Analysis of Snake Robot Locomotion Based on Averaging Theory

Abstract

In the previous chapter, we extended our toolbox with a new and more manageable model of snake robot locomotion. With this new model at our disposal, an intriguing question is whether we can use the model to derive new properties of snake robot dynamics. In this chapter, we will show that this indeed is the case.

The simplified model maps the periodic motion of the joints into the resulting propulsion of the snake robot. Since the joint motion is periodic, there must be some average effect of the joint motion that propels the robot. In this chapter, we use averaging theory to study this average effect of the joint motion during the gait pattern lateral undulation. The analysis reveals new properties of snake robot locomotion that are both fundamental and useful from a motion planning perspective. In particular, we show that the average velocity of a snake robot during lateral undulation converges exponentially fast to a steady-state velocity, and an analytical expression for calculating the steady-state velocity is presented as a function of the gait pattern parameters. We also derive a set of relationships between the gait pattern parameters of lateral undulation and the resulting forward velocity of a planar snake robot. The material in this chapter is accompanied by simulation results and experimental results that support the theoretical findings.