Bipedal Model and Hybrid Zero Dynamics of Human Walking With Foot Slip

Abstract

Foot slip is one of the major causes of falls in human locomotion. Analytical bipedal models provide an insight into the complex slip dynamics and reactive control strategies for slip-induced fall prevention. Most of the existing bipedal dynamics models are built on no foot slip assumption and cannot be used directly for such analysis. We relax the no-slip assumption and present a new bipedal model to capture and predict human walking locomotion under slip. We first validate the proposed slip walking dynamic model by tuning and optimizing the model parameters to match the experimental results. The results demonstrate that the model successfully predicts both the human walking and recovery gaits with slip. Then, we extend the hybrid zero dynamics (HZD) model and properties to capture human walking with slip. We present the closed-form of the HZD for human walking and discuss the transition between the non-slip and slip states through slip recovery control design. The analysis and design are illustrated through human walking experiments. The models and analysis can be further used to design and control wearable robotic assistive devices to prevent slip-and-fall. IntroductionFoot slip is one of the major causes for human falls and injuries. Slip-induced falls cause enormous economic and societal costs [1]. The direct costs for non-fatal fall-related injures among US elderly (≥ 65 years) were 19 billion dollars in the year 2000 [1] and increased to over 31 billion in the year 2015 [2]. Among the occupational population in the US, slips, trips and falls represented 27% of all non-fatal oc- * The authors equally contributed to this work. † Address all correspondence to J. Yi.cupational injuries in year 2015 [3]. To develop effective fall prevention strategies and technologies, it is critical to understand human locomotion and balance recovery under slip. Modeling of human walking locomotion with slip is an effective approach to assist in the design and control of new wearable assistive devices. Slip-and-fall has been extensively studied in the past two decades, for example, [4,5] and references therein. Most of these studies focus on human subjects and clinical experiments and a few use human locomotion dynamics to analyze the slipping mechanism. Simulation-based dynamic models are used to study motion stability of slip and fall. In [5], a 7-link, 9-degree-of-freedom (DOF) walking model in the sagittal plane with a 16-element foot model is used to simulate the human reaction control to a novel slip in gait. In [6], a simulation model is optimized with human experiments. Using this model, stability results are obtained and compared with the dynamic balance analyses by a simple invented pendulum model. The 2D musculoskeletal model in the sagittal plane is also discussed in [7] to determine the impact of the reduced required coefficient of friction (RCOF) on gait kinematics. Kinematic and muscle activity-based data-driven analysis (e.g., Lyapunov exponents) are used to capture the walking stability [8].Robotic bipedal mod...

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