A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

Mathematical and Computational Applications

Zelei, Ambrus¹  Zana, RolandReginald²  Bodor, Bálint³  Bencsik, László⁴ 

[1] Author to whom correspondence should be addressed.;Department of Applied Mechanics, Budapest University of Technology and Economics, Müegyetem rkp. 3, 1111 Budapest, Hungary;MTA-BME Lendület Human Balancing Research Group, Müegyetem rkp. 3, 1111 Budapest, Hungary;MTA-BME Research Group of Dynamics of Machines and Vehicles, Müegyetem rkp. 3, 1111 Budapest, Hungary

关键词: non-linear analysis;    periodic motion;    piecewise-smooth systems;    biomechanics of running;    ground-foot impact;   

DOI  :  10.3390/mca23040074

学科分类：计算数学

来源: mdpi

【 摘 要 】

Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results.

【 授权许可】

CC BY