Abstract:
The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.
Keywords:
non-holonomic systems, rolling constraints, dynamics, motion planning.
Citation:
Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto, “On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors”, Regul. Chaotic Dyn., 18:1-2 (2013), 126–143
\Bibitem{SviMorYam13}
\by Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto
\paper On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 126--143
\mathnet{http://mi.mathnet.ru/rcd100}
\crossref{https://doi.org/10.1134/S1560354713010097}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3040987}
\zmath{https://zbmath.org/?q=an:1272.70049}
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Linking options:
https://www.mathnet.ru/eng/rcd100
https://www.mathnet.ru/eng/rcd/v18/i1/p126
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Anil B, Sneha Gajbhiye, 2024 18th International Conference on Control, Automation, Robotics and Vision (ICARCV), 2024, 76
Bernard Brogliato, “Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives”, Annual Reviews in Control, 55 (2023), 297
Miguel Á. Berbel, Marco Castrillón López, “Rigid body with rotors and reduction by stages”, Rev. Math. Phys., 35:01 (2023)
Seyed Amir Tafrishi, Mikhail Svinin, Motoji Yamamoto, Yasuhisa Hirata, “A geometric motion planning for a spin-rolling sphere on a plane”, Applied Mathematical Modelling, 121 (2023), 542
Yu. L. Karavaev, “Spherical Robots:
An Up-to-Date Overview of Designs and Features”, Rus. J. Nonlin. Dyn., 18:4 (2022), 709–750
Alexander A. Kilin, Elena N. Pivovarova, “Motion control of the spherical robot rolling on a vibrating plane”, Applied Mathematical Modelling, 109 (2022), 492
Alexander A. Kilin, Elena N. Pivovarova, “Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base”, Regul. Chaotic Dyn., 25:6 (2020), 729–752
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Kvaternionnaya model programmnogo upravleniya dvizheniem shara Chaplygina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 408–421
T. B. Ivanova, A. A. Kilin, E. N. Pivovarova, “Controlled motion of a spherical robot with feedback. I”, J. Dyn. Control Syst., 24:3 (2018), 497–510
Yang Bai, Mikhail Svinin, Motoji Yamamoto, “Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot”, Regul. Chaotic Dyn., 23:4 (2018), 372–388
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
H. Kang, C. Liu, Ya.-B. Jia, “Inverse dynamics and energy optimal trajectories for a wheeled mobile robot”, Int. J. Mech. Sci., 134 (2017), 576–588
M. R. Azizi, J. Keighobadi, “Point stabilization of nonholonomic spherical mobile robot using nonlinear model predictive control”, Robot. Auton. Syst., 98 (2017), 347–359
Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
V. Kozlov, “The phenomenon of reversal in the Euler–Poincaré–Suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724
S. Gajbhiye, R. N. Banavar, “Geometric tracking control for a nonholonomic system: a spherical robot”, IFAC-PapersOnLine, 49:18 (2016), 820–825
Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172
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