Stiffness Estimation and Nonlinear Control of Robots with Variable Stiffness Actuation

We consider the problem of estimating on line the nonlinear stiffness of flexible transmissions in robots with variable stiffness actuation in agonistic-antagonistic configuration. Stiffness estimation is obtained using a dynamic residual that provides a filtered version of the unmeasured flexibility torques, combining it with a recursive least squares algorithm that fits a polynomial model to the data, and proceeding then by analytical derivation. Only motor position/velocity and link position measurements are used, while knowledge of dynamic parameters is required for the motors but not for the links. The estimated stiffness function, together with its first two derivatives with respect to the deformation, is used within a feedback linearization controller designed for simultaneous tracking of desired trajectories for the links and the device stiffnesses. Simulation results provided for the VSA-II device demonstrate the perfomance of the estimation process and the effectiveness of the complete control approach.