Switching from hopping to running with HZD controller

Between different modelling of animal hopping, walking and running, the most popular one is Spring Loaded Inverted Pendulum (SLIP) model [1],[2]. Through the representation of the body in SLIP by a point mass, trunk stabilization is not addressed. With addition of trunk, it is extended to TSLIP (Trunk SLIP) in which hip torque is applicable for control. Mostly, the control is performed in two layers; one for leg adjustment and another for trunk stabilization. Various methods are presented by researchers to make a stable running [1],[2], but changing the speed with stability background was not the main focus in the literature. In this research, hopping is defined as jumping vertically without any movement in horizontal direction (running with zero velocity). Unlike running, an asymptotically stable hopping is not achievable with a fixed angle of attack1. Most of the control approaches for running/hopping robots, are variations of Raiberts controller, [3]. The main target of this paper is presenting a controller that has the ability to change the speed based on Hybrid Zero Dynamics (HZD) stability analysis. To reach this goal, two layer controller is designed to produce asymptotically stable hopping and running with upright trunk. Then, a PI controller is employed to switch from hopping to running via leaning the trunk forward. After obtaining the desired speed, returning the trunk to upright position guarantees the stability of running analytically.