Suboptimal approximations in repeatable inverse kinematics for robot manipulators

摘要

In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial con-figuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.