The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Task-space control needs the inverse kinematics solution or Jacobian matrix for the transformation from task space to joint space. However, they are not always available for redundant robots because there are more joint degrees-of-freedom than Cartesian degrees-of-freedom. Intelligent learning methods, such as neural networks (NN) and reinforcement learning (RL) can learn the inverse kinematics solution. However, NN needs big data and classical RL is not suitable for multi-link robots controlled in task space. In this paper, we propose a fully cooperative multi-agent reinforcement learning (MARL) to solve the kinematic problem of redundant robots. Each joint of the robot is regarded as one agent. The fully cooperative MARL uses a kinematic learning to avoid function approximators and large learning space. The convergence property of the proposed MARL is analyzed. The experimental results show that our MARL is much more better compared with the classic methods such as Jacobian-based methods and neural networks.

Multi-agent reinforcement learning for redundant robot control in task-space

Adaptive fuzzy tracking control of robot manipulators actuated by permanent magnet synchronous motors

In the present work, impedance control of robot manipulators is enhanced The controller is designed by using Szasz–Mirakyan operator as Universal approximator Although the Szasz–Mirakyan operator has been extensively used for dealing with approximation of nonlinear functions, the main novelty of this paper is presenting a completely different application of Szasz–Mirakyan operator Since in robust or adaptive control, the nonlinear function which should be approximated is unknown In fact, the Lyapunov theorem must be used to tune its adjustable parameters In accordance with the universal approximation theorem, Szasz–Mirakyan operator which is an extended version of the Bernstein polynomial is able to approximate uncertainties including un-modeled dynamics and external disturbances This fact is completely discussed in this paper It is shown that, using Szasz–Mirakyan operator as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniformly ultimately bounded stability can be assured The transient performance of the controller has been also analyzed Numerical simulations on an electrically driven manipulator are provided Simulation results verify that the role of Szasz–Mirakyan operator in uncertainty compensation and enhancing the tracking error is undeniable

Robust adaptive impedance control of robot manipulators using Szász-Mirakyan operator as universal approximator.

In this paper, a new method for secure communication based on chaos synchronization is proposed. It is consisted of a state feedback controller and a robust control term using the Fourier series expansion for compensation of uncertainties. In comparison with other uncertainty estimators such as neural networks and fuzzy systems, Fourier series are more efficient, since they have fewer tuning. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Fourier series coefficients are estimated online using the adaptation rule obtained from stability analysis. The case study is the Duffing–Holmes oscillator. Also, observer-based secure communication using the Fourier series expansion has been proposed. Simulation results and comparisons, reveal the superiority of the proposed approach.

Chaos synchronization using the Fourier series expansion with application to secure communications

Robust control of electrically driven robots using adaptive uncertainty estimation

An uncertainty estimation and compensation can improve the performance of control systems due to structured and unstructured uncertainty. This paper presents a robust task-space control app...

Task-space control of robots using an adaptive Taylor series uncertainty estimator

The uncertainty estimation and compensation are challenging problems for the robust control of robot manipulators which are complex systems. This paper presents a novel decentralized model-free robust controller for electrically driven robot manipulators. As a novelty, the proposed controller employs a simple Gaussian Radial-Basis-Function network (RBF network) as an uncertainty estimator. The proposed network includes a hidden layer with one node, two inputs and a single output. In comparison with other model-free estimators such as multilayer neural networks and fuzzy systems, the proposed estimator is simpler, less computational and more effective. The weights of the RBF network are tuned online using an adaptation law derived by stability analysis. Despite the majority of previous control approaches which are the torque-based control, the proposed control design is the voltage-based control. Simulations and comparisons with a robust neural network control approach show the efficiency of the proposed control approach applied on the articulated robot manipulator driven by permanent magnet DC motors.

http://jad.shahroodut.ac.ir/article_246_ac7674df063520718b9abae83fcf0960.pdf

Adaptive RBF network control for robot manipulators

This paper presents a robust task-space control approach using a direct adaptive Taylor series controller for electrically driven robot manipulators. In an adaptive Taylor series control scheme, the parameters of controller are directly tuned in order to reduce the task-space tracking error in the presence of structured and unstructured uncertainty. Also, the upper bound of approximation error is estimated to form a robustifying term and the asymptotic convergence of task-space tracking error and its time derivative is proven based on the stability analysis. Simulation results are included to verify the effectiveness of the proposed control method.

Task-space asymptotic tracking control of robots using a direct adaptive Taylor series controller

Achieving the asymptotic tracking control of electrically driven robot manipulators is a challenging problem due to approximation/modelling error arising from parametric and non-parametric uncertainty. Thanks to the specific property of Taylor series systems as they are universal approximators, this research outlines two robust control schemes using an adaptive Taylor series system for robot manipulators, including actuators' dynamics. First, an indirect adaptive controller is designed such as to approximate an uncertain continuous function by using a Taylor series system in the proposed control law. Second, a direct adaptive scheme is established to employ the Taylor series system as a controller. In both controllers, not only a robustifying term is constructed using the estimation of the upper bound of approximation/modelling error, but the closed-loop stability, as well as the asymptotic convergence of joint-space tracking error and its time derivative, is ensured. Due to the design of the Taylor series system in the tracking error space, our technique clearly has an advantage over fuzzy and neural network-based control methods in terms of the small number of tuning parameters and inputs. The proposed methods are simple, model free in decentralized forms, no need for uncertainty bounding functions and perfectly capable of dealing with parametric and non-parametric uncertainty and measurement noise. Finally, simulation results are introduced to confirm the efficiency of the proposed control methods.

Seyed Mohammad Ahmadi

Papers

Robust control of electrically driven robots using adaptive uncertainty estimation

Task-space control of robots using an adaptive Taylor series uncertainty estimator

Adaptive RBF network control for robot manipulators

Task-space asymptotic tracking control of robots using a direct adaptive Taylor series controller

On the Taylor series asymptotic tracking control of robots