Discrete linear quadratic control has been efficiently applied to linear systems as an optimal control. However, a robotic system is highly nonlinear, heavily coupled and uncertain. To overcome the problem, the robotic system can be modeled as a linear discrete-time time-varying system in performing repetitive tasks. This modeling motivates us to develop an optimal repetitive control. The contribution of this paper is twofold. For the first time, it presents discrete linear quadratic repetitive control for electrically driven robots using the mentioned model. The proposed control approach is based on the voltage control strategy. Second, uncertainty is effectively compensated by employing a robust time-delay controller. The uncertainty can include parametric uncertainty, unmodeled dynamics and external disturbances. To highlight its ability in overcoming the uncertainty, the dynamic equation of an articulated robot is introduced and used for the simulation, modeling and control purposes. Stability analysis verifies the proposed control approach and simulation results show its effectiveness.

This paper proposes a discrete-time repetitive optimal control of electrically driven robotic manipulators using an uncertainty estimator. The proposed control method can be used for performing repetitive motion, which covers many industrial applications of robotic manipulators. This kind of control law is in the class of torque-based control in which the joint torques are generated by permanent magnet dc motors in the current mode. The motor current is regulated using a proportional-integral controller. The novelty of this paper is a modification in using the discrete-time linear quadratic control for the robot manipulator, which is a nonlinear uncertain system. For this purpose, a novel discrete linear time-variant model is introduced for the robotic system. Then, a time-delay uncertainty estimator is added to the discrete-time linear quadratic control to compensate the nonlinearity and uncertainty associated with the model. The proposed control approach is verified by stability analysis. Simulation results show the superiority of the proposed discrete-time repetitive optimal control over the discrete-time linear quadratic control.

Purpose – Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and uncertainty to design the discrete optimal control for electrically driven robot manipulators. Design/methodology/approach – Two novel discrete optimal control approaches are presented. In the first approach, a control-oriented model is applied for the discrete linear quadratic control while modeling error is estimated and compensated by a robust time-delay controller. Instead of the torque control strategy, the voltage control strategy is used for obtaining an optimal control that is free from the manipulator dynamics. In the second approach, a discrete optimal controller is designed by using a particle swarm optimization algorithm. Findings – The first controller can overcome uncertainties, guarantee stability and provide a good tracking performance by using an online optimal algorithm whereas the second controller is an off-line optimal algorithm. The first control approach is verified by stability analysis. A comparison through simulations on a three-link electrically driven robot manipulator shows superiority of the first approach over the second approach. Another comparison shows that the first approach is superior to a bounded torque control approach in the presence of uncertainties. Originality/value – The originality of this paper is to present two novel optimal control approaches for tracking control of electrically driven robot manipulators with considering the actuator dynamics. The novelty is that the proposed control approaches are free from the robot's model by using the voltage control strategy. The first approach is a novel discrete linear quadratic control design supported by a time-delay uncertainty compensator. The second approach is an off-line optimal design by using the particle swarm optimization.

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