Alben Silas
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev E. 2019 Jun;99(6-1):062402. doi: 10.1103/PhysRevE.99.062402.
Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction.
蛇的身体覆盖着鳞片，这使得它们在某些方向上比在其他方向上更容易滑动。这种摩擦各向异性使得蛇能够以波动步态进行滑动运动，这是蛇最常见的运动方式之一。各向同性摩擦是一种更简单的情况（例如在蛇形机器人中出现），但人们对其了解较少。在这项工作中，我们对滑动运动模型进行正则化，以考虑静摩擦力。然后，我们提出了一种稳健的迭代数值方法，用于研究在各向同性库仑摩擦下各种运动的效率。我们发现，在各向同性状态下，简单的波动运动产生的净位移很小。我们计算了三连杆体的一般时间谐波运动，并找到了效率的三个局部最优解。前两个在一定程度上涉及静摩擦力。然后，我们提出了一类与伸缩运动相似的平滑身体运动（包括静摩擦力的参与），并且在各向同性和各向异性摩擦情况下都能实现最优效率。
