Trajectory tracking control of spatial three-link flexible manipulators

This study deals with the trajectory tracking control of a spatial three-link articulated manipulator with flexible second and third links. In order to reduce the complexity of the dynamic equations each link is modelled as if unconnected and the joint connections are expressed as constraint equations. Then the Lagrange multipliers are eliminated and the number of equations is reduced by substituting the acceleration level constraint equations into the dynamic equations. The dynamic equations are partitioned as pseudostatic equilibrium equations and deviations from them. The pseudostatic equilibrium is defined here as a hypothetical state where the velocity and acceleration of the end-effector have their desired values while the elastic deformations are instantaneously constant. The portion of the control torques for the pseudostatic equilibrium and their portion for the feedback stabilization of the deviations are generated using the measurement signals taken from the strain gauges, the joint encoders and the end-effector position sensors.