A Stiffness Estimator for Agonistic–Antagonistic Variable-Stiffness-Actuator Devices

Safe physical human-robot interaction, conservation of energy, and adaptability are the main robotic applications that prompted the development of a number of variable stiffness actuators (VSAs). Implemented in a variety of ways, they use various technologies and feature the most diverse mechanical solutions, all of which share a fundamentally unavoidable nonlinear behavior. The control schemes proposed for these actuators typically aim at independent control of the position of the link and its stiffness. Although effective feedback control schemes using position and force sensors are commonplace in robotics, control of stiffness is at present completely open loop: The stiffness is inferred from the mathematical model of the actuator. We consider here the problem of estimating the nonlinear stiffness of VSA in agonistic-antagonistic configuration. We propose an algorithm based on modulating functions that allow us to avoid the need for numerical derivative and for which the tuning is then very simple. An analysis of the error demonstrates the convergence. Simulations are provided, and the algorithm is validated on experimental data.