Dynamic Modeling of Flexible Manipulators Using Finite Element Method and Optimal Control of their Motion

Flexible manipulators have plentiful applications in Aero-Space fields, due to their less weight and maneuverability. In fact, the ratio of their load carrying capacity to their weight, make them more excellent over their rigid ones. Moreover, these manipulators are known as good candidates in Aero-Space applications because of their less energy consumption, and smaller actuators. In this paper, the dynamic modeling of the flexible manipulators are performed using Finite Element Method (FEM), and optimal control of point-to-point motion of robot is done via optimal control method. To dynamic modeling of flexible manipulator, each link of the robot is divided into sufficient elements, and total displacement of the element is presumed as summation of a rigid displacement and a displacement because of flexibility. By means of Lagrange’s principle, dynamic equations of the flexible robot are derived, and the effect of number of the on dynamic motion of the robot is considered. Also, for the optimal point-to-point motion planning of the elastic manipulator, the nonlinear dynamic equations of the robot is assumed as constraints of optimal control problem, and a proper cost function is defined including torque and speed terms. Then, variation of calculus and Pontryagin’s minimum principle are employed and optimality conditions are resulted in a set of nonlinear differential equations, which is solved numerically. The priority of the optimal control method on the optimal motion planning of the flexible manipulator is discussed, and simulations for a single-link elastic robot illustrate the applicability of the method