Optimal trajectory control for a two-link rigid-flexible manipulator with ODE-PDE model

In this paper, the optimal trajectory control problem for a two-link rigid-flexible manipulator is considered. Since the two-link rigid-flexible system is a distributed system, an ordinary differential equation and partial differential equation (ODE-PDE) dynamic model of the manipulator is established by Hamilton's principle. Based on the ODE-PDE model, an optimal trajectory controller is proposed in this paper, which includes 2 stages. In the first stage, the optimal trajectory is created by using the differential evolution algorithm. Energy consumption and deflection of the flexible link are chosen as performance indexes. Cubic spline interpolation is applied to obtain the continuous trajectory. In the second stage, the aim is to regulate 2 joints to follow the optimal trajectory and simultaneously suppress vibration of the flexible link. To achieve it, boundary control laws are designed and the stability analysis is given. In simulations, the effectiveness of the optimal controller is verified by MATLAB.