Reconstruction of Backbone Curves for Snake Robots

Snake robots composed of alternating single-axis pitch and yaw joints have many internal degrees of freedom, which make them capable of versatile three-dimensional locomotion. In motion planning process, snake robot motions are often designed kinematically by a chronological sequence of continuous backbone curves that capture desired macroscopic shapes of the robot. However, as the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, it is challenging for the robot to reconstruct an arbitrary 3D curve. When the robot configuration does not accurately achieve the desired shapes defined by these backbone curves, the robot can have unexpected contacts with the environment, such that the robot does not achieve the desired motion. In this work, we propose a method for snake robots to reconstruct desired backbone curves by posing an optimization problem that exploits the robot's geometric structure. We verified that our method enables fast and accurate curve-configuration conversions through its applications to commonly used 3D gaits. We also demonstrated via robot experiments that 1) our method results in smooth locomotion on the robot; 2) our method allows the robot to approach the numerically predicted locomotive performance of a sequence of continuous backbone curve.

I. Introduction

Snake robots are a class of hyper-redundant mechanisms capable of achieving different types of locomotion by coordinated flexing of their bodies. One of the well-established snake robot designs is composed of alternating one degree of freedom (DOF) pitch and yaw bending joints (as shown in Fig. 1), which allows 3D versatile motion [1]–[4]. Such a robot design is also called “twist-free” since it does not have direct actuation of the twist (rotation about the longitudinal axis of the body) DOF [5]. Inspired by the shapes of biological snakes with many vertebrae, finite-length continuous backbone curves are designed to capture desired macroscopic shapes of robots [6], [7]. Often, the motion of a snake robot is planned kinematically by a chronological sequence of backbone curves [8], [9]. Once properly designed, these sequences of backbone curves have been shown by prior work to generate effective, biologically-inspired, locomotion such as lateral undulation, sidewinding, and sinus lifting [6], [10], [11]. In order to replicate those motions on the physical robot, we have to match the shape of a robot made up of discrete segments to the continuous curves. These backbone curves lie in 3D space, but the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, making this shape-matching problem challenging for twist-free snake robots. When the body shape does not match the desired backbone curve, the desired robot-environment contacts are not achieved. The robot may then have undesired contacts with the environment, impeding locomotion. This letter presents a method for twist-free snake robots to accurately reconstruct desired 3D backbone curves via a constrained optimization problem. This enables the robot to locomote effectively by following a sequence of backbone curves.