Predictive and Sliding Mode Cascade Control for Unmanned Surface Vessels,” Proceedings of the American Control Conference (2011) pp. 184–189.Google Scholar
Nagarajan, U., Kantor, G. and Hollis, R. L., “Trajectory Planning and Control of an Underactuated Dynamically Stable Single Spherical Wheeled Mobile Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (2009) pp. 3743–3748.Google Scholar
Nersesov, S. G., Ashrafiuon, H. and Ghorbanian, P., “On the Stability of Sliding Mode Control for a Class of Underactuated Nonlinear Systems,” Proceedings of the American Control Conference (2010) pp. 3446–3451.Google Scholar
Neusser, Z. and Valasek, M., “Control of the underactuated mechanical systems using natural motion,” Kybernetika 48(2), 223–241 (2012).Google Scholar
Olfati-Saber, R., “Trajectory Tracking for a Flexible One-Link Robot Using a Nonlinear Noncollocated Output,” Proceedings of the 39th IEEE Conference on Decision and Control (2000) pp. 4024–4029.Google Scholar
Pettersen, K. Y. and Nijmeijer, H., “Tracking Control of an Underactuated Surface Vessel,” Proceedings of the 37th IEEE Conference on Decision and Control (1998) pp. 4561–4566.Google Scholar
Qian, D. W., Yi, J. Q. and Zhao, D. B., “Robust Control Using Sliding Mode for a Class of Underactuated Systems with Mismatched Uncertainties,” Proceedings of the IEEE International Conference on Robotics and Automation (2007) pp. 1449–1454.Google Scholar
Ramasamy, S., Wu, G. and Sreenath, K., “Dynamically Feasible Motion Planning Through Partial Differential Flatness,” Proceedings of Robotics: Science and Systems (2014) pp. 125–130.Google Scholar
Coron, J.-M., Control and Nonlinearity (American Mathematical Society, Boston, MA, USA, 2007).Google Scholar
Bai, Y., Svinin, M., Wang, Y. and Magid, E., “Function Approximation Technique Based Control for a Class of Nonholonomic Systems,” Proceedings of IEEE IEEE/SICE International Symposium on System Integration, Honolulu, Hawaii, USA, January 2020.CrossRefGoogle Scholar
Romero-Melendez, C. and Monroy-Perez, F., “The motion planning problem: Differential flatness and nilpotent approximation,” Cybern. Phys. 2(3), 133–142 (2012).Google Scholar
Sankaranarayanan, V. and Mahindrakar, A. D., “Control of a class of underactuated mechanical systems using sliding modes,” IEEE Trans. Robot. 25(2), 459–467 (2009).CrossRefGoogle Scholar
Shammas, E., Generalized Motion Planning for Underactuated Mechanical Systems Ph.D. Thesis (Carnegie Mellon University, Pittsburgh, Pennsylvania, 2006).Google Scholar
Shiriaev, A., Ludvigsen, H., Egeland, O. and Pogromsky, A., “On Global Properties of Passivity Based Control of the Inverted Pendulum,” Proceedings of the 38th IEEE Conference on Decision and Control (1999) pp. 2513–2518.Google Scholar
Slotine, J. E. and Li, W., Applied Nonlinear Control (Prentice Hall International Inc., Englewood Cliffs, New Jersey, 1991).Google Scholar
Sofronniou, M. and Knapp, R., Advanced Numerical Differential Equation Solving in Mathematica (Wolfram Research, Inc., Champaign, IL, 2008).Google Scholar
Spong, M. W., “Partial Feedback Linearization of Underactuated Mechanical Systems,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (1994) pp. 314–321.Google Scholar
Tsai, Y. and Huang, A., “Fat-based adaptive control for pneumatic servo systems with mismatched uncertainties,” Mech. Syst. Signal Process. 22(6), 1263–1273 (2008).CrossRefGoogle Scholar
Tyan, F. and Lee, S., “An Adaptive Control for Rotating Stall and Surge of Jet Engines – A Function Approximation Approach. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 (2005) pp. 5498–5503.Google Scholar
Xin, X. and Kaneda, M., “Analysis of the energy-based control for swinging up two pendulums,” IEEE Trans. Automat. Contr. 50(5), 679–684 (2005).CrossRefGoogle Scholar
Xu, R. and Özgüner, U., “Sliding mode control of a class of underactuated systems,” Automatica 44(1), 233–241 (2008).CrossRefGoogle Scholar
Ladd, A. and Kavraki, L., “Motion Planning in the Presence of Drift, Underactuation and Discrete System Changes.” Proceedings of Robotics: Science and Systems (RSS2005) (2005) pp. 233–240.Google Scholar