Abstract
This paper formally defines a class of multibody rectifier systems that captures the essential aspects of animal locomotion, and formulates an optimal locomotion problem to find a set of harmonic inputs that minimizes a quadratic objective function subject to an equality constraint on the average velocity. Our main result shows that the global optimum is given in terms of a generalized eigenvalue of a pair of Hermitian matrices, with a minimizer characterized by the associated eigenvector. Thus, an optimal harmonic gait can be computed efficiently even for hyper-redundant rectifiers with a large number of variables. We provide case studies for two specific rectifiers; (i) a chain of multiple links mimicking snakes, leeches, and other slender animals, and (ii) a disk-mass system that captures the rectifying dynamics in the simplest way. We examine optimal gaits for three types of objective functions, consisting of input power, input torque, and shape derivative. We compare the multilink results against natural motions observed in leeches, and discuss what optimality criteria appear to be used in nature. Analytical results are obtained for the disk-mass system, providing insights into optimal gaits.
Published Version
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