A comparison of robotic fish speed control based on analytical and empirical models

Abstract

In this paper, a comparative study of speed control efficiencies based on two dynamical models is presented. The common structure of dynamical models is developed using first principles of physics. The complex thrust mechanism is studied using two different techniques. First, we apply a novel data-driven approach to build up the non-linear mapping between tail angular motion and thrust generated, which is essential to specify the input gradient. Further, additional experiments are designed to acquire data necessary for modelling the input delay factor causing a time-delayed input to drive the system output. Second, analytically developed Lighthill's slender body theory is also employed to study thrust mechanism for comparative purposes. Though the theory has been used in robotic fish motion studies, it was originally formulated as an analytical tool for studying biological fish motion. Comparing the two theories help understand the predominant features in a robotic fish speed control. Lastly, because of the highly non-linear system dynamics, robust discrete-time Sliding Mode Controllers (SMC) are developed with the two dynamical models as basis respectively. Experimental verifications confirm that SMC based on data-driven model performs superior to the SMC based on the Lighthill's theory, by efficiently controlling the robotic fish's speed to track the time-varying reference speeds.