Improved measure of orbital stability of rhythmic motions
Date
2017-11-30
Authors
Khazenifard, Amirhosein
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Rhythmic motion is ubiquitous in nature and technology. Various motions of organisms like the heart beating and walking require stable periodic execution. The stability of the rhythmic execution of human movement can be altered by neurological or orthopedic impairment. In robotics, successful development of legged robots heavily depends on the stability of the controlled limit-cycle. An accurate measure of the stability of rhythmic execution is critical to the diagnosis of several performed tasks like walking in human locomotion. Floquet multipliers have been widely used to assess the stability of a periodic motion. The conventional approach to extract the Floquet multipliers from actual data depends on the least squares method. We devise a new way to measure the Floquet multipliers with reduced bias and estimate orbital stability more accurately. We show that the conventional measure of the orbital stability has bias in the presence of noise, which is inevitable in every experiment and observation. Compared with previous method, the new method substantially reduces the bias, providing acceptable estimate of the orbital stability with fewer cycles even with different noise distributions or higher or lower noise levels. The new method can provide an unbiased estimate of orbital stability within a reasonably small number of cycles. This is important for experiments with human subjects or clinical evaluation of patients that require effective assessment of locomotor stability in planning rehabilitation programs.
Description
Keywords
Jacobian matrix, Poincare map, Least squares, Matrix decomposition, Biped robot, Floquet multipliers, Orbital stability