Kinematics for Constrained Continuum Robots Using Wavelet Decomposition

Over the past several years, there has been a rapidly expanding interest in the study and construction of a new class of robot manipulators which utilize high degree of freedom, or continuous, backbone structures. In this paper, we consider some basic properties of these "continuum'' or "hyperredundant'' robots. We base our analysis around remotely-driven, tendon-actuated manipulators such as the Rice/Clemson "Elephant's Trunk''. We briefly discuss the kinematic model, before detailing how to approach the inverse kinematics for a planar continuum robot by decomposition into either a natural or a wavelet basis. We also examine how a wavelet decomposition method can help resolve redundancy in a planar continuum robot. Introduction By observing manipulation methods in nature, one may eventually reach the conclusion that rigid-link, low degree of freedom devices should meet the majority of manipulative and locomotive needs. However, some creatures make use of alternative methods based on very high degree of freedom (HDOF) backbones, such as snakes, or continuous "trunk'' or "tentacle'' structures. These manipulators, a subset of a class termed hyper-redundant, exhibit unique capabilities including extremely enhanced maneuverability. Hyper-redundant manipulators have the potential to navigate extremely complex paths, and to suffer localized damage or faults while still maintaining a healthy degree of functionality. In principle, this makes them suitable for a variety of delicate and dangerous tasks where a traditional robot could not reach, or where failure of a traditional robot would completely paralyze all subsequent operations. Examples of such tasks are nuclear waste inspection and removal, and navigation or inspection of highly cluttered environments such as collapsed buildings. In this paper we will concentrate on the fundamentals of a specific type of hyper-redundant robot, frequently referring to the Rice/Clemson "Elephant's Trunk''[2]. This is a type of remotely-actuated device which uses cables, or tendons generally, to transmit forces from a motor platform into the trunk itself. The salient feature of the Elephant's Trunk is that its high number of links (16), combined with the small size of each link, allow us to closely approximate it as a truly continuous backbone. Similar robots in our laboratory do in fact possess continuous backbones made of various materials, termed continuum robots. The following problems and theories apply to all of these robots. Using a continuous backbone model for the robot kinematics, we address the issue of how to approach inverse kinematics given physical properties of the robot. Background Several researchers have worked in the area of hyper-redundant, including continuum and HDOF manipulators, for various reasons. In Japan, Hirose pioneered the development of snake-like robots, especially with regards to locomotion; an overview of his work exists in [1]. Also, Mochiyama et. al. have investigated the problem of controlling the shape of an HDOF rigid-link robot with two-degree-of-