From walking to running a natural transition in the SLIP model using the hopping gait

In this paper we adopt the spring loaded inverted pendulum (SLIP) model as the mathematical framework to represent biped locomotion, but in contrast with previous studies, we redefine the conditions for valid locomotion. As a consequence we identify new ways to produce gait transitions (e.g. change from walking to running) through the control of the angle of attack, at a constant energy level. Moreover, we show that the new valid conditions of locomotion allow the representation of the hopping gait. This new gait requires two different angles of attack for its execution, hence constant angle of attack policies are not applicable. First, we show the regions of phase space where one step gait transitions exist. Next, we report the region where it is possible to generate a periodic hopping gait. Mainly, the two results imply that through the control of the angle of attack the system can exploit its passive dynamics to induce transitions between running, walking and hooping or keep the system stable in any of these gaits. Finally, we briefly discuss the relation between these findings and the use of complaints legs in robots.