Analysis of Manipulators Using SDRE: A Closed Loop Nonlinear Optimal Control Approach

In this paper, the State Dependent Riccati Equation (SDRE) method is implemented on robotic systems such as a mobile two-links planar robot and a xed 6R manipulator with complicated dynamic equations. Dynamic modelings of both cases are presented using the Lagrange method. Afterwards, the Dynamic Load Carrying Capacity (DLCC), which is an important characteristic of robots, is calculated for these two systems. DLCC is calculated for the prede ned end-e ector path, where motor torque limits and tracking error constraints are imposed for this calculation. For a mobile two-links planar robot, the stability constraint is discussed by applying a zero moment point approach. A nonlinear feedback control law is designed for the fully nonlinear dynamics of two cases using a nonlinear closed-loop optimal control method. For solving the SDRE equation that appears in the optimal control solution, a power series approximation method is applied. DLCC is obtained, subject to accuracy and torque constraints, by applying this feedback control law for the square and linear path of the end-e ector for mobile twolink and a 6R manipulator, respectively. Finally, simulations are done for both cases and the DLCC of manipulators is determined. Also, actual end-e ector positions, required control e orts and the angular position and velocity of joints are presented for full load conditions, and results are discussed