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

An autonomous system is presented to solve the problem of in space assembly, which can be used to further the NASA goal of deep space exploration. A prototype of an autonomous manipulator called "Assemblers" was fabricated from an aggregation of Stewart Platform robots for the purpose of researching autonomous in space assembly capabilities. Selecting inverse kinematic poses, deined by a set of translations and rotations, for the Assembler requires coordination between each Stewart Platform and is an underconstrained non-linear optimization problem. For assembly tasks, it is ideal that the pose selected has the least sensitivity to disturbances possible. A method of sensitivity reduction is proposed by minimizing the Frobenius Norm (FN) of the Jacobian of the forward kinematics. The efectiveness of the FN method will be demonstrated through a Monte Carlo simulation to model random motion internal to the structure.