Geodesic
Steady-state motion of a balancing robot with two coaxial deformable wheels
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 181-193.

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At present, the theory of wheeled robotic systems is being actively developed. In modeling the motion of wheeled robots, one mostly uses the classical nonholonomic motion model, which does not take into account the slip of deformable wheels. Meanwhile, for robots with deformable wheels nonholonomic models can be inadequate for the design and analysis of control algorithms. This can be the case for statically unstable balancing robots with coaxial wheels, similar in design with such vehicles as Segway. Thus, modeling the motion of a two-wheeled robot taking into account the possibility of wheels slip, and analysis of applicability of simplified models are of interest. Such models can be used to develop new control algorithms in active maneuvering, and for preliminary estimates of robustness of algorithms designed using approximate nonholonomic models. This paper focuses on modeling the motion of balancing robots, on analyzing their steady-state motion and on possibilities of their stabilization. It is shown that for models with deformable wheels in the steady-state motion the body has a forward pitch. Such a pitch is not found in most nonholonomic models. 
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P. A. Kruchinin; A. A. Laskin. Steady-state motion of a balancing robot with two coaxial deformable wheels. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 181-193. http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a11/

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