Full State Control of a Slip Model by Touchdown Detection

Abstract

To enhance the well known, self-stabilizing effects of Spring Loaded Inverted Pendulum (SLIP) models, researchers have proposed a variety of dead-beat controllers that adjust model parameters (angel of attack, spring stiffness), such that a disturbance is rejected within a single step. While such laws can be nicely encoded for disturbances in hopping height (by using the time of flight as a measure of vertical position), they suffer from substantial drift due to the missing information about the forward velocity and inaccuracies in the actual system model. Without requiring additional complex sensors, we propose a method to estimate the forward velocity of a SLIP model based solely on measuring the time of stance. This method is additionally able to perform realtime parameter estimation, which paves the road to implement a full state dead-beat controller that can reject arbitrary disturbances even in the presence of model and sensor errors.

Extension and customization of self-stability control in compliant legged systems

“…However, including the energy variation requires to adapt the return map R(y i ) and therefore the control [k, α](t fall ) from step to step to altered system energies. This can be achieved for instance, through an additional feedback of the horizontal velocity v x at apex or of the value of the previous contact time t c (Raibert 1986, Hutter et al 2010. Thus, although including an energy control improves the guaranteed tolerance, it cannot be formulated as a pure self-stability control.…”