Virtual and physical prototyping of a beam-based variable stiffness actuator for safe human-machine interaction

This paper reports about the virtual and physical prototyping of an antagonistic Variable Stiffness Actuator (VSA) to be used on robotic arms specifically realized for physical human-robot interaction. Such antagonistic actuation system, which comprises purposely conceived Compliant Transmission Elements (CTEs) characterized by a nonlinear relation between the deflection and the applied torque, allows to simultaneously control both the joint's position and stiffness. The CTE's beams geometry, namely slender spline beams, has been defined by means of an automatic routine leveraging on Matlab and ANSYS and allowing for the shape optimization of complex flexures. The synthesized springs are characterized by a predefined quadratic torque-deflection characteristic, which is shown to guarantee a precise stiffness modulation while avoiding the need for a joint's position sensor. After shape optimization, the CTE is fabricated via additive manufacturing and subsequently tested. The acquired data show a very good consistency with the numerical results, although highlighting a non-negligible hysteresis due to material damping. Therefore, in order to cope with such unavoidable effect along with other parameter uncertainties and unmodeled effects (e.g. static friction), a robust feedback controller is proposed, allowing for the simultaneous and decoupled regulation of joint position and stiffness. Finally, a VSA prototype is produced and tested. Experimental results confirm that the VSA behaves as expected.