Motion control optimization of robotic fish tail

"In the daily life people, animals, fishes, birds and insects constantly interact with continuous media such as air or water. It means that synthesis of new robotic systems inside this continuous media and imitation of motion of real objects must be investigated together with media surrounding them. In this report motion of robotic fish tail vibration and simplified interaction with water flow is investigated. The study comprises: (a) preliminary analysis of main goal that is given to scientist to solve the problem; (b) optimization of a main fundamental system; (c) analysis of ideal control actions; (d) synthesis a new structural schemes; (e) calculation of optimal parameters. The preliminary analysis includes 5 steps: analysis of technological processes, choice of base system, choice of control actions, clarification of criteria for optimization and selection of limits. In this report criterion of optimization (for robotic fish tail model inside water) is maximal positive impulse of water forces in the fish tail and hull contact pivot. The main idea is to find out optimal control law for variation of additional area of vibrating tail within limits. The limits are maximal and minimal area of tail interaction with water. For task solution the maximum principle of Pontryagin is used [5 – 14]. It is demonstrated that optimal control action is on bounds of area limits. Examples of synthesis of real mechatronic systems are provided. One example of synthesis is a system with time harmonic moment excitation of tail in the pivot. The other example is a system with adaptive force moment as function of phase coordinates. In both systems area exchange (from maximal to minimal values) has control action as a function of phase coordinates. It is demonstrated that real tail vibration motion is highly stable and provides satisfactory real criterion in the hull contact point"