Design of holonomic loops for repeatability in redundant manipulators

Redundant manipulators under pseudoinverse control are nonholonomic systems in general. The nonholonomy manifests itself when closed paths in the workspace of the manipulator fail to produce closed paths in the joint space. Previous research indicates that repeatability may be guaranteed if the initial manipulator configuration lies on a stable surface. In such cases repeatability is achieved due to the integrability of the nonholonomic constraints. Since stable surfaces are rare, we look into the design of holonomic loops that will guarantee repeatability in the absence of integrability. We present a necessary condition for the existence of holonomic loops and we design holonomic loops for redundant manipulators in three dimensions. The extension of our results to higher dimensional systems lies in the scope of our future research