Inheritance of SLIP running stability to a single-legged and bipedal model with leg mass and damping

Abstract

Spring-like leg behavior is found in the global dynamics of human and animal running. The corresponding template model, the conservative spring-loaded inverted pendulum (SLIP), shows stability for a large range of speeds and, therefore, is a promising concept for the design of legged robots. However, an anchoring of this template is needed in order to provide functions of biological structures (e.g. mass configuration, leg design) and to provide engineers with detailed guidelines for robot construction. We extend the template model by adding considerable leg mass (M-SLIP) to investigate the influence of leg inertia on running stability. We question whether the model with mass distributed to leg and trunk inherits stable running patterns of the underlying SLIP model. Separately, we investigate single-legged running and alternating bipedal running like humans. Here, we ask for the mass effect of the swing leg on running stability. The results show that the domain of stable SLIP running is anchored in the M-SLIP model. The stability domain is almost completely conserved for bipedal human-like running and reduces slightly for singlelegged running. Our study reveals clearly that the SLIP can be anchored in a leg mass model with minimal control effort in using simple hip actuation policies. Our model enhances the theoretical foundation of biologically inspired robotic systems and is a promising candidate for nature-inspired engineering.

The effects of swing-leg retraction on running performance: analysis, simulation, and experiment

“…To better relate the findings to previous studies, we also compare the results of the realistic model simulations with those of the simpler models. Whenever possible, the Spring Loaded Inverted Pendulum (SLIP, Figure 2) model is used as the simple simulation model for comparison to 5,6,[12][13][14][15] . However, the SLIP model does not capture all the relevant dynamics; aspects related to energy loss and replacement are not captured because the model is energetically conservative, and other consequences of impact with the ground such as reaction forces and foot slipping cannot be studied accurately without leg mass.…”

“…However, the SLIP model does not capture all the relevant dynamics; aspects related to energy loss and replacement are not captured because the model is energetically conservative, and other consequences of impact with the ground such as reaction forces and foot slipping cannot be studied accurately without leg mass. To study these, we use an extension of the SLIP, a Prismatic Leg model ( Figure 3) similar to that in 14,15,18 , and a new Kneed Leg model ( Figure 5), a simplification of the realistic model of Phides. Besides their utility as bridges to prior studies, these simple models permit either symbolic analysis or more efficient computation and help us gain insight by removing complexities of the realistic model.…”

Actuator Sizing for Highly-Dynamic Quadruped Robots Based on Squat Jumps and Running Trots

“…First of all, suitable SLIP parameters (spring stiffness and angle of attack) had to be calculated for each input pair based on the steps-to-fall map. 16 The SLIP parameters with the lowest spring stiffness that resulted in stable hopping of 50 or more steps were then selected, shown in a Fig. 3.…”

Analysis of Foot Slippage Effects on an Actuated Spring-Mass Model of Dynamic Legged Locomotion

“…Another addition (which is not essential) is a viscous damper c connected in parallel with the spring in order to attenuate its oscillations during flight. Inspired by the names M-SLIP [42] and TD-SLIP [4], our model is named TDMF-SLIP -torqued damped (foot-) mass frictional SLIP. The model is shown in Figure 4 …”

“…Many extensions of the SLIP model have been considered in the literature, such as incorporating the leg's mass [42], or a large body with a moment of inertia [53]. Some works introduced damping as a mechanism for dissipating energy [4,48], while others studied the influence of a suspended load on the dynamic behaviour of the SLIP model [1].…”