Real-Time Estimation of Intrinsic and Reflex Stiffness

Joint stiffness is defined as the dynamic relationship between the position of the joint and torque acting about it. Joint stiffness is composed of two components: intrinsic and reflex stiffness. Measuring the two stiffness components cannot be done simply because the two components appear and change together. A number of approaches have been used to estimate the components, but all those approaches are inherently off-line. We have developed novel algorithm that separates and estimates the two components in real-time. Intrinsic stiffness was estimated by finding the cross-correlations between the position, its derivatives and the torque. Reflex stiffness was estimated by finding the IRF between the half-wave rectified velocity and the estimated reflex torque. A novel position perturbation, consisting of pseudo random series of pulses of different lengths, was used to eliminate covariance of intrinsic and reflex stiffness estimates. Using simulated data, the real-time estimates were shown to be estimated accurately. The real-time estimation algorithm was validated by comparing the real-time estimates with estimates generated by the parallel-cascade identification, an established off-line intrinsic and reflex stiffness identification algorithm, using simulated and experimental data. The estimates produced by the two algorithms were in agreement for both simulated and experimental data