Designing dynamics and control of isotropic Gough-Stewart micromanipulators

A new, seven parameter class of micromanipulators is found with decoupled dynamics. The flexibility of the new class is demonstrated by designing a Stewart platform with fully equalized and decoupled dynamics (i.e., all resonant frequencies are equal). Although this has been attempted before by other researchers, it has not been previously accomplished. The ability to design the dynamics so they are amenable to control leads to significant increases in closed loop performance and robustness. The dynamically decoupled and equalized manipulator is compared to an asymmetric manipulator in closed loop. Even though both manipulators control the same payload over the same bandwidth with exactly the same struts, the H_∞ controller for the equalized manipulator is five times less sensitive to worst case disturbances than the H_∞ controller for the asymmetric manipulator. Moreover, the decoupling facilitates the design of Nyquist stable compensators which give the decoupled manipulator one hundred times higher performance at low frequencies. This greatly increased performance and robustness requires implementation of only the six compensators along the diagonal of the six degree-of-freedom system, versus implementation of all 36 compensators for the asymmetrical manipulator.