This paper deals with manipulator systems comprising a long-reach manipulator (LRM) with a short-reach dextrous manipulator (SRM) attached to its end. The former, due to its size, is assumed to have significant structural flexibility, while the latter is modeled as a rigid robot. The particular problem addressed is that of active damping, or vibration suppression, of the LRM by using SRM specifically for that purpose Such a scenario is envisioned for operations where the large manipulator is used to deploy the small robot and it is necessary to damp out vibrations in LRM prior to operating SRM. The proposed solution to the problem uses the reaction force from SRM to LRM as a control variable which allows to effectively decouple the controller design problems for the two manipulators. A two-stage controller is presented that involves first, determining the trajectory of the short manipulator required to achieve a desired damping wrench to the supporting flexible arm and subsequently, brings the small manipulator to rest. Performance of the active damping algorithm developed is illustrated with a six-degree-of-freedom rigid manipulator on a flexible mast. Comparison to an independent derivative joint controller is included. The paper also discusses how the proposed methodology can be extended to address other issues related to operation of long-reach manipulator systems.
H∞ controller design for spectral MIMO models by convex optimization
