In this paper, we develop a model of a controlled spherical robot of combined type moving by displacing the center of mass and by changing the internal gyrostatic momentum, with a feedback that stabilizes given partial solutions for a free system at the final stage of motion. According to the proposed approach, feedback depends on phase variables (current position, velocities) and does not depend on the specific type of trajectory. We present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulations of motion with feedback that demonstrate the efficiency of the proposed model.
Spherical robot Nonholonomic constraint Control Feedback
Mathematics Subject Classification (2010)
70F25 70Q05 93D15
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The authors extend their gratitude to A. V. Borisov and I. S. Mamaev for fruitful discussions of the results obtained.
This work is supported by the Russian Science Foundation under grant 14-50-00005 and was performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.
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