Reduced Power Method: how to evoke low-bandwidth behaviour while estimating full-bandwidth dynamics

Abstract

Many human motion control studies use system identification methods to estimate the human admittance (the frequency response function from force to position). Admittance was found to be affected by task instruction, environmental properties and perturbation properties. From literature it is known the frequency content (bandwidth) of the perturbation modulates the admittance, due to modulation of the reflexive feedback. However, reducing the perturbation bandwidth reduces the identifiable admittance bandwidth. Yet, the full dynamic range is necessary to understand the changes in control behaviour, and also to ensure accurate parametric fits of neuromusculoskeletal models to the estimated admittance. The goal of this study is to develop a perturbation signal that evokes low bandwidth control behaviour while it enables identification over the full admittance bandwidth. This study introduces the Reduced Power Method. Effectively, multisine torque perturbations are supplemented with reduced power (a small percentage of full power) beyond the perturbation bandwidth, large enough to allow accurate identification, and small enough not to influence control behaviour. The method was tested in an experimental study. The dynamic ankle control behaviour of subjects (n=10) was measured while performing a variety of tasks in face of continuous torque perturbations with and without the addition of reduced power. The estimated admittance varied substantially as a result of task instruction and perturbation bandwidth, but not as a result of the additional reduced power. In conclusion, the proposed method was successful in estimating the full dynamics of the admittance while the resulting control behaviour was adapted to the low-frequent full power perturbations.