Baiquan Su, Tianmiao Wang, Shaolong Kuang, and Junchen Wang
Parameter effect, non-holonomic system, rolling robot, spherical inverted pendulum
Effects of physical parameters on open- and closed-loop performance of a non-holonomic sphere-driven spherical inverted pendulum robot (ballbot) are studied in this paper. Falling time is used as a performance index to evaluate the effects of physical parameters on the open-loop behaviour. The relationships between the falling time and the physical parameters, including mass of sphere, mass of upper body, moment of inertial of sphere, length from centre of mass (CoM) of upper body to centre of sphere, are obtained by solving a system of second-order ordinary differential equations (ODEs) representing the open-loop ballbot. Next, performance indices are defined to evaluate the effects of the physical parameters on the closed-loop behaviour. Based on an exact trajectory tracking controller, the relationships between the defined indices and the physical parameters are established via solving another system of second-order ODEs representing the closed-loop ballbot. The results in the paper are useful for physical parameter selection for ballbot design.
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