Continuum and Snake Robots

Most robots are chains of rigid links. Continuum robots instead bend smoothly along their whole length, like an elephant's trunk or an octopus arm, often by pulling on tendons running through them. They can snake into tight spaces, such as inside the body or inside a jet engine. Snake robots, chains of many small joints, move by sending waves along their bodies.

Robot Section 1 curvature Section 2 curvature Snake wave amplitude

Constant curvature

A common model treats each section as an arc of constant curvature $\kappa$, set by the difference in tendon lengths. A section of length $L$ bends through an angle $\kappa L$, and its tip lands at

$$x = \frac{1 - \cos(\kappa L)}{\kappa}, \qquad y = \frac{\sin(\kappa L)}{\kappa}$$

The serpenoid gait

Snake robots move by a traveling wave: joint $i$ of $n$ follows $\phi_i(t) = A\sin(\omega t + \beta i)$. With more friction sideways than forward, like a real snake's scales, the wave pushes the body forward.

What to notice

Two sections bent in opposite directions make an S-shape that can reach around an obstacle, something a rigid arm with few joints cannot do. The snake's forward speed depends on the wave amplitude: too small and it barely moves, too large and it wastes energy swinging sideways. Continuum robots are used for minimally invasive surgery and pipe inspection.