Kinematic transformations for remotely-actuated planar continuum robots

We consider a class of robotic manipulators generally termed "hyper-redundant". Specifically, we seek to examine some of the kinematic properties of "continuum" hyper-redundant robots. Unlike the case with rigid-link robots, there is no commonly accepted formula for describing continuum robot kinematics. Although these manipulators are continuously flexible, they are actuated with a finite number of actuators. We discuss two possible options for mapping desired infinite-dimensional robot shapes to the finite-dimensional actuator space, using "natural" and "wavelet" decompositions. We compare and contrast these kinematic descriptions, illustrating how the wavelet decomposition can simplify the inverse kinematics for redundant planar continuum robots.