Model-based Locomotion Control of Underactuated Snake Robots

Abstract

Snake robots are a class of biologically inspired robots which are built
\nto emulate the features of biological snakes. These robots are underactuated,
\ni.e. they have fewer control inputs than degrees of freedom, and are
\nhyper redundant, i.e. they have many degrees of freedom. Furthermore,
\nsnake robots utilize complex motion patterns and possess a complicated
\nbut highly flexible physical structure. These properties make locomotion
\ncontrol of snake robots a complicated and challenging control problem.
\nThis thesis considers model-based locomotion control of planar snake
\nrobots. In particular, based on kinematic and dynamic models of the snake
\nrobot locomotion, using different control approaches we derive feedback
\ncontrol laws in order to solve various control problems. Moreover, through
\nrigorous mathematical stability analysis, we prove the stability of the controlled
\nsystem. It is noteworthy to mention that due to the complicated dynamical
\nbehavior of snake robots which gives rise to a complex dynamic
\nmodel, and also the underactuation which is characterized by the lack of
\ndirect and independent control inputs for at least three degrees of freedom
\nof the snake robot, the vast majority of the previous works on snake robots
\nand similar multi-link robotic structures use numerical simulations and
\nexperimental results which are obtained using different robotic snakes, as
\nthe main tools to show the performance of the proposed controllers. In
\ncontrast, however, in this work based on nonlinear control theory, we take
\na model-based control design approach and we present formal stability
\nproofs for the closed-loop systems along with numerical simulations and
\nexperimental results. The simulations and experiments are performed for
\na snake robot which is composed of N similar links which are serially connected
\nthrough N - 1 joints. The first N - 1 links are independently actuated
\nusing electric motors, however, the N-th link which we refer to as
\nthe head link of the snake robot is passive. This makes the orientation and
\nposition of the center of mass of the robot underactuated.
\nThe contributions of the thesis are presented in six chapters, and can
\nbe categorized in two types; contributions to modelling and contributions
\nto control design for snake robots. The contributions and contents of each
\nchapter are as follows.
\nIn Chapter 1, we discuss the fundamental properties of the snake robot
\nlocomotion, and we investigate the most common types of gait patterns
\nused by biological snakes. Furthermore, in this chapter we review the
\nrelevant previous works on snake robots and we present the abstracts of the academic papers which form the basis of the thesis.
\nIn Chapter 2, we present three different modelling techniques for the
\nsnake robot locomotion on horizontal and flat surfaces. The first dynamic
\nmodel is derived based on the Lagrangian approach to modelling mechanical
\nsystems, and the equations of motion are written in the standard
\nsecond-order form. The second dynamic model is derived using the
\ntechniques of differential geometry, and this model contains the effects of
\nparametric modelling uncertainties on the locomotion of the robot. The
\nfirst and the second models which are referred to as the complex model of
\nthe snake robot, are among the contributions of the thesis and to our best
\nknowledge have not been presented in any previous works. The third
\nmodel that we present in Chapter 2 is a simplified model of the snake
\nrobot locomotion which is previously presented in [11]. In this simplified
\nmodel, the rotational motion of the joints is mapped to translational
\nlink displacements. Through this mapping, which is shown to be valid for
\nsmall joint