A wavelet-based CMAC for enhanced multidimensional learning

The CMAC (Cerebellar Model Articulation Controller) neural network has been successfully used in control systems and other applications for many years. The network structure is modular and associative, allowing for rapid learning convergence with an ease of implementation in either hardware or software. The rate of convergence of the network is determined largely by the choice of the receptive field shape and the generalization parameter. This research contains a rigorous analysis of the rate of convergence with the standard CMAC, as well as the rate of convergence of networks using other receptive field shape. The effects of decimation from state-space to weight space are examined in detail. This analysis shows CMAC to be an adaptive lowpass filter, where the filter dynamics are governed by the generalization parameter. A more general CMAC is derived using wavelet-based receptive fields and a controllable decimation scheme, that is capable of convergence at any frequency within the Nyquist limits. The flexible decimation structure facilitates the optimization of computation for complex multidimensional problems. The stability of the wavelet-based CMAC is also examined

Error minimising gradients for improving cerebellar model articulation controller performance

In motion control applications where the desired trajectory velocity exceeds an actuator’s maximum velocity limitations, large position errors will occur between the desired and actual trajectory responses. In these situations standard control approaches cannot predict the output saturation of the actuator and thus the associated error summation cannot be minimised.An adaptive feedforward control solution such as the Cerebellar Model Articulation Controller (CMAC) is able to provide an inherent level of prediction for these situations, moving the system output in the direction of the excessive desired velocity before actuator saturation occurs. However the pre-empting level of a CMAC is not adaptive, and thus the optimal point in time to start moving the system output in the direction of the excessive desired velocity remains unsolved. While the CMAC can adaptively minimise an actuator’s position error, the minimisation of the summation of error over time created by the divergence of the desired and actual trajectory responses requires an additional adaptive level of control.This thesis presents an improved method of training CMACs to minimise the summation of error over time created when the desired trajectory velocity exceeds the actuator’s maximum velocity limitations. This improved method called the Error Minimising Gradient Controller (EMGC) is able to adaptively modify a CMAC’s training signal so that the CMAC will start to move the output of the system in the direction of the excessive desired velocity with an optimised pre-empting level.The EMGC was originally created to minimise the loss of linguistic information conveyed through an actuated series of concatenated hand sign gestures reproducing deafblind sign language. The EMGC concept however is able to be implemented on any system where the error summation associated with excessive desired velocities needs to be minimised, with the EMGC producing an improved output approximation over using a CMAC alone.In this thesis, the EMGC was tested and benchmarked against a feedforward / feedback combined controller using a CMAC and PID controller. The EMGC was tested on an air-muscle actuator for a variety of situations comprising of a position discontinuity in a continuous desired trajectory. Tested situations included various discontinuity magnitudes together with varying approach and departure gradient profiles.Testing demonstrated that the addition of an EMGC can reduce a situation’s error summation magnitude if the base CMAC controller has not already provided a prior enough pre-empting output in the direction of the situation. The addition of an EMGC to a CMAC produces an improved approximation of reproduced motion trajectories, not only minimising position error for a single sampling instance, but also over time for periodic signals

Stability and weight smoothing in CMAC neural networks

Although the CMAC (Cerebellar Model Articulation Controller) neural network has been successfully used in control systems for many years, its property of local generalization, the availability of trained information for network responses at adjacent untrained locations, although responsible for the networks rapid learning and efficient implementation, results in network responses that is, when trained with sparse or widely spaced training data, spiky in nature even when the underlying function being learned is quite smooth. Since the derivative of such a network response can vary widely, the CMAC\u27s usefulness for solving optimization problems as well as for certain other control system applications can be severely limited. This dissertation presents the CMAC algorithm in sufficient detail to explore its strengths and weaknesses. Its properties of information generalization and storage are discussed and comparisons are made with other neural network algorithms and with other adaptive control algorithms. A synopsis of the development of the fields of neural networks and adaptive control is included to lend historical perspective. A stability analysis of the CMAC algorithm for open-loop function learning is developed. This stability analysis casts the function learning problem as a unique implementation of the model reference structure and develops a Lyapunov function to prove convergence of the CMAC to the target model. A new CMAC learning rule is developed by treating the CMAC as a set of simultaneous equations in a constrained optimization problem and making appropriate choices for the weight penalty matrix in the cost equation. This dissertation then presents a new CMAC learning algorithm which has the property of weight smoothing to improve generalization, function approximation in partially trained networks and the partial derivatives of learned functions. This new learning algorithm is significant in that it derives from an optimum solution and demonstrates a dramatic performance improvement for function learning in the presence of widely spaced training data. Developed from a completely unique analytical direction, this algorithm represents a coupling and extension of single- and multi-resolution CMAC algorithms developed by other researchers. The insights derived from the analysis of the optimum solution and the resulting new learning rules are discussed and suggestions for future work are presented

The control of a manipulator using cerebellar model articulation controllers

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2003Includes bibliographical references (leaves: 72-74)Text in English; Abstract: Turkish and Englishviii, 91 leavesThe emergence of the theory of artificial neural networks has made it possible to develop neural learning schemes that can be used to obtain alternative solutions to complex problems such as inverse kinematic control for robotic systems. The cerebellar model articulation controller (CMAC) is a neural network topology commonly used in the field of robotic control which was formulated in the 1970s by Albus. In this thesis, CMAC neural networks are analyzed in detail. Optimum network parameters and training techniques are discussed. The relationship between CMAC network parameters and training techniques are presented. An appropriate CMAC network is designed for the inverse kinematic control of a two-link robot manipulator

Active disturbance cancellation in nonlinear dynamical systems using neural networks

A proposal for the use of a time delay CMAC neural network for disturbance cancellation in nonlinear dynamical systems is presented. Appropriate modifications to the CMAC training algorithm are derived which allow convergent adaptation for a variety of secondary signal paths. Analytical bounds on the maximum learning gain are presented which guarantee convergence of the algorithm and provide insight into the necessary reduction in learning gain as a function of the system parameters. Effectiveness of the algorithm is evaluated through mathematical analysis, simulation studies, and experimental application of the technique on an acoustic duct laboratory model

Pole -mounted sonar vibration prediction using CMAC neural networks

The efficiency and accuracy of pole-mounted sonar systems are severely affected by pole vibration, Traditional signal processing techniques are not appropriate for the pole vibration problem due to the nonlinearity of the pole vibration and the lack of a priori knowledge about the statistics of the data to be processed. A novel approach of predicting the pole-mounted sonar vibration using CMAC neural networks is presented. The feasibility of this approach is studied in theory, evaluated by simulation and verified with a real-time laboratory prototype, Analytical bounds of the learning rate of a CMAC neural network are derived which guarantee convergence of the weight vector in the mean. Both simulation and experimental results indicate the CMAC neural network is an effective tool for this vibration prediction problem