Nonlinear Control of Motion of A Spherical Robot on Inclined Surfaces Based on Feedback Linearization Method

Document Type : Original Article

Authors

• Mohammad Aalipour ¹
• Ali Mokhtarian ²
• Hossein Karimpour ²

¹ , Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran.

² Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran.

10.22067/fum-mech.v31i2.74433

Abstract

Spherical robots are the mobile robots with spherical shape equipped to internal drive mechanism that move on the ground due to their external shell rolling. In this research, after modeling of a pendulum type of the spherical robots, dynamic analysis of their model during planar motion on an inclined surface is performed. The motion equations of spherical robot are derived using Lagrange method. Also, a nonlinear controller based on feedback linearization methods is designed. In the following, considering non-confirm initial conditions on trajectory, parametric uncertainty and also disturbance torque on robot, the motion of robot is simulated. The results indicate that the designed controller has proper and resistant performance in tracking selected trajectory for sphere shell rotation during moving on specified inclined surface.

Keywords

• Spherical Robot
• Dynamic Equations
• Disturbance Torque
• Parametric Uncertainty
• Non-linear Control

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References

1.    Bicchi, A., Balluchi, A., Prattichizzo, D., Gorelli, A., "Introducing the Sphericle: An Experimental Testbed for Research and Teaching in Non-holonomy", IEEE. International Conference on Robotics and Automation, Vol. 3, Albuquerque, NM, USA, (1997).

2.    Halme, A., Schonberg, T., Wang, Y., "Motion Control of a Spherical Mobile Robot", IEEE. International Conference on Advanced Motion Control, Vol. 1, Mie, Japan, (1996).

3.    Bhattacharya, S., Agrawal, S., "Design Experiments and Motion Planning of a Spherical Rolling Robot", IEEE. International Conference on Robotics and Automation, Vol. 2, San Francisco, CA, USA, (2000).

4.    Zhan, Q., Zhou, T., Chen, M., Cai, S., "Dynamic Trajectory Planning of a Spherical Mobile Robot", IEEE. International Conference on Robotics and Automation, Vol. 1, Bangkok, Thailand, (2006).

5.    Zhang, W., Liu, X., Fang, C., Sun, H., "Dynamics Modeling of Spherical Robot with Arms by Using Kane’s Method", IEEE. International Conference on Natural Computation, Vol. 4, Jinan, China, (2008).

6.    Joshi, V., Banavar, R., Hippalgaonkar, R., "Design and Analysis of a Spherical Mobile Robot", Mechanism and Machine Theory, Vol. 45, Issue 2, pp. 130–136, (2010).

7.    Liu, D., Sun, H., Jia, Q., "Stabilization and Path Following of Spherical Robot", IEEE. Conference on Robotics, Automation and Mechatronics, Vol. 1, Chengdu, China, (2008).

8.    Azizi, M., Naderi, D., "Dynamic Modeling and Trajectory Planning for a Mobile Spherical Robot with a 3DOF Inner Mechanism", Mechanism and Machine Theory, Vol. 64, pp. 251–261, (2013).

9.    Yu, T., Sun, H., Jia, Q., Zhao, W., "Path Following Control of a Spherical Robot Rolling on an Inclined Plane", IEEE. International Frequency Sensor Association, Vol. 21, pp. 42-47, (2013).

10.  Gajbhiye, S., Banavar, R. N., "Geometric 0Tracking Control for a Nonholonomic System: a Spherical Robot", International Federation of Automatic Control, Vol. 49, pp. 820–825, (2016).

11.  Ivanova, T. b., Kilin, A. a., Pivovarova, E. n., "Controlled Motion of a Spherical Robot with Feedback. I", Journal of Dynamical and Control Systems, Vol. 24, pp. 497–510, (2017).

12.  Ivanova, T. b., Kilin, A. a., Pivovarova, E. n., "Control of the Rolling Motion of a Spherical Robot on an Inclined Plane",Doklady Physics, Vol. 63, pp. 435–440, (2018).

13.  Sadigh, M. j., Salehi, A., Keshmiri, M., "A Semi-Manual Master-Slave Algorithm for Control of Flexible Micro-Macro Manipulators", IEEE. International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, (2007).