Adaptive Optimization in Path Tracking of Manipulators Using Voltage Control Strategy

In this article, the linear quadratic regulator method (LQR) for voltage control of a linear time-varying model of a robot is used to design an on line adaptive optimal stable controller to trace the robot arm path. Normally, off line solving of Riccati differential equations in backward with final conditions for linear time-varying system or converting the Riccati differential equation to algebraic one in linear time-invariant system is inevitable in LQR. However, in this paper, the differential Riccati equations are considered as the adaptation laws along with a voltage control strategy to be solved on line in forward method with initial conditions. Choosing a proper Lyapunov function guarantees the asymptotic stability of the tracking. Furthermore, parametric model uncertainties such as mass parameter variation and external disturbances which affect the dynamics of the model, are also taken into account. Simulation results show the energy used by dc motors of the voltage optimal control strategy is less than that of the torque control strategy and as well as the classical PID one. The superior performance of the voltage optimal control over torque control strategy is also shown in presence of disturbance.