The Control of a Mathematical Analog of a Tentacle

Abstract

A 2-dimensional dynamic analog of squid tentacles was presented. The tentacle analog consists of a multi-cell structure, which can be easily replicated to a large scale. Each cell of the model is a quadrilateral with unit masses at the corners. Each side of the quadrilateral is a spring-damper system in parallel. The spring constants are the controls for the system. The dynamics are subject to the constraint that the area of each quadrilateral must remain constant. The system dynamics was analyzed, and various equilibrium points were found with different controls. Then these equilibrium points were further determined experimentally, demonstrated to be asymptotically stable. A simulation built in MATLAB was used to find the convergence rates under different controls and damping coefficients. Finally, a control scheme was developed and used to drive the system to several configurations observed in real tentacle.