A hybrid model of snake robot locomotion in cluttered environments

Abstract

We begin the second part of this book by extending the model presented at the beginning of this book to include contact forces from external obstacles in the environment around the snake robot. Since the interaction with an obstacle represents a discrete event that only occurs when a link of the snake robot comes into contact with an obstacle, the robot will be subjected to both continuous and discontinuous dynamics in this environment. We will therefore describe the dynamics of the snake robot in terms of a hybrid model. An important difference between models of continuous dynamical systems and models of hybrid dynamical systems is that while most continuous models always exhibit a unique solution to the evolution of the state vector, a hybrid model may have a single solution, several solutions, or no solution at all. For the hybrid model of the snake robot, we will handle this existence and uniqueness issue by formulating the equations governing the obstacle contact forces as a linear complementarity problem (LCP). This formulation enables us to apply existing general results concerning existence and uniqueness of solutions to LCPs to the model of the snake robot. A long-term goal of the model proposed in this chapter is to facilitate development of model-based control laws for obstacle-aided locomotion with provable stability properties. We will therefore make several simplifying assumptions during the modelling process so that the environment interaction model maintains a simple and analytical form. In particular, we will model the interaction with obstacles by introducing a unilateral velocity constraint on each contacted link of the snake robot. This approach simplifies the equations of motion since the shape of the obstacles does not have to be considered explicitly. In order to illustrate the validity of the proposed modelling approach, this chapter includes a simulation study where simulation results from the proposed model of the snake robot are shown to agree well with simulation results from a more extensive model of obstacle-aided locomotion previously proposed by our research group.