Robotica (2009) volume 27, pp. 999–1015. © Cambridge University Press 2009 doi:10.1017/S0263574709005414 A survey on snake robot modeling and locomotion Aksel Andreas Transeth† ∗ , Kristin Ytterstad Pettersen‡ and P˚ al Liljeb¨ ack‡ †SINTEF ICT, Applied Cybernetics, NO-7465 Trondheim, Norway ‡Department of Engineering Cybernetics, Norwegian University of Science and Technology, O.S.Bragstadsplass 2D, NO-7491 Trondheim, Norway (Received in Final Form: January 27, 2009. First published online: March 3, 2009) SUMMARY Snake robots have the potential to make substantial contri- butions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed. KEYWORDS: Snake robots; Dynamics; Kinematics; Locomotion. 1. Introduction The wheel is an amazing invention, but it does not roll everywhere. Wheeled mechanisms constitute the backbone of most ground-based means of transportation. On relatively smooth surfaces, such mechanisms can achieve high speeds and have good steering ability. Unfortunately, rougher terrain makes it harder, if not impossible, for such mechanisms to move. In nature, the snake is one of the creatures that exhibits excellent mobility in various types of terrain. It is able to move through narrow passages and climb on rough ground. This property of mobility is attempted to be recreated in robots that look and move like snakes. Snake robots usually have a high number of degrees of freedom (DOF) and they are able to move without using active wheels or legs. Snake robots may one day play a crucial role in search and rescue operations, firefighting, and inspection and maintenance. The highly articulated body allows the snake robot to traverse difficult terrains such as collapsed buildings or the chaotic environment caused by a car collision in a tunnel. The snake robot could crawl through destroyed buildings looking for people, while simultaneously bringing communication equipment together with small amounts of food and water to anyone trapped in the shattered building. A rescue operation involving a snake robot has been envisioned * Corresponding author. E-mail: Aksel.A.Transeth@sintef.no by Miller. 1 Moreover, the snake robot can be used for surveillance and maintenance of complex and possibly hazardous areas of industrial plants such as nuclear facilities. In a city, it could inspect the sewerage system looking for leaks or aiding firefighters. Also, snake robots with one end fixed to a base can be used as a robot manipulator which can reach hard-to-get-to places. Compared to wheeled and legged mobile mechanisms, the snake robot offers high stability and good terrainability. The exterior can be completely sealed to keep dust and fluids out. Due to high redundancy and modularity, the snake robot is robust to mechanical failure. The downside is its limited payload capacity, poor power efficiency, and a very large number of DOF that have to be controlled. The first qualitative research on snake locomotion was done by Gray in 1946. 2 The first working biologically inspired serpentine robot was constructed by Hirose in 1972. 3 He presented a 2-m long serpentine robot with 20 revolute 1-DOF joints called the Active Cord Mechanism model ACM III shown in Fig. 1. Passive casters were put on the underside of the robot. Forward motion was obtained by moving the joints to the left and right in selected patterns. Since Hirose presented his Active Cord Mechanism, many multi-link articulated robots intended for crawling locomotion have been developed and have had many names. Some examples are multi-link mobile robot, 4 snake-like or snake robot, 5 −11 hyper-redundant robot, 12 and G-snake. 13 To emphasize that this paper deals with robots that mainly resemble the locomotion of snakes, the term “snake robot” will be employed. The snake robots referred to in this paper are implemented either with passive wheels 3, 4, 14, 15 or without wheels. 16–21 The joints are mostly revolute, but extensible (prismatic) joints are also employed. 17, 22 Motion patterns of snakes, inchworms, and caterpillars are used as an inspiration about how the snake robots should move. Mathematical models of the snake robots are needed to analyze the motion patterns and to simulate their motion. Because of the high number of DOF, the construction of such models is a challenge. During the last 10–15 years, the literature published on snake robots has increased significantly, and the purpose of this paper is to provide a concise overview and comparison of the various mathematical models and locomotion principles of snake robots presented during this period. The relationship between