Motion control of flexible-link manipulators

A new method is proposed for the end-effector trajectory tracking control of flexible robot manipulators. The equations of motion are separated into two parts that represent the pseudostatic equilibrium and the deviations from it. The part of the control input for the pseudostatic equilibrium is determined algebraically, and the other part of the control input for the stabilization of the deviations is obtained by a state variable feedback law, by using strain, joint variable, and end-effector position measurements. The feedback gain matrix is determined online by continuously updated pole placement. The pseudostatic equilibrium is defined here as a hypothetical state, in which the velocity and acceleration of the end-effector have their desired values whereas the elastic deformations are instantaneously constant. In order to demonstrate the method, a planar two-link robot with a flexible forearm is taken into consideration. The elasticity of the forearm is approximately described by the first two modes, and a controller is designed by using this two-mode model. Furthermore, in order to investigate the effects of modelling discrepancies, a ‘submodel controller’ is designed by using a model with only the first mode and it is applied to the same system with the two-mode model. The performances of these two controllers are compared by means of simulations. The behaviour of the flexible robot is also simulated by using the computed torque method as if the robot is rigid in order to illustrate the importance of including the flexibility effects in the formation of an appropriate control law. The spillover effect that causes the dominant poles to approach towards the imaginary axis is inspected by monitoring the real parts of the dominant poles of the closed-loop system under the effect of the ‘submodel’ and ‘computed torque’ controllers.