End Point Position Control of Multi-Link Flexible Manipulators Using SDRE Method

This paper treats end point regulation of multi-link light-weight flexible manipulators using the State Dependent Riccati Equation: SDRE method. It is well known that end point trajectory control using widely used feedback linearization techniques is not possible when the equilibrium state of the zero dynamics of the system is unstable or weakly stable. Furthermore, control saturation is a major problem in controlling nonlinear systems. In this paper, an optimal control problem is formulated for the derivation of control law with and without control constraints on the joint torques for a multi-link flexible manipulator and suboptimal control laws are designed using the SDRE method. For the purpose of control, pseudo joint angles and elastic modes of each link are regulated to their equilibrium values which correspond to the target end point. Weighting matrices in the quadratic performance index provide flexibility in shaping the pseudo angles and elastic modes trajectories. In the closed-loop system, the equilibrium state is asymptotically stable, and vibration is suppressed. Simulation results are presented for a two-link flexible manipulator, which show that in the closed-loop system, end point trajectory tracking is accomplished even with constraints on the control torque. Results also show that the transient characteristics of the pseudo angles and elastic modes can be easily shaped by the choice of the performance criterion.