Variable Aerodynamic Damping via Co-Contraction: A Dynamic Isomorphism with Variable Stiffness Actuators

Abstract: We prove that aerodynamic co-contraction in a redundant dual-rotor actuator can tune a passive, trim-defined aero-mechanical damping while keeping the commanded net force constant. In particular, we define an incremental damping coefficient as the local sensitivity of net thrust to air-relative velocity at a trim and prove that it increases monotonically along constant-force fibers under a mild aerodynamic hardening condition. We then validate the required damping and hardening properties from a first-principles Blade Element Theory derivation, which yields a minimal thrust model affine in inflow and explicitly reveals the speed--inflow coupling driving the effect. The resulting mechanism is formalized as a Variable Aerodynamic Damping Actuator (VADA) and shown to be dynamically isomorphic to stiffness modulation in antagonistic variable-stiffness actuation (VSA), similar to the co-contraction of tendons by muscle co-activation. The same fiber-density principle also enhances the active aerodynamic promptness measure of redundant multirotors. Finally, an impedance-form representation clarifies the roles of common-mode and differential-mode actuation in the control of passive impedance and the equilibrium velocity of the VADA system.