Stabilizing Time-Dependent Stiffness Gains in Adaptive Shared Control

Kurzfassung

Recent approaches in adaptive shared control introduce Virtual Fixtures that use time-dependent stiffness gains. However, these can lead to a loss of passivity if stiffness increases too fast. This work introduces two novel variable impedance controllers that follow the desired stiffness gains, but modify parameters of the virtual spring if passivity is lost otherwise. The first approach scales the spring deflection with a scalar and thus keeps the structure of the desired position gains. However, jumps in stiffness lead to approximation errors in this method, which result in a minor loss of passivity. The second method directly scales the change in stiffness gains. It ensures that stationary stiffness gains in a specific degree of freedom remain stationary, while also ensuring passivity for jumps in the desired stiffness profile. Compared to the first method, the implementation of the desired position gains can be slower. Both controllers ensure that the system remains passive, converges to the attractor point, and is applicable to trajectories. These properties are also verified experimentally on a 1-DOF device and the 7-DOF redundant robotic arm SARA.