Ellipse-based leg-trajectory generation for galloping quadruped robots

Controlling the motions of the front and rear legs and regulating the compliance of the legs are important for stable gallop. In this paper, a new method called ellipse-based trajectory generation method (ETGM) to generate foot trajectories for galloping quadrupeds is proposed. Unlike many previous works which attempted controlling foot trajectory, which need a sophisticated algorithm to avoid forcing the feet out of the workspace and thus making galloping unstable, a new trajectory generation method is based on an elliptic trajectory with constant radii but with changes in its center position. The rotational speed of the elliptic trajectory or the orbit trajectory is determined by the desired height of galloping and the running speed. It is assumed that each leg of a galloping quadruped robot has passive ankle joints with passive springs, thus acting as a spring loaded inverted pendulum (SLIP). To check the performance and effectiveness of the proposed method, a series of computer simulations of a 2-D quadruped robot galloping in the sagittal plane were performed. The simulation results show that the proposed method is simple to implement and very effective in generating stable gallop. This paper was recommended for publication in revised form by Associate Editor Doo Yong Lee Jong Hyeon Park received his B.S. degree in mechanical engineering from Seoul National University in 1981 and his M.S. and Ph.D. degrees from the Massachusetts Institute of Technology in 1983 and 1991, respectively. Since 1992, he has been with the School of Mechanical Engineering at Hanyang University. He was a KOSEF-JSPS Visiting Researcher with Waseda University, Tokyo, Japan, in 1999, and a KOSEFCNR Visiting Researcher with Scuola Superiore Sant’Anna, Pisa, Italy in 2000, a Visiting scholar with MIT, Cambridge, USA, in 2002–2003. He was also associated with Brooks Automation Inc., Chelmsford, MA, in 1991–1992 and 2001–2002.