In Situ Variable Stiffness Strategy for a Planar Tensegrity Manipulator Using Quadratic Programming

Tensegrity manipulators are rigid-flexible coupling elastic mechanisms with complex stiffness characteristics. By changing the prestress levels of tensile cables, the manipulators become versatile mechanisms with variable stiffness. This allows them to maneuvering steadily in high stiffness mode during transport tasks while exhibiting good carrying capacity and hold enhanced compliance for interactive safety in lower stiffness mode. However, it is difficult to achieve the desirable pose and desired stiffness simultaneously for tensegrity manipulators due to the strong correlation between the equilibrium pose and the prestress state. This article proposes an in situ variable stiffness strategy for the dual-triangle planar tensegrity manipulator (DTPTM), which can change the manipulator’s stiffness without changing its pose. First, a static model is developed for the tensegrity manipulator under external constraints in terms of natural coordinates. Then, the tangent stiffness matrix is derived and reduced based on the statics model and the corresponding null space matrix. By constructing the objective function, the variable stiffness strategy is established as a quadratic programming problem to vary the stiffness of all joints. On the basis of numerical results, we analyze the range of variable stiffness for the dual-triangle tensegrity (DTT) module and discuss the feasibility of the variable stiffness strategy. Finally, the variable stiffness strategy is verified by various simulation results and validated by hardware experiments of the 2-degrees-of-freedom manipulator prototype.