Path Following Control of Snake Robots Through a Cascaded Approach

Abstract

In this chapter, we return to the problem of enabling a snake robot to track a planar path. Previously in this book, we proposed a straight line path following controller and employed a Poincaré map to prove that the state variables of the snake robot, except for the position along the path, trace out a locally exponentially stable periodic orbit during motion along the desired path. The drawback of the analysis based on the Poincaré map, however, is that we are only able to infer conclusions regarding the local stability properties in the vicinity of the desired path. Moreover, since the analysis is based on simulating the model of the snake robot, the stability proof is only valid for the given choice of numerical controller parameters.

In order to elude the shortcomings of the previous analysis, this chapter extends the path following controller by employing the simplified model of the snake robot. Using cascaded systems theory, we prove that the modified path following controller $\mathcal{K}$-exponentially stabilises the snake robot to any desired straight path. In particular, under the assumption that the forward velocity of the snake robot is non-zero and positive, we show that the model of the snake robot and the controller can be written as a cascaded system where the body shape changes affect the global orientation of the robot, which subsequently affects the cross-track error between the robot and the desired path. The $\mathcal{K}$-exponential stability of the cascaded system guarantees that the cross-track error and the heading of the snake robot with respect to the direction of the path converge to zero. The performance of the path following controller is investigated through simulations and through experiments with the snake robot Wheeko. The simulations and the experimental results show that the proposed controller successfully steers the snake robot towards and along the desired straight path.

This chapter also considers path following of more general paths. In particular, we propose a waypoint guidance strategy which provably steers a snake robot along a path defined by waypoints interconnected by straight lines. In addition, we describe how the straight line path following controller can be extended to path following of general curved paths.