Abstract
The underlying theme of this book is analytical approaches aimed at increasing our understanding of snake robot locomotion. The mathematical model of the snake robot is the basis for these analytical studies, which means that the analysis relies heavily on the form and complexity of the model. In this chapter, we employ first principles to develop a mathematical model of the kinematics and dynamics of a snake robot with N links moving on a horizontal and flat surface. The links of the robot are influenced by ground friction forces which propel the motion. Due to the many degrees of freedom of the robot and the dynamical couplings between the links, the resulting model will turn out to be quite complex. We will eliminate some of this complexity by partially linearising the model. This is achieved by introducing a change of coordinates which enables us to partition the model into an actuated part (the joint angles of the snake robot) and an unactuated part (the position and orientation of the snake robot). Through an input transformation, we are then able to linearise the actuated part of the model.
In later chapters of this book, the model presented in this chapter is analysed in order to deduce several fundamental properties of snake robot dynamics. Moreover, the derived properties are used to develop a simplified model which only captures the ‘essential’ part of the snake robot dynamics. In Part II of this book, which considers snake robot locomotion in cluttered environments, the model presented in this chapter will be extended to include contact forces from external obstacles in the environment around the snake robot.
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Liljebäck, P., Pettersen, K.Y., Stavdahl, Ø., Gravdahl, J.T. (2013). A Complex Model of Snake Robot Locomotion on Planar Surfaces. In: Snake Robots. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2996-7_2
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DOI: https://doi.org/10.1007/978-1-4471-2996-7_2
Publisher Name: Springer, London
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