A Torque-actuated dissipative spring loaded inverted pendulum model with rolling contact and Its application to hexapod running.

We report on the development and analysis of a new torque-actuated dissipative spring loaded inverted pendulum model with rolling contact (TDR-SLIP), which is a successor to the previously developed spring loaded inverted pendulum model with rolling contact (R-SLIP) model. The stability properties of the models were analyzed numerically via steps-to-fall analysis and return map analysis, wherein the dimensionless parameters are varied to analyze their effects on the dynamic performance of the model, including torque, damping constant, spring constant, touchdown angle, touchdown speed, and landing angle. Because the involvement of torque and damping in the TDR-SLIP model is similar to other recently developed torque-actuated dissipative spring loaded inverted pendulum studies, their performance was compared so that the unique features of the TDR-SLIP model, such as rolling contact, could be investigated. To undertake the comparison, a method for yielding parameter equivalency between these two models is also reported. In addition to its analytical role, the TDR-SLIP model served as a template to initiate the stable running behavior of the empirical robot acted as the anchor. Two sets of legs were evaluated-the original compliant half-circular leg of the robot and the new mechanical legs, which resemble the morphology of the TDR-SLIP model. Two types of control strategies were tested-position-based control and hybrid control. The experimental results reveals that the low-damped compliant half-circular leg and the mechanical leg match the behaviors of the R-SLIP model and the TDR-SLIP model, respectively, and the robot with hybrid control performs more stably and more closely to the model profile. In addition, when the robot's motion follows the template's stable dynamics, the energy cost of the leg in stance can be significantly lower than that in flight.