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

Abstract

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

All common bipedal gaits emerge from a single passive model

“…These double-stance solutions are not running (there is no flight phase); but they retain a single-hump vGRF profile, similar to that of running. Therefore, motions like this have been referred to as grounded running (GR) [31,42]. This type of solution only exists when the forward speed is larger than 0:24 ffiffiffiffiffi ffi gl o p .…”

Numerical bifurcation analysis of the bipedal spring-mass model

“…During transitions from walking to running at the same energy level, the intermediate steps are also asymmetric [33,47]. Interestingly, leg asymmetry is commonly observed in able-bodied human subjects [48,49].…”

“…It is often observed in avian locomotion and may also correspond to human jogging or race walking. Since grounded running also serves as an intermediate step between walking and running [32,33], the calculation of these period-doubling bifurcations is helpful for investigations of gait transitions.…”

“…[33,47,59]). For instance, it is still not fully clear, how the transition is mechanically triggered.…”

“…In particular, inset 6 in Fig. 2 shows a special case of periodic locomotion pattern called grounded running [32,33]. These patterns are different from periodic walking solutions, because the CoM crosses the touch-…”