Analysis and Synthesis of Snake Robot Locomotion
Research on snake robots has been conducted for several decades. However, our understanding of snake locomotion so far is for the most part based on empirical studies of biological snakes and simulation-based synthesis of relationships between parameters of the snake robot. Armed with the mathematical model of the snake robot presented earlier in this book, we attempt in this chapter to contribute to the understanding of snake robots by employing nonlinear system analysis tools for investigating fundamental properties of their dynamics. We will also derive several interesting properties of snake robot locomotion simply by investigating the equations of motion of the robot, some of which will be instrumental in the development of a simplified model later in this book.
In this chapter, we also investigate the motion pattern which is most common among biological snakes, namely lateral undulation. This motion pattern is considered in the majority of the snake robot literature, and will also receive much attention throughout this book. The serpenoid curve is a well-known mathematical description of the shape of a snake during lateral undulation, and was proposed in an early work of the snake robot literature based on empirical studies of biological snakes. In this chapter, we develop analytical results that support this mathematical description.
KeywordsKelly Body Wave
- Brockett, R.: Asymptotic stability and feedback stabilization. In: Differential Geometric Control Theory, pp. 181–191 (1983) Google Scholar
- Gray, J.: The mechanism of locomotion in snakes. J. Exp. Biol. 23(2), 101–120 (1946) Google Scholar
- Harville, D.A.: Matrix Algebra from a Statistician’s Perspective. Springer, Berlin (2000) Google Scholar
- Hicks, G.P.: Modeling and control of a snake-like serial-link structure. Ph.D. thesis, North Carolina State University (2003) Google Scholar
- Hirose, S.: Biologically Inspired Robots: Snake-Like Locomotors and Manipulators. Oxford University Press, Oxford (1993) Google Scholar
- Krishnaprasad, P.S., Tsakiris, D.P.: G-snakes: nonholonomic kinematic chains on lie groups. In: Proc. 33rd IEEE Conf. Decision and Control, Lake Buena Vista, FL, USA, vol. 3, pp. 2955–2960 (1994) Google Scholar
- Morgansen, K.A., Duidam, V., Mason, R.J., Burdick, J.W., Murray, R.M.: Nonlinear control methods for planar carangiform robot fish locomotion. In: Proc. IEEE Int. Conf. Robotics and Automation, vol. 1, pp. 427–434 (2001) Google Scholar
- Morgansen, K.A., Vela, P.A., Burdick, J.W.: Trajectory stabilization for a planar carangiform robot fish. In: Proc. IEEE Int. Conf. Robotics and Automation, vol. 1, pp. 756–762 (2002) Google Scholar
- Ostrowski, J.P.: The mechanics and control of undulatory robotic locomotion. Ph.D. thesis, California Institute of Technology (1996) Google Scholar
- Vela, P.A., Morgansen, K.A., Burdick, J.W.: Underwater locomotion from oscillatory shape deformations. In: Proc. IEEE Conf. Decision and Control, vol. 2, pp. 2074–2080 (2002a) Google Scholar