Department of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA.
Bioinspir Biomim. 2012 Dec;7(4):046010. doi: 10.1088/1748-3182/7/4/046010. Epub 2012 Sep 18.
New models and theories of legged locomotion are needed to better explain and predict the robustly stable legged locomotion of animals and some bio-inspired robots. In this paper we observe that a hip-torque and leg-damping mechanism is fundamental to many legged robots and some animals and determine its affect on locomotion dynamics. We discuss why this hip-torque-and-leg-damping mechanism is not so easily understood. We investigate how hip-torque and leg-damping affect the stability and robustness of locomotion using a mathematical model: First, we extend the canonical spring-loaded-inverted-pendulum model to include constant hip torque and leg damping proportional to leg length speed. Then, we calculate the stability and robustness of locomotion as a function of increasing levels of torque and damping, starting from zero-the energy conserving and marginally stable special case-to high levels of torque and damping. We find that the stabilizing effects of hip-torque and leg-damping occur in the context of the piecewise-continuous dynamics of legged locomotion, and so linear intuition does not apply. We discover that adding hip torque and leg damping changes the stability of legged locomotion in an unexpected way. When a small amount of torque and damping are added, legged locomotion is initially destabilized. As more torque and damping are added, legged locomotion turns stable and becomes increasingly more stable and more robust the more torque and damping are added. Also, stable locomotion becomes more probable over the biologically-relevant region of the parameter space, indicating greater prediction and explanatory capabilities of the model. These results provide a more clear understanding of the hip-torque-and-leg-damping mechanism of legged locomotion, and extend existing theory of legged locomotion towards a greater understanding of robustly stable locomotion.
需要新的腿部运动模型和理论来更好地解释和预测动物和一些仿生机器人强大稳定的腿部运动。在本文中，我们观察到，髋关节扭矩和腿部阻尼机制是许多腿部机器人和一些动物的基础，并确定了其对运动动力学的影响。我们讨论了为什么这种髋关节扭矩和腿部阻尼机制不容易理解。我们使用数学模型研究髋关节扭矩和腿部阻尼如何影响运动的稳定性和鲁棒性：首先，我们将经典的弹簧加载倒立摆模型扩展到包括与腿部长度速度成比例的恒定髋关节扭矩和腿部阻尼。然后，我们计算了随着扭矩和阻尼的增加，从零（能量守恒和边缘稳定的特殊情况）到高扭矩和阻尼水平，运动的稳定性和鲁棒性。我们发现，髋关节扭矩和腿部阻尼的稳定作用发生在腿部运动的分段连续动力学的背景下，因此线性直觉不适用。我们发现，添加髋关节扭矩和腿部阻尼以意想不到的方式改变了腿部运动的稳定性。当添加少量扭矩和阻尼时，腿部运动最初会失稳。随着更多扭矩和阻尼的添加，腿部运动变得稳定，并随着更多扭矩和阻尼的添加而变得越来越稳定和鲁棒。此外，稳定的运动在生物相关的参数空间区域变得更有可能，这表明模型具有更大的预测和解释能力。这些结果提供了对腿部运动的髋关节扭矩和腿部阻尼机制的更清晰的理解，并将现有的腿部运动理论扩展到对强大稳定的运动的更好理解。
