Optimal control of an elastic two-link manipulator in gravity

This paper develops a control algorithm for end point position control of an elastic two-link manipulator. First, an algotithm is developed to solve for the state variables as a function of end point position. This is used to determine a set of traget state variables. A control algorithm is developed using a linear quadratic optimal control technique on an infinite time interval with the prescribed degree of stability method to control the movement of the end point from a specified initial end point position to a specified terminal end point position. For the system dynamic equations, second order nonlinear differential equations including the shortening effect are linearized with respect to the terminal position and are put into first order. The simulation shows that the developed control allgorithm results in effective end effector control with short response time and little overshoot. Also, the simulation shows that the results with one and two flexible modes for each arm have small differences in the early stage of the end point control but the results are almost identical later in the simulation.