A Limited Interval Gradient Projection Algorithm for Inverse Kinematics

2012 ◽  
Vol 490-495 ◽  
pp. 7-12
Author(s):  
Wei Song ◽  
Guang Hu
Keyword(s):  
Inverse Kinematics ◽  
Nonlinear Function ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Motion Generation ◽  
Local Linearization ◽  
Gradient Projection Algorithm ◽  
Inverse Kinematics Problem ◽  
Jacobian Inverse ◽  
Programming Time

The Jacobian inverse(JI) method is a well-known algorithms used for inverse kinematics solutions in motion generation. JI algorithm can be easily implemented, but it can generate singularity problems and it is not straight forward to implement constraints in the JI method. This paper presents a novel gradient projection algorithm that can convert the inverse kinematics problem to a constraint nonlinear programming problem. Meanwhile, by changing the programming time of each frame, local linearization of the nonlinear function and limited interval computing can be achieved simultaneously. Experimental results are presented to show the performance benefits of the proposed algorithm over JI methods.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

scholarly journals A Regularized Gradient Projection Method for the Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Yao ◽  
Shin Min Kang ◽  
Wu Jigang ◽  
Pei-Xia Yang
Keyword(s):  
Projection Method ◽  
Minimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Gradient Projection Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Gradient Projection Algorithm

We investigate the following regularized gradient projection algorithmxn+1=Pc(I−γn(∇f+αnI))xn,n≥0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problemminx∈Cf(x).

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