An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model

Abstract

Chaos is a central feature of human locomotion and has been suggested to be a window to the control mechanisms of locomotion. In this investigation, we explored how the principles of chaos can be used to control locomotion with a passive dynamic bipedal walking model that has a chaotic gait pattern. Our control scheme was based on the scientific evidence that slight perturbations to the unstable manifolds of points in a chaotic system will promote the transition to new stable behaviors embedded in the rich chaotic attractor. Here we demonstrate that hip joint actuations during the swing phase can provide such perturbations for the control of bifurcations and chaos in a locomotive pattern. Our simulations indicated that systematic alterations of the hip joint actuations resulted in rapid transitions to any stable locomotive pattern available in the chaotic locomotive attractor. Based on these insights, we further explored the benefits of having a chaotic gait with a biologically inspired artificial neural network (ANN) that employed this chaotic control scheme. Remarkably, the ANN was quite robust and capable of selecting a hip joint actuation that rapidly transitioned the passive dynamic bipedal model to a stable gait embedded in the chaotic attractor. Additionally, the ANN was capable of using hip joint actuations to accommodate unstable environments and to overcome unforeseen perturbations. Our simulations provide insight on the advantage of having a chaotic locomotive system and provide evidence as to how chaos can be used as an advantageous control scheme for the nervous system.

Assessing the stability of human locomotion: a review of current measures

“…Many studies have focused on ways to enable dynamic walkers to handle larger perturbations. One solution is to add a controller [24,25]. This controller would be inactive most of the time (since the gait is within its passively stable region), but would be active when a larger perturbation occurs, or when effects of smaller perturbations have accumulated over time [24].…”

Gait dynamics, fractals and falls: Finding meaning in the stride-to-stride fluctuations of human walking

“…These include deterministic models, stochastic models, as well as combinations of the two (Ashkenazy et al, 2002;Hausdorff, Ashkenazy et al, 2001;Hausdorff, Peng et al, 1995;Kurz & Stergiou, 2005;West & Latka, 2005;West & Scafetta, 2003). Some of these models are able to reproduce and explain the fractal-like fluctuations and many of the observed alterations with aging and disease have been captured as well.…”

“…Before beginning, it is important to note that because of space constraints, this review considers only a subset of the reports on this topic. For complementary perspectives, the reader is referred to other pertinent reviews (Chau, 2001a(Chau, , 2001bChau, Young, & Redekop, 2005;Hausdorff, 2005) as well as parallel studies by others (Buzzi, Stergiou, Kurz, Hageman, & Heidel, 2003;Costa, Peng, Goldberger, & Hausdorff, 2003;Dingwell, Cusumano, Cavanagh, & Sternad, 2001;Dingwell, Gu Kang, & Marin, 2006;England & Granata, 2007;Georgoulis, Moraiti, Ristanis, & Stergiou, 2006;Granata & England, 2006;Kurz et al, 2003;Kurz & Stergiou, 2005;Stergiou, Harbourne, & Cavanaugh, 2006). …”

Minimalistic control of a compass gait robot in rough terrain

“…A few potential research directions in the future include the extension of physical model with knee and ankle joints as previously shown in [10], [12], [19], and the enhancement of the control architecture with more dynamic features [13], [18], [20], [21].…”