Control of an elastic manipulator with a payload under weight

Problem of manipulator motion control under weight is considered. The manipulator consists of an elastic beam and a rigid body placed at the end of the beam. The manipulator hand can rotate in horizontal plane and move along the vertical directrix. Purpose of control is to transfer the manipulator from the given initial position to the given final position without longitudal and bending oscillations. Required control moments are constructed as power series with respect to small value, which is inversely proportional to Young module. Recurrent formulas are received for all terms of expansions.