Memory-based learning schemes are characterized by their memorization of observed events. A memory-based learning scheme either memorizes the collected data directly or reorganizes such information and stores it distributively into a tabular memory. For the tabular type, the system requires a training process to determine the contents of the associative memory. This training process helps filter out zero-mean noise. Since the stored data are associated to pre-assigned input locations, memory management and data retrieval are easier and more efficient. Despite these merits, a drawback of tabular schemes is the difficulty in applying it to high-dimensional problems due to the curse of dimensionality. As the input dimensionality increases, the number of quantized elements in the input space increases at an exponential rate and that causes a huge demand of memory. In this paper, a dynamic tabular structure is proposed for possible relaxation of such a demand. The memorized data are organized as part of a k-d tree. Nodes in the tree, called vertices, correspond to some regularly assigned input points. Memory resource is allocated only at locations where it is needed. Being able to easily compute the vertex positions helps reduce the searching cost in data retrieval. In addition, the learning process is able to expand the tree structure into one covering the problem domain. With memory allocated based on demand, memory consumption becomes closely related to task complexity instead of input dimensionality, and is minimized. Algorithms for structure construction and training are presented in this paper. Simulation results demonstrate that the memory can be efficiently utilized. The developed scheme offers a solution for high-dimensional learning problems with a manageable size of effective input domain.

The paper presents a novel memory-based Self-Generated Basis Function Neural Network (SGBFN) that is composed of small CMACs. The SGBFN requires much smaller memory space than the conventional CMAC and has an excellent learning convergence property compared to multilayer neural networks. Each CMAC in the new structure takes a subset of problem inputs as its inputs. Several CMACs that have different subsets of inputs form a submodule and a group of submodules form a neural network. The output of a submodule is the product of its CMACs' outputs. Each submodule implements a self-generated basis function, which is developed during the learning. The output of the neural network is the sum of the outputs from the submodules. Using only a subset of inputs in each CMAC significantly reduces the required memory space in high-dimensional modeling. With the same size of memory, the new structure is able to achieve a much smaller learning error compared to the conventional CMAC.

Cerebellar model articulation controllers (CMAC) have attractive properties of learning convergence and speed. Many studies have used CMAC in learning control and demonstrated successful results. However, due to the fact that CMAC is a table lookup technique, a model implemented by a CMAC does not provide a derivative of its output. This is an inconvenience when using CMAC in learning structures that require such derivatives. This paper presents a new scheme that integrates the CMAC addressing technique with weighted regression to resolve this problem. Derivatives exist everywhere except on the boundaries of quantized regions. Compared with the conventional CMAC, the new scheme requires the same amount of memory and has similar learning speed, but provides output differentiability and more precise output. Compared with the typical weighted regression technique, the new scheme offers an efficient way to organize and utilize collected information.

CMAC is one useful learning technique that was developed two decades ago but yet lacks adequate theoretical foundation. Most past studies focused on development of algorithms, improvement of the CMAC structure, and applications. Given a learning problem, very little about the CMAC learning behavior such as the convergence characteristics, effects of hash mapping, effects of memory size, the error bound, etc. can be analyzed or predicted. In this paper, we describe the CMAC technique with mathematical formulation and use the formulation to study the CMAC convergence properties. Both information retrieval and learning rules are described by algebraic equations in matrix form. Convergence characteristics and learning behaviors for the CMAC with and without hash mapping are investigated with the use of these equations and eigenvalues of some derived matrices. The formulation and results provide a foundation for further investigation of this technique.

The CMAC-based adaptive critic learning structure consists of two CMAC modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms the system response, usually some occasionally provided reinforcement signal, into organized useful information. Based on the knowledge developed in the critic module, the action module learns the control technique. One difficulty in using this scheme lies on selection of learning parameters. In our previous study on the CMAC-based scheme, the best set of learning parameters were selected from a large number of test simulations. The picked parameter values are not necessarily adequate for generic cases. A general guideline for parameter selection needs to be developed. In this study, the problem is investigated. Effects of parameters are studied analytically and verified by simulations. Results provide a good guideline for parameter selection.

A technique that integrates the cerebellar model articulation controller (CMAC) into a self-learning control scheme developed by A.G. Barto et al. (IEEE Trans. Syst. Man., Cybern., vol.SMC-13, p.834-46, Sept./Oct. 1983) is presented. Instead of reserving one input line (as a memory) for each quantized state, the integrated technique distributively stores learned information; this reduces the required memory and makes the self-learning control scheme applicable to problems of larger size. CMAC's capability with regard to information interpolation also helps improve the learning speed.

Invariants of three-dimensional contours are derived from the elliptic Fourier descriptor. A 3-D closed curve is described by a set of feature ellipses in 3-D space. These feature ellipses will have fixed lengths of major and minor axes no matter where the contour is located. Besides, the relative orientations among the ellipses will not vary. The derived invariants are implicit functions of these axes lengths as well as the angles defining the relative orientations. These invariants can be used for object recognition without having the complete surface data.>

A method is developed for planning the point-to-point path that the manipulator may adopt to minimize a specified performance index, under the realistic physical constraints on Joint torques, accelerations, velocities and position limits. The purpose of such path planning is either to provide the best input for the manipulator controller or to evaluate the arm performance for various designs. Because there is no analytic function available for describing the optimum path, cubic spline functions are proposed for an approximation. For a selected number of polynomial segments, the flexible polyhedron search is used to search for the optimum path arrangement. During the search period, it is often necessary to convert an infeasible arrangement into a feasible one. Methods for these required conversions have been studied. The number of concatenated polynomials is increased until there is no significant improvement on the approximation. Computer programs have been written to implement the algorithm.

A visual identification system for planar shapes based on the elliptic features is presented. The edge detection results in a list of run codes, which contain the edge information. The connectivity analysis then obtains the edge points in consecutive order. Three sets of invariants are computed from the elliptic Fourier features and used for recognition. Location and orientation are also computed from elliptic Fourier coefficients.

Methods of joint trajectory generation for mechanical manipulators usingX-spline and quartic spline functions are presented. A sequence of Cartesian knots, i.e. positions and orientations of the hand, are selected from the desired Cartesian path. Joint values corresponding to these selected knots are solved from the kinematic equation. Approximate joint paths are constructed by interpolating these joint positions. At any instant, two or more future knots need to be known in advance in order to determine the current joint trajectories. Approximate errors for Cartesian paths are discussed. An illustrative example is used for comparing these trajectories to other existent polynomial-type trajectories.