Bayesian Curve Fitting Based on RBF Neural Networks

AbstractThis article introduces a method for realizing the Gaussian activation function of radial-basis (RBF) neural networks with their hardware implementation on field-programmable gaits area (FPGAs). The results of modeling of the Gaussian function on FPGA chips of different families have been presented. RBF neural networks of various topologies have been synthesized and investigated. The hardware component implemented by this algorithm is an RBF neural network with four neurons of the latent layer and one neuron with a sigmoid activation function on an FPGA using 16-bit numbers with a fixed point, which took 1193 logic matrix gate (LUTs—LookUpTable). Each hidden layer neuron of the RBF network is designed on an FPGA as a separate computing unit. The speed as a total delay of the combination scheme of the block RBF network was 101.579 ns. The implementation of the Gaussian activation functions of the hidden layer of the RBF network occupies 106 LUTs, and the speed of the Gaussian activation functions is 29.33 ns. The absolute error is ± 0.005. The Spartan 3 family of chips for modeling has been used to get these results. Modeling on chips of other series has been also introduced in the article. RBF neural networks of various topologies have been synthesized and investigated. Hardware implementation of RBF neural networks with such speed allows them to be used in real-time control systems for high-speed objects.

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Task-space regulation of rigid-link electrically-driven robots with uncertain kinematics using neural networks

Measurement and Control ◽

10.1177/0020294020983383 ◽

2021 ◽

Vol 54 (1-2) ◽

pp. 102-115

Author(s):

Wenhui Si ◽

Lingyan Zhao ◽

Jianping Wei ◽

Zhiguang Guan

Keyword(s):

Neural Networks ◽

Asymptotic Stability ◽

Control Method ◽

Joint Space ◽

Robot Kinematics ◽

Rbf Neural Networks ◽

Task Space ◽

Actuator Dynamics ◽

Rigid Link ◽

On Line

Extensive research efforts have been made to address the motion control of rigid-link electrically-driven (RLED) robots in literature. However, most existing results were designed in joint space and need to be converted to task space as more and more control tasks are defined in their operational space. In this work, the direct task-space regulation of RLED robots with uncertain kinematics is studied by using neural networks (NN) technique. Radial basis function (RBF) neural networks are used to estimate complicated and calibration heavy robot kinematics and dynamics. The NN weights are updated on-line through two adaptation laws without the necessity of off-line training. Compared with most existing NN-based robot control results, the novelty of the proposed method lies in that asymptotic stability of the overall system can be achieved instead of just uniformly ultimately bounded (UUB) stability. Moreover, the proposed control method can tolerate not only the actuator dynamics uncertainty but also the uncertainty in robot kinematics by adopting an adaptive Jacobian matrix. The asymptotic stability of the overall system is proven rigorously through Lyapunov analysis. Numerical studies have been carried out to verify efficiency of the proposed method.

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Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219834611 ◽

2019 ◽

Vol 41 (13) ◽

pp. 3612-3625 ◽

Cited By ~ 1

Author(s):

Wang Qian ◽

Wang Qiangde ◽

Wei Chunling ◽

Zhang Zhengqiang

Keyword(s):

Neural Networks ◽

Tracking Control ◽

Large Scale ◽

Inverse Dynamics ◽

Small Neighborhood ◽

High Order ◽

Interconnected Systems ◽

Delay Systems ◽

Rbf Neural Networks ◽

Stochastic Input

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

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Augmenting Around-Device Interaction by Geomagnetic Field Built-in Sensor Utilization

Sensors ◽

10.3390/s21093087 ◽

2021 ◽

Vol 21 (9) ◽

pp. 3087

Author(s):

Sandi Ljubic ◽

Franko Hržić ◽

Alen Salkanovic ◽

Ivan Štajduhar

Keyword(s):

Magnetic Field ◽

Neural Networks ◽

Curve Fitting ◽

Absolute Error ◽

Interaction Space ◽

Text Entry ◽

Proof Of Concept ◽

Field Sensor ◽

Device Interaction ◽

Input Techniques

In this paper, we investigate the possibilities for augmenting interaction around the mobile device, with the aim of enabling input techniques that do not rely on typical touch-based gestures. The presented research focuses on utilizing a built-in magnetic field sensor, whose readouts are intentionally affected by moving a strong permanent magnet around a smartphone device. Different approaches for supporting magnet-based Around-Device Interaction are applied, including magnetic field fingerprinting, curve-fitting modeling, and machine learning. We implemented the corresponding proof-of-concept applications that incorporate magnet-based interaction. Namely, text entry is achieved by discrete positioning of the magnet within a keyboard mockup, and free-move pointing is enabled by monitoring the magnet’s continuous movement in real-time. The related solutions successfully expand both the interaction language and the interaction space in front of the device without altering its hardware or involving sophisticated peripherals. A controlled experiment was conducted to evaluate the provided text entry method initially. The obtained results were promising (text entry speed of nine words per minute) and served as a motivation for implementing new interaction modalities. The use of neural networks has shown to be a better approach than curve fitting to support free-move pointing. We demonstrate how neural networks with a very small number of input parameters can be used to provide highly usable pointing with an acceptable level of error (mean absolute error of 3 mm for pointer position on the smartphone display).

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