An Efficient Algorithm for Global Optimization in Redundant Manipulations

1989 ◽  
Vol 111 (4) ◽  
pp. 488-493 ◽  
Author(s):  
Z. Wang ◽  
K. Kazerounian
Keyword(s):  
Global Optimization ◽  
Boundary Value Problem ◽  
Objective Function ◽  
Efficient Algorithm ◽  
Boundary Value ◽  
Robotic Manipulators ◽  
Exact Boundary ◽  
Task Period

A method is developed to resolve the redundancy of serial robotic manipulators. The main characteristics of this method are as follows: (a) The solution is conservative (unique); (b) It globally (over the task period) optimizes the objective function; (c) It is computationally very fast. In fact, it is about three orders of magnitude faster than solving for the exact boundary value problem.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

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