Directional Stiffness Modulation of Parallel Robots With Kinematic Redundancy and Variable Stiffness Joints

Parallel robots have been primarily investigated as potential mechanisms with stiffness modulation capabilities through the use of actuation redundancy to change internal preload. This paper investigates real-time stiffness modulation through the combined use of kinematic redundancy and variable stiffness actuators. A known notion of directional stiffness is used to guide the real-time geometric reconfiguration of a parallel robot and command changes in joint-level stiffness. A weighted gradient-projection redundancy resolution approach is demonstrated for resolving kinematic redundancy while satisfying the desired directional stiffness and avoiding singularity and collision between the legs of a Gough/Stewart parallel robot with movable anchor points at its base and with variable stiffness actuators. A simulation study is carried out to delineate the effects of using kinematic redundancy with or without the use of variable stiffness actuators. In addition, modulation of the entire stiffness matrix is demonstrated as an extension of the approach for modulating directional stiffness.