Estimation of Joint Stiffness with a Compliant Load

Joint stiffness defines the dynamic relationship between the position of the joint and the torque acting about it. It consists of two components: intrinsic and reflex stiffness. Many previous studies have investigated joint stiffness in an open-loop environment, because the current algorithm in use is an open-loop algorithm. This paper explores issues related to the estimation of joint stiffness when subjects interact with compliant loads. First, we show analytically how the bias in closed-loop estimates of joint stiffness depends on the properties of the load, the noise power, and length of the estimated impulse response functions (IRF). We then demonstrate with simulations that the open-loop analysis will fail completely for an elastic load but may succeed for an inertial load. We further show that the open-loop analysis can yield unbiased results with an inertial load and document IRF length, signal-to-noise ratio needed, and minimum inertia needed for the analysis to succeed. Thus, by using a load with a properly selected inertia, open-loop analysis can be used under closed-loop conditions.