Experimental Validation of a Feed-Forward Predictor for the Spring-Loaded Inverted Pendulum Template

Abstract

Cataloged from PDF version of article.Widely accepted utility of simple spring-mass models for running behaviors as descriptive tools, as well as literal control targets, motivates accurate analytical approximations to their dynamics. Despite the availability of a number of such analytical predictors in the literature, their validation has mostly been done in simulation, and it is yet unclear how well they perform when applied to physical platforms. In this paper, we extend on one of the most recent approximations in the literature to ensure its accuracy and applicability to a physical monopedal platform. To this end, we present systematic experiments on a well-instrumented planar monopod robot, first to perform careful identification of system parameters and subsequently to assess predictor performance. Our results show that the approximate solutions to the spring-loaded inverted pendulum dynamics are capable of predicting physical robot position and velocity trajectories with average prediction errors of 2% and 7%, respectively. This predictive performance together with the simple analytic nature of the approximations shows their suitability as a basis for both state estimators and locomotion controllers. © 2004-2012 IEEE

Extending the lossy Spring-Loaded Inverted Pendulum model with a slider-crank mechanism

“…Both the initial condition and control input ranges as well as system parameters used for our simulation studies are given in Table II. The robot parameters are chosen to be consistent with our one-legged hopping robot platform [7]. Our goal is to evaluate the prediction performance off with respect to numerical solution, f .…”

“…However, anchoring the SLIP model for lossy physical robot * Marked authors contributed equally. platforms requires some extensions on the original template such as addition of viscous damping in the leg [5]- [7].…”

“…Therefore, we propose an approximate analytical solution for the SLIP-SCM model to represent its COM trajectories for a single stride. Approximate analytical solutions have also been frequently used in literature to solve non-integrable legged locomotion trajectories [6], [22]- [24] with some has been verified in experimental robot platforms [7].…”

Identification of a vertical hopping robot model via harmonic transfer functions

“…Despite the seemingly simple nature of these models, however, their dynamics during stance include non-integrable parts (Holmes, 1990), which prevent the derivation of exact closed-form solutions. Various approximate solutions have been developed in the literature to address this problem (Ankarali and Saranli, 2010;Geyer et al, 2005;Saranli et al, 2010;Schwind and Koditschek, 2000), some of which have also been verified experimentally (Uyanik et al, 2015).…”

Independent Estimation of Input and Measurement Delays for a Hybrid Vertical Spring-Mass-Damper via Harmonic Transfer Functions

“…Modeling and analysis of even seemingly simple legged systems can be surprisingly complex due to the hybrid dynamics arising from intermittent foot contact as well as challenging nonlinearities in the equations of motion (Ankarali and Saranli, 2010;Saranli et al, 2010;Uyanik et al, 2015c;Westervelt et al, 2007;Grizzle et al, 2001). …”