Safa Ali Tehrani, Biswas Tirthabir, Ramakrishnan Arun, Bhandawat Vikas
School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA 19104, USA.
Department of Neurobiology, Northwestern University, Evanston, IL 60208, USA.
bioRxiv. 2025 Mar 10:2024.09.23.612940. doi: 10.1101/2024.09.23.612940.
Two simple models - vaulting over stiff legs and rebounding over compliant legs - are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking under the assumption that the compliance of the leg during walking is high enough to be considered stiff. Here we study gait choice and walk-to-run transition in a biped with compliance and show that the principles underlying gait choice and transition are completely different from stiff legs. Two findings underpin our conclusions: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose the (normal) gait with M-shaped vertical ground reaction forces (vGRF) not just because of energy considerations but also constraints from forces. Second, the transition from walking to running occurs because of three factors: vGRF minimum at mid-stance characteristic of normal walking, synchronization of horizontal and vertical motions during single support, and velocity redirection during the double support. The insight above required an analytical approximation of the double spring-loaded pendulum (DSLIP) model describing the intricate oscillatory dynamics that relate single and double support phases. Additionally, we also examined DSLIP as a quantitative model for locomotion and conclude that DSLIP speed-range is limited. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.
我们采用了两种简单模型——越过僵硬腿部的跳跃模型和越过柔顺腿部的反弹模型——来描述有腿运动的力学原理。人们一致认为，柔顺的腿部对于描述跑步是必要的，而且在行走时腿部是柔顺的。尽管有此共识，但在假设行走时腿部的柔顺性足够高以至于可被视为僵硬的情况下，僵硬腿部模型仍继续被用于模拟行走。在此，我们研究了具有柔顺性的两足机器人的步态选择和从行走至跑步的转变，并表明步态选择和转变背后的原理与僵硬腿部模型完全不同。我们的结论有两个发现作为支撑：第一，在相同速度、步长和站立持续时间下，腿部收缩周期数量不同的多种步态都是可能的。其中，人类和其他动物选择具有M形垂直地面反作用力（vGRF）的（正常）步态，不仅是出于能量方面的考虑，还受到力的限制。第二，从行走转变为跑步是由三个因素导致的：正常行走时支撑中期的vGRF最小值、单支撑期间水平和垂直运动的同步以及双支撑期间的速度重新定向。上述见解需要对双弹簧加载摆（DSLIP）模型进行解析近似，该模型描述了将单支撑和双支撑阶段联系起来的复杂振荡动力学。此外，我们还将DSLIP作为一种运动定量模型进行了研究，并得出DSLIP的速度范围有限的结论。然而，从对DSLIP的解析处理中获得的见解具有普遍性，将为构建更精确的行走模型提供参考。
