TY - JOUR
T1 - Towards a robust solution of the non-linear kinematics for the general stewart platform with estimation of distribution algorithms
AU - Martinez, Eusebio Eduardo Hernández
AU - Peña, Sergio Ivvan Valdez
AU - Soto, Eduardo Sánchez
PY - 2013/1/15
Y1 - 2013/1/15
N2 - In robotics, solving the direct kinematics problem (DKP) for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non-linear system of equations. In addition, given that the system could be non-convex, Newton or Quasi-Newton (Dogleg) based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well-known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non-linear system of equations, and of course, to non-linear optimization problems.
AB - In robotics, solving the direct kinematics problem (DKP) for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non-linear system of equations. In addition, given that the system could be non-convex, Newton or Quasi-Newton (Dogleg) based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well-known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non-linear system of equations, and of course, to non-linear optimization problems.
KW - Direct kinematics
KW - Hybrid optimizer
KW - Parallel robots
KW - Probabilistic learning
UR - http://www.scopus.com/inward/record.url?scp=84872911424&partnerID=8YFLogxK
U2 - 10.5772/52172
DO - 10.5772/52172
M3 - Artículo
SN - 1729-8806
VL - 10
JO - International Journal of Advanced Robotic Systems
JF - International Journal of Advanced Robotic Systems
M1 - 41
ER -