Controlled Motion of a Spherical Robot with Feedback. I
- 254 Downloads
In this paper, we develop a model of a controlled spherical robot with an axisymmetric pendulum-type actuator with a feedback system suppressing the pendulum’s oscillations at the final stage of motion. According to the proposed approach, the feedback depends on phase variables (the current position and velocities) and does not depend on the type of trajectory. We present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulation of motion using feedback to illustrate compensation of the pendulum’s oscillations.
KeywordsSpherical robot Nonholonomic constraint Control Feedback
Mathematics Subject Classification (2010)70F25 70Q05 93D15
The authors extend their gratitude to A. V. Borisov, I. S. Mamaev and Yu. L. Karavaev for fruitful discussions of the results obtained.
The work of T. B. Ivanova (Sections 1 and 2) was carried out within the framework of the state assignment to the Ministry of Education and Science of Russia (1.2404.2017/4.6) and was supported by a grant of RFBR (15-08-09261-a). The work of A. A. Kilin (Section 3) was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation. The work of E. N. Pivovarova (Section 4) was supported by the grant of RSF (15-12-20035).
- 5.Bloch AM, Leonard NE, Marsden JE. Stabilization of mechanical systems using controlled lagrangians. Proceedings 36th conference on decision and control; 1997. p. 2356–2361.Google Scholar
- 11.Borisov AV, Mamaev IS, Karavaev YL. Mobile robots: robot-wheel and robot-ball. Russian: Moscow–Izhevsk: Institute of Computer Science; 2013.Google Scholar
- 14.Chowdhury AR, Vibhute A, Soh GS, Foong SH, Wood KL. Implementing caterpillar inspired roll control of a spherical robot. Proceedings 2017 IEEE international conference on robotics and automation; 2017. p. 4167–4174.Google Scholar
- 16.Halme A, Schonberg T, Wang Y. Motion control of a spherical mobile robot. Proceedings 4th international workshop on advanced motion control; 1996. p. 259–264.Google Scholar
- 18.Ivanova TB, Pivovarova EN. Dynamics and control of a spherical robot with an axisymmetric pendulum actuator. Rus J Nonlin Dyn 2013;9(3):507–520. (Russian).Google Scholar
- 26.Lewis AD, Ostrowski JP, Burdickz JW, Murray RM. Nonholonomic mechanics and locomotion: the Snakeboard example. Proc 1994 IEEE Int Conf Robot Autom. 1994;3:2391–2397.Google Scholar
- 27.Madhushani TWU, Maithripala DHS, Berg JM. 2017. Feedback Regularization and Geometric PID Control for Trajectory Tracking of Coupled Mechanical Systems: Hoop Robots on an Inclined Plane. arXiv:1609.09557v2.
- 28.Madhushani TWU, Maithripala DHS, Wijayakulasooriya JV, Berg JM. 2017. Semi-globally Exponential Trajectory Tracking for a Class of Spherical Robots. arXiv:1608.01494v2.
- 30.Muraleedharan N, Cohen DS, Isenberg DR. 2016. Omnidirectional locomotion control of a pendulum driven spherical robot. SoutheastCon. https://doi.org/10.1109/SECON.2016.7506648.
- 36.Sugiyama Y, Shiotsu A, Yamanaka M, Hirai S. Circular/Spherical Robots for crawling and jumping. Proceedings 2005 IEEE international conference on robotics and automation; 2005. p. 3595–3600.Google Scholar
- 37.Svinin M, Bai Y, Yamamoto M. Dynamic model and motion planning for a pendulum-actuated spherical rolling robot. Proceedings 2015 IEEE international conference on robotics and automation; 2015. p. 656–661.Google Scholar
- 41.Ylikorpi T, Forsman P, Halme A. Dynamic obstacle overcoming capability of pendulum-driven ball-shaped robots. 17th IASTED international conference on robotics and applications; 2014. p. 329–338.Google Scholar
- 42.Yu T, Sun H, Jia Q, Zhang Y, Zhao W. Stabilization and control of a spherical robot on an inclined plane. Res J Appl Sci Eng Technol 2013;5(6):2289–2296.Google Scholar