A simplified model of snake robot locomotion on planar surfaces

Abstract

Faced with the problem of proving that a control strategy for the snake robot satisfies some control objective, an attractive idea is to base the controller analysis on a simplified model of the snake robot that avoids the complex expressions contained in the model presented earlier in this book. The hypothesis behind this idea is of course that the more complex model contains nonlinear dynamics that is not essential to the overall locomotion of the snake robot. We have already seen support of this claim in the simulation results of the path following controller proposed in the previous chapter, which clearly show that the heading and position of a snake robot display an oscillating behaviour during locomotion. However, for control design and analysis purposes, we are not particularly interested in this oscillatory dynamics as we are primarily concerned with the overall motion of the heading and position of the robot. In this chapter, we therefore propose a simplified model of a planar snake robot aimed at simplifying analytical investigations of the equations of motion. The basic idea behind the model is to capture only the essential properties of snake robot dynamics that we derived in a previous chapter, i.e. the features that determine the overall behaviour of the snake. In particular, we propose to describe the body shape dynamics of the snake robot in terms of the translational motion of the links by assuming that the snake robot consists of a serial connection of prismatic (translational) joints instead of joints. This approach significantly simplifies the equations of motion since translational motion is generally less complex to model than rotational motion. In order to support the claim that the essential features of snake robot locomotion are contained in the simplified model, we show that the stabilisability and controllability properties of the simplified model are similar to the properties of the more complex model. Simulation results that compare the complex and the simplified model are presented to provide further support of this claim.