Optimal control based in a mathematical model applied to robotic arms

The major contributions of this paper are as follows: 1) The mathematical model of the cylindrical robotic arm is presented. This model is obtained by using the Euler Lagrange method. 2) The method to obtain the mathematical model of this paper is different to others because they use the Jacobians, the inertia tensors, or the Christoffel symbols, while in this paper, none of these methods is used. 3) It is proposed that the torque or the force used to move each link needs to compensate the initial value of the gravity to obtain the home position. 4) It is proposed that an optimal control is online applied to robotic arms for the regulation case. The proposed optimal control can be online applied to rigid robotic arms. The Riccati equation used in the proposed optimal control is online solved at the same time than the optimal control works. 5) The proposed optimal control is compared with a proportional control for the regulation case where the first is better than the second. 6) It is proposed that an optimal control is online applied to robotic arms for a reference point different of zero. The proposed optimal control can be online applied to any kind of rigid robotic arm. The Riccati equation of the proposed optimal control is online solved at the same time than the optimal control works.