Pitch angular velocity dynamics property in transverse galloping pattern from the passive dynamic perspective

This paper employs the simplified quadrupedal passive dynamic model to analyze the underlying property of the transverse gallop. First, the simplified sagittal quadrupedal planar model of the transverse gallop, the trot, and searching methods for achieving the periodic motion are introduced. Next, we explore the dynamic performance of the transverse galloping pattern on the simplified quadrupedal passive dynamic model at different forward speeds and different stiffnesses of legs in a range of initial angular velocities at which the periodic motion is achieved, and there exists a particular property that is defined as the pitch angular velocity dynamics (PAVD) property. If the forward speed and the stiffness of legs are adequate in the transverse galloping pattern, the PAVD emerges and the forces (e.g. peak ground reaction force and average vertical force) that the model undergoes during locomotion are sharply reduced. The Froude numbers of the minimum forward speed where PAVD holds at a fixed stiffness of legs for different samples are virtually the same. Moreover, a comparison between the trot and the transverse gallop illustrates that a trot is more favorable in the range of forward speeds where the PAVD property is not achieved, while a transverse gallop is better after the property emerges.