Locomotion of Multi-link Systems in Liquid

The motions of multi-link systems in a liquid based on models with a finite number of degrees of freedom are investigated. It is assumed that the environment influences the elements of the bodies that move in it through the friction forces that are modeled by power-law functions of the velocities of these elements and are oriented opposite to the velocity vector. Under certain conditions, such laws, especially in the case of quadratic-law resistance, describe fairly well the forces of resistance to the motion of bodies in liquids possessing a viscosity. Equations of motion are derived for systems the links of which are connected by cylindrical or prismatic joints. The focus is put on the periodic motions at which the system configuration changes periodically and its center of mass moves by the same distance for each period along the given straight line. Parametric optimization and optimal control problems are solved with the aim to maximize the average velocity of the locomotion system movement in a periodic mode. The systems studied in this chapter model the swimming of fish and some animals as well as dynamics of artificial swimming vehicles. The results presented may be used to develop mobile robots moving in liquid.