Bio-Inspired Snake Robots: Design, Modelling, and Control

Introduction

Learning from natural organisms is conceived to be one of the key methods for developing innovative mechanisms. There are many biological organisms with smart structure, incredibly efficient locomotion mechanisms or intelligent sensing and processing capabilities, which are natural sources of inspiration for engineering designs. For instance, the amazing ability of some animals such as birds and turtles to use geomagnetic information for navigation is imitated to develop a navigation system for autonomous underwater vehicles in (Liu, Liu, Zhang, & Li, 2016).

One of the fascinating topics in the field of bio-inspired design is snake locomotion. Snake’s locomotion is a relatively efficient type of locomotion, which despite frictional opposition, consumes less energy compared to other biological forms with similar sizes, weights, and speeds. Also, small cross section of snake body is ideal for locomotion in narrow and remote environments, such as pipes and tankers. Snake robots have also been used as a flexible robot manipulators in Minimally Invasive Surgeries (MIS) by (Tully and Choset, 2016), who used highly articulated snake robots for performing surgeries with fewer incisions and consequently decreases the recovery time of patients

Snake’s movement has always been a peculiar phenomenon for scientist. The elegant locomotion of snakes on smooth and uneven surfaces, under water and through narrow channels have motivated many scientists to study biological snake locomotion, years before considering it as an alternative way of locomotion for robots. However, it was not until twentieth century that the first accurate explanation of snake locomotion mechanism revealed.

The first discussion about snake’s movement goes back to ancient times, when Aristotle studied snake locomotion as a part of a book about animal locomotion capabilities. However, for centuries, humans understanding of snake’s unique movement mechanisms was very limited. The general belief even among zoologist was that snakes use their scales or tips of their ribs in a similar manner that other animals use their legs as means of locomotion.

(Hutchinson, 1879) challenged this theory. By observing a snake, which could easily ascend to the top of a glass jar, he argued that there should be some other justifications for snake-like movement. To explain this peculiar behavior, obviously contradicting the existing theory, (Fokker, 1927) came up with an alternative explanation, which can be considered as the first accurate description of snake movement mechanism. In this work, originally published in Dutch, the snake is modeled as a thin elastic body confined in a groove curved in a board and it is argued that snakes move in such a way that the total potential energy decreases. (Mosauer, 1932), without mentioning Fokker’s results, categorized snake locomotion into three different categories, namely Horizontal Undulation, Sidewinding and Caterpillar movement, however did not discuss mechanical modelling or mathematical foundation of each types of movements. Later on, (Jones, 1933) motivated by a simplified Fokker’s model, modeled the snake body as serially connected spools and mathematically showed that Mosauer results can indeed be supported theoretically, made Mosauer’s work the foundation of the almost all published works after that.

In the 1940s, (Gray, 1946) conducted a comprehensive study on snake locomotion by observing a common grass snake. Motivated by Fokker and Mosauer’s work, he searched for the answer to the basic question that how axial muscular activity generate propulsive force. To address this question, he considered the snake as a serially connected rigid rods hinged together, where axial muscles are regarded as elastic elements operating laterally to the hinges. Using this model, he empirically explained the mechanism behind each types of snake locomotion. One of the most important consequence of Gray’s experiments was that each part of the body of the snake should be in contact with external obstacles preventing it to move in the direction normal to that segment of the snake body to enable the snake move forward. (Gans, 1962) further discussed limbless locomotion and described the dynamics of four major types of locomotion pattern qualitatively.