Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods

1986 ◽  
Vol 16 (1) ◽  
pp. 93-101 ◽  
Author(s):  
Charles Wampler
Keyword(s):  
Least Squares ◽  
Inverse Kinematic ◽  
Damped Least Squares

Applications of Damped Least-Squares Methods to Resolved-Rate and Resolved-Acceleration Control of Manipulators

1988 ◽  
Vol 110 (1) ◽  
pp. 31-38 ◽  
Author(s):  
C. W. Wampler ◽  
L. J. Leifer
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Sensory Feedback ◽  
Inverse Kinematic ◽  
Redundant Manipulators ◽  
Approximate Inverse ◽  
Singular Configurations ◽  
Large Joint ◽  
Resolved Acceleration Control ◽  
Damped Least Squares

Resolved-rate and resolved-acceleration controllers have been proposed for manipulators whose trajectories are determined by real-time sensory feedback. For redundant manipulators, these controllers have been generalized using the pseudoinverse of the manipulator Jacobian. However, near singular configurations, these controllers fail in that they require infeasibly large joint speeds. A damped least-squares reformation of the problem gives approximate inverse kinematic solutions that are free of singularities. Away from singularities the new controllers closely approximate their conventional counterparts; near singular configurations the new controllers remain well-behaved, although the rate of convergence decreases. This paper defines the new controllers and proves their stability. Some aspects of the behavior of the new resolved-rate controller are illustrated in simulations.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Analysis of NMR spectra by damped least squares

1966 ◽  
Vol 21 (1-4) ◽  
pp. 106-107 ◽  
Author(s):  
J. Plíva ◽  
V. Špirko ◽  
S. Toman
Keyword(s):  
Least Squares ◽  
Nmr Spectra ◽  
Damped Least Squares
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