A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)

Abstract

CM AC is an adaptive system by which control functions for many degrees of freedom operating simultaneously can be computed by referring to a table rather than by mathematical solution of simultaneous equations. CM AC combines input commands and feedback variables into an input vector which is used to address a memory where the appropriate output variables are stored. Each address consists of a set of physical memory locations, the arithmetic sum of whose contents is the value of the stored variable. The CM AC memory addressing algorithm takes advantage of the continuous nature of the control function in a way which promises to make it possible to store the necessary data in a physical memory of practical size.

A Regularized Inverse QR Decomposition Based Recursive Least Squares Algorithm for the CMAC Neural Network

“…In the non-regularized solution, ( ) k A and ( ) k y in (5.12) are replaced with ( ) k X and ( ) k d . Thus, in [11] it is shown that an ( 1) ( 1) w w n n + × + orthogonal matrix ( ) k T exists that will perform the non-regularized update by updating using the latest entry of ( ) k X and ( ) k d , which are ( ) k x and ( ) d k respectively, ( 1) ( ) ( ) ( )…”

“…For IQR-RLS we need the 1 ( ) k − R matrix however, so the derivation continues. Now the problem becomes how to update ( 1) k…”

“…In the standard CMAC, the LMS algorithm shown in (2.1) is used for this purpose, where k is the training sample iteration, β is the learning rate, ( ) d k is the desired output, and ( ) ( 1) T k k− x w is the actual CMAC output. ( )…”

“…respectively, so we must update with the latest entries of ( ) k X , ( and similarly to update ( 1) k…”

Q-Learning in Continuous State and Action Spaces

“…Santamaria, Ashwin and Sutton [6] have presented results for Q-learning systems using Albus's CMAC (Cerebellar Model Articulation Controller) [10]. The CMAC is a function approximation system which features spatial locality, avoiding the unlearning problem described in Sect.…”