Stiffness Modulation for a Planar Mobile Cable-Driven Parallel Manipulators via Structural Reconfiguration

Mobile Cable-Driven Parallel Manipulators (m-CDPM) are a sub-class of CDPM with greater-capabilities (antagonistic cable-tensioning and reconfigurability) by virtue of mobility of the base-winches. In past work, we had also explored creation of adjustable spring-stiffness modules, in-line with cables, which decouple cable-stiffness and cable-tensions. All these internal-freedoms allow an m-CDPM to track desired trajectories while equilibrating end-effector wrenches and improving lateral disturbance-rejection. However, parameter and configuration selection is key to unlocking these benefits. To this end, we consider an approach to partition task-execution into a primary (fast) winch-tension control and secondary (slow) reconfiguration and joint-stiffness modulation. This would enable a primary trajectory-tracking task together with secondary task-space stiffness tailoring, using system-reconfiguration and joint-stiffness modulation. In this paper, we limit our scope to feasibility-evaluation to achieve the stiffness modulation as a secondary goal within an offline design-optimization setting (but with an eye towards real-time implementation). These aspects are illustrated in the context of a 3-PRP m-CDPM for tracking a desired trajectory within its wrench-feasible workspace. The secondary-task is the directional-alignment and shaping of the stiffness ellipsoid to shape the disturbance-rejection characteristics along the trajectory. The optimization is solved through constrained minimization of a multi-objective weighted cost function subject to non-linear workspace feasibility, and inequality stiffness and tension constraints.