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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.
Gravagne et al. (Thu,) studied this question.