Inverse Kinematics and Sensitivity Minimization of an n-Stack Stewart Platform

摘要

The method of Frobenius Norm (FN) minimization of forward kinematic Jacobians is presented to minimize the sensitivity of a robotic manipulator. We demonstrate the effectiveness of this approach with a Monte Carlo simulation of an Assembler robot. The Assembler is described as a stack of Stewart Platforms designed for in-space assembly to aide NASA in deep space exploration. The translations and rotations between each Stewart Platform define the forward kinematics of the Assember, which analytically determine the end effector position and orientation. However, selecting the poses of each Stewart Platform which yield a desired end effector state, defined as the inverse kinematics, is an underconstrained nonlinear optimization problem for large Assembler stacks.