Trajectory optimization of a flexible manipulator using backstepping in the form of partial differential equations

In this paper, optimal trajectory control of a flexible manipulator is studied on the basis of partial differential equation (PDE) model. The PDE model of the flexible manipulator is established by Hamilton principle. Using singular perturbation theory, the original PDE model is divided into two decomposed subsystems. Differential evolution (DE) algorithm and cubic spline interpolating function method are applied to generate the optimal trajectory, which will minimize the deformation of flexible manipulator. Then, a backstepping boundary control scheme is proposed to regulate the joint along the optimal trajectory and suppress vibration simultaneously. In simulation, the optimum algorithm and backstepping controller are verified by MATLAB.