Abstract
This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First, kinematic and dynamic models for the rolling robot are introduced. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a nontrivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, a geometric phase-based approach has been employed and tested under simulation. Compared with the minimum effort optimal control, the proposed technique is less computationally expensive while providing similar system performance, and thus it is more suitable for real-time applications.
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Bhattacharya, S. and Agrawal, S.K., Spherical Rolling Robot: A Design and Motion Planning Studies, IEEE Trans. Robot. Autom., 2000, vol. 16, no. 6, pp. 835–839
Bicchi, A., Balluchi, A., Prattichizzo, D., and Gorelli, A., Introducing the “SPHERICLE”: An Experimental Testbed for Research and Teaching in Nonholonomy, in Proc. of the IEEE Internat. Conf. on Robotics and Automation (Albuquerque,N.M., USA, 1997): Vol. 3, pp. 2620–2625.
Borisov, A. V., Kilin, A.A., and Mamaev, I. S., How to Control Chaplygin’s Sphere Using Rotors, Regul. Chaotic Dyn., 2012, vol. 17, nos. 3–4, pp. 258–272.
Borisov, A. V., Kilin, A.A., and Mamaev, I. S., How to Control Chaplygin’s Sphere Using Rotors: 2, Regul. Chaotic Dyn., 2013, vol. 18, nos. 1–2, pp. 144–158.
Chase, R. and Pandya, A., A Review of Active Mechanical Driving Principles of Spherical Robots, Robotics, 2012, vol. 1, no. 1, pp. 3–23
Das, T., Mukherjee, R., and Yuksel, H., Design Considerations in the Development of a Spherical Mobile Robot, in Proc. of the 15th SPIE Annual International Symposium on Aerospace/Defense Sensing, Simulation, and Controls (Orlando, Fla., Apr 2001): Vol. 4364, pp. 61–71.
Halme, A., Schonberg, T., and Wang, Y., Motion Control of a Spherical Mobile Robot, in Proc. of the 4th Internat. Workshop on Advanced Motion Control (Mie, Japan, 1996): Vol. 1, pp. 259–264.
Harada, K., Kawashima, T., and Kaneko, M., Rolling Based Manipulation under Neighborhood Equilibrium, Int. J. Rob. Res., 2002, vol. 21, nos. 5–6, pp. 463–474.
Ishikawa, M., Kitayoshi, R., and Sugie, T., Volvot: A Spherical Mobile Robot with Eccentric Twin Rotors, in Proc. of the IEEE International Conference on Robotics and Biomimetics (Phuket, Thailand, Dec 7–11 2011), pp. 1462–1467.
Ishikawa, M., Kobayashi, Y., Kitayoshi, R., and Sugie, T., The Surface Walker: A Hemispherical Mobile Robot with Rolling Contact Constraints, in Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’2009, St. Louis, USA, Oct 10–15 2009), pp. 2446–2451.
Ivanov, A.P., On the Control of a Robot Ball Using Two Omniwheels, Regul. Chaotic Dyn., 2015, vol. 20, no. 4, pp. 441–448
Ivanova, T. B. and Pivovarova, E. N., Dynamics and Control of a Spherical Robot with an Axisymmetric Pendulum Actuator, Nonlinear Dynamics & Mobile Robotics, 2013, vol. 1, no. 1, pp. 71–85
Javadi, A. and Mojabi, P., Introducing Glory: A Novel Strategy for an Omnidirectional Spherical Rolling Robot, ASME J. Dyn. Syst. Meas. Control., 2004, vol. 126, no. 3, pp. 678–683
Joshi, V. A. and Banavar, R.N., Motion Analysis of a Spherical Mobile Robot, Robotica, 2009, vol. 27, no. 3, pp. 343–353
Karavaev, Yu. L. and Kilin, A.A., Nonholonomic Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform: Theory and Experiments, Proc. Steklov Inst. Math., 2016, vol. 295, pp. 158–167 see also: Tr. Mat. Inst. Steklova, 2016, vol. 295, pp. 174–183
Karavaev, Yu. L. and Kilin, A.A., The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform, Regul. Chaotic Dyn., 2015, vol. 20, no. 2, pp. 134–152
Kelly, S. D. and Murray, R. D., Geometric Phases and Robotic Locomotion, J. Robotic Systems, 1995, vol. 12, no. 6, pp. 417–431
Kilin, A. A., Pivovarova, E. N., and Ivanova, T.B., Spherical Robot of Combined Type: Dynamics and Control, Regul. Chaotic Dyn., 2015, vol. 20, no. 6, pp. 716–728
Li, Z. and Canny, J., Motion of Two Rigid Bodies with Rolling Constraint, IEEE Trans. Robot. Autom., 1990, vol. 6, no. 1, pp. 62–72
Luenberger, D., Optimization by Vector Space Methods, New York: Wiley, 1969.
Lurie, A. I., Analytical Mechanics, Berlin: Springer, 2002.
Mahboubi, S., Seyyed Fakhrabadi, M.M., and Ghanbari, A., Design and Implementation of a Novel Spherical Mobile Robot, J. Intell. Robot. Syst., 2013, vol. 71, no. 1, pp. 43–64
Marigo, A. and Bicchi, A., Rolling Bodies with Regular Surface: Controllability Theory and Applications, IEEE Trans. Autom. Control, 2000, vol. 45, no. 9, pp. 1586–1599
Morinaga, A., Svinin, M., and Yamamoto, M., A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors, IEEE Trans. on Robotics, 2014, vol. 30, no. 4, pp. 993–1002
Mukherjee, R., Minor, M., and Pukrushpan, J., Motion Planning for a SphericalMobile Robot: Revisiting the Classical Ball-Plate Problem, ASME J. Dyn. Syst. Meas. Control., 2002, vol. 124, no. 4, pp. 502–511
Murray, R. M., Li, Z., and Sastry, S. Sh., A Mathematical Introduction to Robotic Manipulation, Boca Raton, Fla.: CRC, 1994.
Neimark, Ju. I. and Fufaev, N. A., Dynamics of Nonholonomic Systems, Trans. Math. Monogr., vol. 33, Providence,R.I.: AMS, 1972.
O’Neill, B., Elementary Differential Geometry, 2nd ed., rev., New York: Acad. Press, 2006.
Oriolo, G. and Vendittelli, M., A Framework for the Stabilization of General Nonholonomic Systems with an Application to the Plate-Ball Mechanism, IEEE Trans. Robot., 2005, vol. 21, no. 2, pp. 162–175
Sofronniou, M. and Knapp, R., Advanced Numerical Differential Equation Solving in MATHEMATICA, Wolfram Research, Inc., 2008.
Sugiyama, Y., Shiotsu, A., Yamanaka, M., and Hirai, S., Circular/Spherical Robots for Crawling and Jumping, in Proc. of the 2005 IEEE International Conference on Robotics and Automation (Barcelona, Spain, Apr 2005), pp. 3595–3600.
Suzuki, K., Svinin, M., and Hosoe, S., Motion Planning for Rolling Based Locomotion, J. Robot. Mechatron., 2005, vol. 17, no. 5, pp. 537–545
Svinin, M. and Hosoe, S., Motion Planning Algorithms for a Rolling Sphere with Limited Contact Area, IEEE Trans. Robot., 2008, vol. 24, no. 3, pp. 612–625
Svinin, M., Morinaga, A., and Yamamoto, M., On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors, Regul. Chaotic Dyn., 2013, vol. 18, nos. 1–2, pp. 126–143.
Wittenburg, J., Dynamics of Systems of Rigid Bodies, 2nd ed., Stuttgart: Teubner, 1977.
Ylikorpi, T. J., Halme, A. J., and Forsman, P. J., Dynamic Modeling and Obstacle-Crossing Capability of Flexible Pendulum-Driven Ball-Shaped Robots, Rob. Auton. Syst., 2017, vol. 87, pp. 269–280
CRC Standard Mathematical Tables and Formulae, D. Zwillinger (Ed.), Boca Raton,Fla.: CRC, 1995, pp. 468–471.
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Bai, Y., Svinin, M. & Yamamoto, M. Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot. Regul. Chaot. Dyn. 23, 372–388 (2018). https://doi.org/10.1134/S1560354718040020
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DOI: https://doi.org/10.1134/S1560354718040020