Dynamic Modeling of the Dissipative Contact and Friction Forces of a Passive Biped-Walking Robot

Abstract

This work presents and discusses a general approach for the dynamic modeling and analysis of a passive biped walking robot, with a particular focus on the feet-ground contact interaction. The main purpose of this investigation is to address the supporting foot slippage and viscoelastic dissipative contact forces of the biped robot-walking model and to develop its dynamics equations for simple and double support phases. For this investigation, special attention has been given to the detection of the contact/impact between the legs of the biped and the ground. The results have been obtained with multibody system dynamics applying forward dynamics. This study aims at examining and comparing several force models dealing with different approaches in the context of multibody system dynamics. The normal contact forces developed during the dynamic walking of the robot are evaluated using several models: Hertz, Kelvin-Voight, Hunt and Crossley, Lankarani and Nikravesh, and Flores. Thanks to this comparison, it was shown that the normal force that works best for this model is the dissipative Nonlinear Flores Contact Force Model (hysteresis damping parameter - energy dissipation). Likewise, the friction contact/impact problem is solved using the Bengisu equations. The numerical results reveal that the stable periodic solutions are robust. Integrators and resolution methods are also purchased, in order to obtain the most efficient ones for this model.

Nonlinear phenomena of contact in multibody systems dynamics: a review

“…Applied to the study of contact forces, it can be said that a model of this kind can approximate the contact phenomenon in such a way it can be properly modelled. Penalty methods are characterized by their simplicity, computational efficiency and implementation easiness [31,91], allowing them to deal with specific events such as repeated impacts properly [8,92]. These approaches are widely used in nowadays commercial FEM and MBD software [93][94][95][96].…”

“…In the last decades, several authors have developed new models based on the work of Hunt and Crossley, some of them being applicable to certain types of impacts [106,107] and others being generalizable to the entire range of the coefficient of restitution [89,108,109]. Again, some works based on these methods are left to the interested reader [8,19,24,110].…”

“…The mathematical relation that associates the stresses (forces) experienced by the material with the deformations suffered throughout the process is called material constitutive law [45]. Dynamic analysis of multibody systems requires models that provide reliable and accurate results of the contact forces [8,46]. Thus, the study of the force-indentation relation and the determination of the exact value of the coefficient restitution are two key tasks.…”

“…The value of v was obtained by comparing the output values with the experimental results, in order to get the highest possible consistency. This model was used by Corral and his co-authors to define the contact interaction between a passive robot and the ground [8]. A similar approach to the one presented by Ristow was defined by Lee and Hermann [153].…”

“…At the end of the twentieth century, the technological development of computers took this methodology to a new level, with figures such as Shabana, Pfeiffer, Nikravesh or Lankarani, who started the modern MSD [2][3][4][5][6][7]. Nowadays, its applications are countless: robotics [8,9], mechanical components analysis [10,11], vehicle dynamics [12][13][14], biomechanical studies [15][16][17], among others [18][19][20].…”