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CMAC neural networks structures

Profile image of Kamran MohajeriKamran Mohajeri

2009

Abstract

Cerebellar Model Articulation Controller (CMAC) NN is a computational model of cerebellum introduced as an alternative to backpropagated multilayer networks to control robot arms. From then it has seen many improvements and has been applied in many other areas as a general NN. These improvements have been in the context of generalization, learning techniques, differentiability, memory size, fuzzification and hardware implementation. This paper is a systematic review of CMAC's different structures and applications.

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Theory and development of higher-order CMAC neural networks
Jack Gelfand

IEEE Control Systems, 2000

T h e Cerebellar Model Articulation Controller (CMAC) neural network is capable of learning nonlinear functions extremely quickly due to the local nature of its weight updating. The rectangular shape of CMAC receptive field functions, however, produces d i s c o n t i n u o u s ( s t a i r c a s e ) f u n c t i o n approximations without inherent analytical derivatives. The ability to learn both functions and function derivatives is important for the development of many on-line adaptive filter, estimation, and control algorithms. It is shown that use of B-Spline receptive field functions in conjunction with more general CMAC weight addressing schemes allows higher-order CMAC neural networks to be developed that can learn both functions and function derivatives. This also allows novel hierarchical and multi-layer CMAC network architectures to be constructed that can be trained using standard error back-propagation learning techniques.

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High-order MS CMAC neural network
Shih-lin Hung

IEEE Transactions on Neural Networks, 2001

A macro structure cerebellar model articulation controller (CMAC) or MS_CMAC was developed by connecting several one-dimensional (1-D) CMACs as a tree structure, which decomposes a multidimensional problem into a set of 1-D subproblems, to reduce the computational complexity in multidimensional CMAC. Additionally, a trapezium scheme is proposed to assist MS_CMAC to model nonlinear systems. However, this trapezium scheme cannot perform a real smooth interpolation, and its working parameters are obtained through cross-validation. A quadratic splines scheme is developed herein to replace the trapezium scheme in MS_CMAC, named high-order MS_CMAC (HMS_CMAC). The quadratic splines scheme systematically transforms the stepwise weight contents of CMACs in MS_CMAC into smooth weight contents to perform the smooth outputs. Test results affirm that the HMS_CMAC has acceptable generalization in continuous function-mapping problems for nonoverlapping association in training instances. Nonoverlapping association in training instances not only significantly reduces the number of training instances needed, but also requires only one learning cycle in the learning stage. Index Terms-Cerebellar model articulation controller (CMAC), high-order MS_CMAC, macro structure cerebellar model articulation controller (MS_CMAC), quadratic splines.

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Cerebellar Dynamic State Estimation for a Biomorphic Robot Arm
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2005 IEEE International Conference on Systems, Man and Cybernetics, 2005

The cerebellum has been called the brain's "engine of agility". This paper presents a cerebellarinspired neural network that performs dynamic state estimation and predictive control. The model combines two types of learning within a radial basis function network. Its performance was demonstrated on a 2-link robot arm built with antagonistic pairs of McKibben air muscles. The arm has a gripper end effector to hold and throw a tennis ball. Trajectory data was collected during multiple throwing trials and used to train the model offline. The data were projected onto 2-dimensional state space maps, from which the network learns to estimate state variables and decision boundaries. It successfully learned to trigger the grip release at the proper state for the ball to hit a target. This algorithm should generalize to benefit a wide variety of biomorphic robots.

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Dynamic control of a robot arm using CMAC neural networks
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Neural identification and control techniques are well-suited to the problem of controlling robot dynamics. This paper describes the use of CMAC networks for the adaptive dynamic control of an orange-harvesting robot. Among the various neural-network p~,~ligms available, the CMAC model was chosen in this c~c because of its f~t convergence and on-line adaptation capability. The solution of this dynamic control problem with CMAC is an encouraging demonstration of "experience-based', as opposed to model-based, control techniques ,and is a good example of the use of on-line learning in adaptive neural control

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Cerebellar adaptive control of a biomimetic manipulator
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Neurocomputing, 1999

We present a learning cerebellar model to control reaching movements of a simulated biomimetic manipulator. The system utilizes the servo mechanism of the spinal re#ex circuitry to allow kinematic control of slow movements while learning predictive dynamic compensation. Key elements of the model are: (1) parallel postural and dynamics controllers; (2) a neural network model explicitly based on the physiology of the cerebellum, utilizing the cerebelloolivary loop for stable learning; (3) modulation of gamma-motoneurons during movements to sense trajectory errors from Ia spindle e!erents. Results demonstrate the ability to rapidly learn to accurately control stereotyped fast movements.

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A Scalable Neuro-inspired Robot Controller Integrating a Machine Learning Algorithm and a Spiking Cerebellar-Like Network
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Biomimetic and Biohybrid Systems

Combining Fable robot, a modular robot, with a neuroinspired controller, we present the proof of principle of a system that can scale to several neurally controlled compliant modules. The motor control and learning of a robot module are carried out by a Unit Learning Machine (ULM) that embeds the Locally Weighted Projection Regression algorithm (LWPR) and a spiking cerebellar-like microcircuit. The LWPR guarantees both an optimized representation of the input space and the learning of the dynamic internal model (IM) of the robot. However, the cerebellar-like sub-circuit integrates LWPR input-driven contributions to deliver accurate corrective commands to the global IM. This article extends the earlier work by including the Deep Cerebellar Nuclei (DCN) and by reproducing the Purkinje and the DCN layers using a spiking neural network (SNN) implemented on the neuromorphic SpiN-Naker platform. The performance and robustness outcomes from the real robot tests are promising for neural control scalability.

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Cerebellum-inspired neural network solution of the inverse kinematics problem
Mitra Asadi

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

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A Neuropsychologically-Inspired Computational Approach to the Generalization of Cerebellar Learning
Edmund M Lai

International Conference on Neural Information Processing, 2006

The CMAC neural network is a well-established computational model of the human cerebellum. A major advantage is its localized generalization property which allows for efficient computations. However, there are also two major problems associated with this localized associative property. Firstly, it is difficult to fully-train a CMAC network as the training data has to fully cover the entire set of

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A Novel Self-organizing Fuzzy Cerebellar Model Articulation Controller Based Overlapping Gaussian Membership Function for Controlling Robotic System
Thành Ngô

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL

This paper introduces an effective intelligent controller for robotic systems with uncertainties. The proposed method is a novel self-organizing fuzzy cerebellar model articulation controller (NSOFC) which is a combination of a cerebellar model articulation controller (CMAC) and sliding mode control (SMC). We also present a new Gaussian membership function (GMF) that is designed by the combination of the prior and current GMF for each layer of CMAC. In addition, the relevant data of the prior GMF is used to check tracking errors more accurately. The inputs of the proposed controller can be mixed simultaneously between the prior and current states according to the corresponding errors. Moreover, the controller uses a self-organizing approach which can increase or decrease the number of layers, therefore the structures of NSOFC can be adjusted automatically. The proposed method consists of a NSOFC controller and a compensation controller. The NSOFC controller is used to estimate the i...

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Adaptive Robotic Control Driven by a Versatile Spiking Cerebellar Network
Niceto Luque

PLoS ONE, 2014

The cerebellum is involved in a large number of different neural processes, especially in associative learning and in fine motor control. To develop a comprehensive theory of sensorimotor learning and control, it is crucial to determine the neural basis of coding and plasticity embedded into the cerebellar neural circuit and how they are translated into behavioral outcomes in learning paradigms. Learning has to be inferred from the interaction of an embodied system with its real environment, and the same cerebellar principles derived from cell physiology have to be able to drive a variety of tasks of different nature, calling for complex timing and movement patterns. We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. Encoding and decoding strategies based on neuronal firing rates were applied. Adaptive motor control protocols with acquisition and extinction phases have been designed and tested, including an associative Pavlovian task (Eye blinking classical conditioning), a vestibulo-ocular task and a perturbed arm reaching task operating in closed-loop. The SNN processed in real-time mossy fiber inputs as arbitrary contextual signals, irrespective of whether they conveyed a tone, a vestibular stimulus or the position of a limb. A bidirectional long-term plasticity rule implemented at parallel fibers-Purkinje cell synapses modulated the output activity in the deep cerebellar nuclei. In all tasks, the neurorobot learned to adjust timing and gain of the motor responses by tuning its output discharge. It succeeded in reproducing how human biological systems acquire, extinguish and express knowledge of a noisy and changing world. By varying stimuli and perturbations patterns, real-time control robustness and generalizability were validated. The implicit spiking dynamics of the cerebellar model fulfill timing, prediction and learning functions.

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Weights Behavior in the Solution Space of the Cerebellar Model Articulation Controller (CMAC) learning
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CMAC is an artificial neural network which represents the cerebellum model. This network has the capability to learn fast and to store information locally. The important aspect of learning capability is weights convergence. In line with that, this paper presents weights behavior in the solution space of CMAC learning. First, CMAC learning was formulated into the least square problem. Second, the least square solutions including LU, QR, and SVD methods were examined. Third, the LMS algorithm of CMAC learning was presented to compute the least square solution iteratively. In the implementation, sequential image “Claire” were used to arrange the dataset in which the row, column, and frame numbers are the network input and the corresponding pixel value is the desired output. Results show that the LMS solution with zero weights initialization converges to the SVD solution. The order of methods based on the norm values from smallest to largest are SVD, LMS, QR, and LU respectively. In the solution space, the LU, QR, and LMS weights with random initialization are segmented into subspaces based on CMAC generalization values. Weights on the same subspace have a uniform distance to the corresponding SVD subspace. In addition, the speed and stability of the weight training influenced by the convergence parameter μ in which the higher the value of μ, the faster the speed of weight convergence, and the more erratic the weight convergence tracking.

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Application of Cerebellar Model Articulation Controller in Nonlinear System Tracking Control
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This paper presents an online learning control algorithm based on CMAC network to realize the tracking control problem of nonlinear system. Compared with the traditional two-dimensional input extended to multi-input multi-output nonlinear system, a new address space mapping method is introduced in the cerebellum controller to avoid collision of address space and improve the stability of the microcomputer image controller.

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Hardware implementation of CMAC type neural network on FPGA for command surface approximation
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The hardware implementation of neural networks is a new step in the evolution and use of neural networks in practical applications. The CMAC cerebellar model articulation controller is intended especially for hardware implementation, and this type of network is used successfully in the areas of robotics and control, where the real time capabilities of the network are of particular importance. The implementation of neural networks on FPGA's has several benefits, with emphasis on parallelism and the real time capabilities.This paper discusses the hardware implementation of the CMAC type neural network, the architecture and parameters and the functional modules of the hardware implemented neuro-processor.

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Two Novel Learning Algorithms for CMAC Neural Network Based on Changeable Learning Rate
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Cerebellar Model Articulation Controller Neural Network is a computational model of cerebellum which acts as a lookup table. The advantages of CMAC are fast learning convergence, and capability of mapping nonlinear functions due to its local generalization of weight updating, single structure and easy processing. In the training phase, the disadvantage of some CMAC models is unstable phenomenon or slower convergence speed due to larger fixed or smaller fixed learning rate respectively. The present research deals with offering two solutions for this problem. The original idea of the present research is using changeable learning rate at each state of training phase in the CMAC model. The first algorithm deals with a new learning rate based on reviation of learning rate. The second algorithm deals with number of training iteration and performance learning, with respect to this fact that error is compatible with inverse training time. Simulation results show that this algorithms have faster convergence and better performance in comparison to conventional CMAC model in all training cycles .

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Building Practical Classifiers Using Cerebellar Model Associative Memory Neural Networks
David Cornforth

Proc. Conf Artificial Neural Networks and Expert …, 2001

How can cerebellar model neural networks be successfully applied to automated classification? Simple modifications and a new training scheme are applied to the Cerebellar Model Articulation Controller (CMAC). This results in a classifier with fast training time, guaranteed convergence and a small number of parameters. How can model parameters be set to achieve optimum classifier accuracy, without lengthy empirical trials? A consideration of the most significant sources of classification error results in a simple method for estimating the optimum range for the parameters. The method is tested using empirical trials, and shown to be reliable. This makes the modified CMAC a desirable choice for automated classification in the context of pattern recognition and data mining.

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