Using locally weighted regression for robot learning

The use of locally weighted regression in memory-based robot learning is explored. A local model is formed to answer each query, using a weighted regression in which close points (similar experiences) are weighted more than distant points (less relevant experiences). This approach implements a philosophy of modeling a complex function with many simple local models. The author explains how an appropriate distance metric or measure of similarity can be found, and how the distance metric is used. How irrelevant input variables and terms in the local model are detected is also explained. An example from the control of a robot arm is used to compare this approach with other robot control and learning techniques.<<ETX>>

[1]  Catherine W. M. Sherriff,et al.  XIII.—On a Class of Graduation Formulæ , 2022 .

[2]  Frederick Robertson Macaulay,et al.  The Smoothing of Time Series , 1931 .

[3]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[4]  I. K Crain,et al.  Treatment of non-equispaced two-dimensional data with a digital computer , 1967 .

[5]  C. Pelto,et al.  AUTOMATIC CONTOURING OF IRREGULARLY SPACED DATA , 1968 .

[6]  R. F. Walters Contouring by Machine: A User's Guide , 1969 .

[7]  D. H. McLain,et al.  Drawing Contours from Arbitrary Data Points , 1974, Comput. J..

[8]  James S. Albus,et al.  Data Storage in the Cerebellar Model Articulation Controller (CMAC) , 1975 .

[9]  James S. Albus,et al.  New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)1 , 1975 .

[10]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[11]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

[12]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[13]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1976, TOMS.

[14]  W. Cleveland Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[15]  P. Lancaster Moving Weighted Least-Squares Methods , 1979 .

[16]  Richard Franke,et al.  Smooth interpolation of large sets of scattered data , 1980 .

[17]  Norman R. Draper,et al.  Applied regression analysis (2. ed.) , 1981, Wiley series in probability and mathematical statistics.

[18]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[19]  L. Devroye On the Almost Everywhere Convergence of Nonparametric Regression Function Estimates , 1981 .

[20]  John E. Dennis,et al.  Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4] , 1981, TOMS.

[21]  C. J. Stone,et al.  Optimal Global Rates of Convergence for Nonparametric Regression , 1982 .

[22]  R. Franke Scattered data interpolation: tests of some methods , 1982 .

[23]  Ker-Chau Li Consistency for Cross-Validated Nearest Neighbor Estimates in Nonparametric Regression , 1984 .

[24]  P. Cheng Strong consistency of nearest neighbor regression function estimators , 1984 .

[25]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[26]  R. Farwig Multivariate interpolation of scattered data by moving least squares methods , 1987 .

[27]  H. Müller Weighted Local Regression and Kernel Methods for Nonparametric Curve Fitting , 1987 .

[28]  Filson H. Glanz,et al.  Application of a General Learning Algorithm to the Control of Robotic Manipulators , 1987 .

[29]  David L. Waltz,et al.  Applications of the Connection Machine , 1990, Computer.

[30]  W. Cleveland,et al.  Regression by local fitting: Methods, properties, and computational algorithms , 1988 .

[31]  W. Cleveland,et al.  Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting , 1988 .

[32]  Barak A. Pearlmutter,et al.  Using a neural network to learn the dynamics of the CMU Direct-Drive Arm II , 1988 .

[33]  J. Doyne Farmer,et al.  Exploiting Chaos to Predict the Future and Reduce Noise , 1989 .

[34]  M. C. Jones,et al.  Spline Smoothing and Nonparametric Regression. , 1989 .

[35]  Christopher G. Atkeson,et al.  Task-level robot learning: juggling a tennis ball more accurately , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[36]  C. Atkeson,et al.  Learning arm kinematics and dynamics. , 1989, Annual review of neuroscience.

[37]  Andrew W. Moore,et al.  Acquisition of Dynamic Control Knowledge for a Robotic Manipulator , 1990, ML.