Realtime Delayless Estimation of Derivatives of Noisy Sensor Signals for Quasi-Cyclic Motions With Application to Joint Acceleration Estimation on an Exoskeleton

The control of mechatronic systems can often be enhanced if realtime information on the derivatives of a signal is available. These derivatives are not always measurable by sensors and should be estimated. Simple numerical derivatives cannot be applied, due to noise on the measured signals. Several researchers managed to reduce the noise and calculate the derivative but as a drawback the estimation has a time delay. In this letter, we focus on the realtime derivative estimation of quasi-cyclic signals. Cycles of these signals are very similar but not exactly alike. At each time instant, the derivatives of the previous cycle are fed to a linear state estimator as virtual measurements. This allows to have a delay-free estimation. The proposed method is tested experimentally on a human walking in an exoskeleton with rotary joint encoders. Results show that it is possible to estimate the angular acceleration of hip, knee, and ankle joint in realtime without delay. The algorithm is compared with the technique of adaptive oscillators with non-linear filter, used in literature for a similar application. Our method estimates acceleration better both in steady-state and transient periods.