An experimental study of resolved acceleration control in singularities: damped least-squares approach

2002 ◽  
Author(s):  
M. Kircanski ◽  
N. Kircanski ◽  
D. Lekovic ◽  
M. Vukobratovic
Keyword(s):  
Experimental Study ◽  
Least Squares ◽  
Resolved Acceleration Control ◽  
Damped Least Squares ◽  
Least Squares Approach

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.

An Experimental Study of Resolved Acceleration Control of Robots at Singularities: Damped Least-Squares Approach

1997 ◽  
Vol 119 (1) ◽  
pp. 97-101 ◽  
Author(s):  
M. Kirc´anski ◽  
N. Kirc´anski ◽  
D. Lekovic´ ◽  
M. Vukobratovic´
Keyword(s):  
Least Squares ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Control Level ◽  
Singular Values ◽  
Control Scheme ◽  
Resolved Acceleration Control ◽  
Robot Task ◽  
Damped Least Squares ◽  
Value Decomposition

Most of the robot task space control methods based on inverse Jacobian matrix suffer from instability in singular regions of workspace. Methods based on damped least-squares algorithm (DLS) for matrix inversion have been developed but not experimentally confirmed. The application of DLS method at the kinematic control level has been reported in (Chiaverini et al., 1994). In this article, a modified DLS method combined with the resolved-acceleration control scheme, is experimentally verified on two degrees of freedom of a PUMA-560 robot. In order to decrease the position error introduced by the damping, only small singular values are damped, in contrast to the conventional damping method were all the singular values are damped. The symbolic expressions of the singular value decomposition of the Jacobian matrix were used, to decrease the computational burden.

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.

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