A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability

The solution of the inverse kinematics is required in many technical applications. In this contribution a concept is proposed which reformulates the inverse kinematics (IK) of kinematically redundant manipulators as a linear programming (LP) problem. This formulation enables the explicit consideration of technical constraints as for example mechanical end-stops, velocity and, if necessary, acceleration limits as linear inequality constraints. Besides that, automatic collision avoidance within the workspace of the manipulator can be included. The kinematic redundancy is resolved with respect to quadratic criteria. As the LP problem at hand belongs to the small-size problems, the optimal solution can be found numerically in appropriate time using standard algorithms such as the simplex algorithm or interior point methods. This article closes with a numerical example of the LP-IK of a planar 4-link manipulato

A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability

The solution of the inverse kinematics is required in many technical applications. In this contribution a concept is proposed which reformulates the inverse kinematics (IK) of kinematically redundant manipulators as a linear programming (LP) problem. This formulation enables the explicit consideration of technical constraints as for example mechanical end-stops, velocity and, if necessary, acceleration limits as linear inequality constraints. Besides that, automatic collision avoidance within the workspace of the manipulator can be included. The kinematic redundancy is resolved with respect to quadratic criteria. As the LP problem at hand belongs to the small-size problems, the optimal solution can be found numerically in appropriate time using standard algorithms such as the simplex algorithm or interior point methods. This article closes with a numerical example of the LP-IK of a planar 4-link manipulato

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory. Published July 201