• Journal of the Korean Society for Precision Engineering
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• v.14 no.12
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• pp.86-94
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• 1997

This paper proposes the robot inverse calibration method using a neural networks. A high-order networks called Pi-Sigma networks has been used. The Pi-Sigma networks uses linear summing units in the hidden layer and product unit in output layer. The inverse calibration model which compensates the diff- erence of joint variables only between measuring value and analytic value about the desired pose(position, orientation) of a robot is proposed. The compensated values are determined by using the weights obtained from the learning process of the neural networks previously. To prove the reasonableness, the SCARA type direct drive robot(4-DOF) and anthropomorphic robot(6-DOF) are simulated. It shows that the proposed calibration method can reduce the errors of the joint variables from .+-. 5 .deg. to .+-. 0.1 .deg. .

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.158-161
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• 2003

A cascade structured neural network called Sigma-Pi$_{t}$ Cascaded Hybrid Neural Network ($\sigma$$\pi$$_{t}$-CHNN) is Proposed. It is an extended version of the Sigma-Pi Cascaded extended Hybrid Neural Network ($\sigma$$\pi$-CHNN), where the classical multiplicative neuron ($\pi$-neuron) is replaced by the translated multiplicative ($\pi$$_{t}$-neuron) model. The learning algorithm of $\sigma$$\pi$$_{t}$-CHNN is composed of an evolutionary programming method, responsible for determining the network architecture, and of a Levenberg-Marquadt algorithm, responsible for tuning the weights of the network. The $\sigma$$\pi$$_{t}$-CHNN is evaluated in 2 pattern classification problems: the 2 spirals and the sonar problems. In the 2 spirals problem, $\sigma$$\pi$$_{t}$-CHNN can generate neural networks with 10％ less hidden neurons than that in previous neural models. In the sonar problem, $\sigma$$\pi$$_{t}$-CHNN can find the optimal solution for the problem i.e., a network with no hidden neurons. These results confirm the expanded information processing capabilities of $\sigma$$\pi$$_{t}$-CHNN, when compared to previous neural network models. network models.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.131-136
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• 1999

This paper proposes the robot inverse calibration method using a neural networks. A highorder networks called Pi-Sigma networks has been used. The Pi-Sigma networks uses linear summing units in the hidden layer and product unit in output layer. The inverse calibration model which compensates the difference of joint variables only between measuring value and analytic value about the desired pose(position, orientation) of a robot is proposed. The compensated values are determined by using the weights obtained from the learning process of the neural networks previously. To prove the reasonableness, the SCARA type direct drive robot(4-DOF) and anthropomorphic robot(6-DOF) are simulated. It shows that the proposed calibration method can reduce the errors of the joint variables from $\pm$2$^{\circ}$to $\pm$ 0.1$^{\circ}$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.2
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• pp.108-115
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• 1999

This paper proposes the robot inverse calibration method using a neural networks. A highorder networks called Pi-Sigma networks has been used. The Pi-Sigma networks uses linear summing units in the hidden layer and product unit in output layer. The inverse calibration model which compensates the difference of joint variables only between measuring value and analytic value about the desired pose(position orientation) of a robot is proposed. The compensated values are determined by using the weights obtained from the learning process of the neural networks previously. To prove the reasonableness the SCARA type direct drive robot(4-DOF) and anthropomorphic robot(6-DOF) are simulated. It shows that the proposed calibration method can reduce the errors of the joint variables from $\pm$3 to $\pm$0.1.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.7
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• pp.66-72
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• 1999

Robot calibration is very important to improve the accuracy of robot manipulators. However, the calibration procedure is very time consuming and laborious work for users. In this paper, we propose a method of relative error compensation to make the calibration procedure easier. The method is completed by a Pi-Sigma network architecture which has sufficient capability to approximate the relative relationship between the accuracy compensations and robot configurations while maintaining an efficient network learning ability. By experiment of 4-DOF SCARA robot, KIRO-3, it is shown that both the error of joint angles and the positioning error of end effector are drop to 15$\%$. These results are similar to those of other calibration methods, but the number of measurement is remarkably decreased by the suggested compensation method.

• Journal of Aerospace System Engineering
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• v.11 no.1
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• pp.14-21
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• 2017

A Linear parameterized Sigma-Pi neural network (SPNN) is applied to a tilt-duct unmanned aerial vehicle (UAV) which has a very large longitudinal stability ($C_{L{\alpha}}$). It is uncontrollable by a proportional, integral, derivative (PID) controller due to heavy stability. It is shown that the combined inner loop and outer loop of SPNN controllers could overcome the sluggish longitudinal dynamics using a method of dynamic inversion and pseudo-control to compensate for reference model error. The simulation results of the way point guidance are presented to evaluate the performance of SPNN in comparison to a PID controller.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.2
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• pp.13-21
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• 1996

The necessity and usefulness of higher-order neural networks have been well-known since early days of neurocomputing. However the explosive number of terms has hampered the design and training of such networks. In this paper we present an evolutionary learning method for efficiently constructing problem-specific higher-order neural models. The crux of the method is the neural tree representation employing both sigma and pi units, in combination with the use of an MDL-based fitness function for learning minimal models. We provide experimental results in classification and prediction problems which demonstrate the effectiveness of the method. I. Introduction topology employs one hidden layer with full connectivity between neighboring layers. This structure has One of the most popular neural network models been very successful for many applications. However, used for supervised learning applications has been the they have some weaknesses. For instance, the fully mutilayer feedforward network. A commonly adopted connected structure is not necessarily a good topology unless the task contains a good predictor for the full *d*dWs %BH%W* input space.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.199-204
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• 1999

The robot inverse calibration method using a neural networks is proposed in this paper. A high-order networks has been used in this study. The Pi-Sigma networks uses linear summing units in the hidden layer and product unit in output layer. The inverse calibration model which compensates the difference of joint variables only between measuring value and analytic value about the desired pose(position orientation) of a robot is proposed. The compensated values are determined by using the weights obtained from the learning process of the neural networks previously. To prove the reasonableness, the selected compliance automatic robot arm type direct drive robot and anthropomorphic robot are simulated. It shows that the proposed calibration method can reduce the errors of the joint variables from ${\pm}$0.15$^{\circ}$to ${\pm}$0.12$^{\circ}$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.251-268
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• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1041-1044
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• 2000

The enhancement to the back-propagation algorithm presented in this paper has resulted from the need to extract sparsely connected networks from networks employing product terms. The enhancement works in conjunction with the back-propagation weight update process, so that the actions of weight zeroing and weight stimulation enhance each other. It is shown that the error measure, can also be interpreted as rate of weight change (as opposed to ${\Delta}W_{ij}$), and consequently used to determine when weights have reached a stable state. Weights judged to be stable are then compared to a zero weight threshold. Should they fall below this threshold, then the weight in question is zeroed. Simulation of such a system is shown to return improved learning rates and reduce network connection requirements, with respect to the optimal network solution, trained using the normal back-propagation algorithm for Multi-Layer Perceptron (MLP), Higher Order Neural Network (HONN) and Sigma-Pi networks.