Abstract
In this paper, we perform bifurcation analysis on instability arising in a pair of acrobots connected by a mechanical coupling. For this purpose, we propose a coupled acrobots model consisting of two identical acrobots stabilized at their standing position in terms of feedback control and connect them with the mechanical linkage composed by a linear spring and a linear damping. It is shown numerically that the proposed model exhibits four types of dynamics such as a simple-stable, a buckled-stable, a simple-vibration and a buckled-vibration response when the strength of coupling changes. Then, we employ bifurcation diagrams to examine correspondence between the coupling strength and the resulting dynamics. For more detailed feature of the change of stability, we also derive bifurcation sets with respect to the linear spring and damping coefficient. The result shows that the parameter condition of each dynamics can be divided by supercritical pitchfork bifurcation set and supercritical Hopf bifurcation set.
