An analysis of the rolling dynamics of a hexapod robot using a three-dimensional rolling template

Multi-legged robots are analyzed and controlled based on a reduced-order single-legged planar model. However, the rolling motion is ignored in the discussion of the planar model, making a quantitative discussion of comprehensive stability and energy cost impossible to conduct. In this paper, a progressive process for analyzing the rolling motion of an RHex-style robot is presented. A planar bounding-in-place model whose stiffnesses of the left leg and right leg are different is analyzed. Two new orbits that represent the rolling motion more appropriately than the pronking orbit are found. To further investigate the rolling motion with the consideration of a half-circular compliant leg, a three-dimensional model, called the roll two-leg, clock-torqued, spring-loaded inverted pendulum model with a rolling contact (RTL-CTR-SLIP), is developed. It is proved via the simulation that the pronking orbit fails to serve as a passively stable rolling orbit in the three-dimensional model. The dynamics of rolling motion and the power consumption are also investigated via the simulation. Finally, the empirical data show a regular periodic rolling motion exists as an RHex-style robot runs, and the simulation of the RTL-CTR-SLIP model partially predicts the rolling dynamic and the energy cost of a real-world RHex-style robot.