Control of snake-like robot based on nonlinear controllability analysis

Snake-like robot is a stimulating example of nonlinear and nonholonomic system for its versatile locomotive behavior and complicated controllability structure. In this paper, we investigate locomotion control of a snake robot using oscillatory inputs based on nonlinear controllability analysis and the principle of holonomy. First, we give a mathematical model of the n-link snake robot as a driftless system on a principal fiber bundle whose structure group is SE(2). Second, we introduce a method to choose oscillatory control inputs corresponding to the desired motion, based on the analysis of the local curvature form defined on the principal fiber bundle. This primary choice of control inputs is supposed to work in the case of 3 links with 2 joints, that is the minimal configuration of controllable snake robot. We then extend it to work in the 4-link case, by considering periodic stability of the additional 4th joint under the pre-specified control inputs. Finally, the proposed method is tested with physical experiments.