Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot

Abstract

Network-based control systems have been emerging technologies in the control of nonlinear systems over the past few years. This paper focuses on the implementation of the approximate dynamic programming algorithm in the network-based tracking control system of the two-wheeled mobile robot, Pioneer 2-DX. The proposed discrete tracking control system consists of the globalised dual heuristic dynamic programming algorithm, the PD controller, the supervisory term, and an additional control signal. The structure of the supervisory term derives from the stability analysis realised using the Lyapunov stability theorem. The globalised dual heuristic dynamic programming algorithm consists of two structures: the actor and the critic, realised in a form of neural networks. The actor generates the suboptimal control law, while the critic evaluates the realised control strategy by approximation of value function from the Bellman’s equation. The presented discrete tracking control system works online, the neural networks’ weights adaptation process is realised in every iteration step, and the neural networks preliminary learning procedure is not required. The performance of the proposed control system was verified by a series of computer simulations and experiments realised using the wheeled mobile robot Pioneer 2-DX.

Approximate Dynamic Programming in Tracking Control of a Robotic Manipulator

“…The performance of the presented discrete tracking control system of the Scorbot-ER 4pc robotic manipulator was verified by a series of computer simulations and experiments. The results of the research presented in this article continue the authors' earlier works related to the problems of the control of nonlinear dynamic systems like a ball and beam system [22], a wheeled mobile robot [17, 23, 24] and a robotic manipulator [13, 25, 26] using NNs and ADP algorithms. In [13], the authors discussed the application of MNNs in the tracking control problem of a robotic manipulator.…”

“…where Γ Aj ∈ ℜ n A xn A is the fixed diagonal matrix of the positive learning rates of the j -th actor's NN and This signal is the input to the critic's NNs, which generate the prediction of the difference of the value function with respect to the state. The signal λ {k +1,l } , taking into account the dynamics model of the controlled object, is used to generate the error e A{k ,l } according to equation (17). Next,…”

“…The ADP structure adaptation process is organized in the following way, at the beginning of every k -th iteration step l = 0. The actor's NNs' weights are adapted according to the assumed adaptation law (18) by the minimization of the error rate (17). This part of the algorithm is called the "control law improvement routine" [9].…”

“…Solutions for the control problem of robotic manipulators using ADP algorithms presented in the literature often involve theoretical considerations [13,14]. There are not many applications of ADP algorithms in real control problems, which suggests that literature is concerned instead with the control problem of dynamic objects like mobile robots [15,16,17], turbo-generators [18], underactuated systems like an inverted pendulum [19], and other applications of ADP algorithms (e.g., target recognition [20] and a static compensator connected to a power system [21]). The performance of the presented discrete tracking control system of the Scorbot-ER 4pc robotic manipulator was verified by a series of computer simulations and experiments.…”

Research on Open-Closed-Loop Iterative Learning Control with Variable Forgetting Factor of Mobile Robots

“…So some good methods should be adopted in order to obtain a good effect. So far, there are many researches on the mobile robot tracking control strategy [7][8][9].…”