End Point Control of Nonlinear Flexible Manipulators With Control Constraint Using SDRE Method

The paper treats the question of end point regulation of multi-link light-weight manipulators using the state dependent Riccati equation (SDRE) method. It is assumed that each link is flexible and deforms when maneuvered. It is well known that end point trajectory control using widely used feedback linearization technique is not possible since the system is nonminimum phase. 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 and suboptimal control laws are designed using the SDRE method. This design approach is applicable to minimum and as well as nonminimum phase nonlinear systems. For the purpose of control, psuedo joint angles and elastic modes of each link are regulated to their equilibrium values which correspond to the target end point under gravity. Weighting matrices in the quadratic performance index provide flexibility in shaping the psuedo angle and elastic mode trajectories. In the closed-loop system, the equilibrium state is asymptotically stable, and vibration is uppressed. Simulation results are presented for a single link flexible manipulator which shows that in the closed-loop system, end point regulation is accomplished even with hard bounds on the control torque, and that the transient characteristics of the psuedo angles and elastic modes are easily shaped by the choice of the the performance criterion.