Real-time estimate of period derivatives using adaptive oscillators: Application to impedance-based walking assistance

Abstract

Inferring temporal derivatives (like velocity and acceleration) from a noisy position signal is a well-known challenge in control engineering, due to the intrinsic trade-off between noise filtering and estimation bandwidth. To tackle this problem, in this paper we propose a new approach specifically designed for periodic movements. This approach uses an adaptive oscillator as fundamental building block. It is a tool capable of synchronizing to a periodic input while learning its features (frequency, amplitude, . . . ) in dedicated state variables. Since the oscillator's input and output are perfectly synchronized during steady-state regime, a non-delayed estimate of the input temporal derivatives can be obtained simply by deriving the output analytical form. Pending a (quasi-)periodic input signal, these temporal derivatives are thus synchronized with the actual kinematics, while the signal bandwidth can be arbitrarily tuned by the intrinsic dynamics of the oscillator. We further validate this approach by developing an impedance-based strategy for assisting human walking in the LOPES lower-limb exoskeleton. Preliminary results with a single participant give rise to three main conclusions. First, our method indeed provides velocity and acceleration estimates of the participant's joint kinematics which are smoother and less delayed with respect to the actual kinematics than using a standard Kalman filter. Second, closing the human-robot loop with a high-gain impedance field depending on the acceleration is not possible with a Kalman filter approach, due to unstable dynamics. In contrast, our approach tolerates high gains (up to 70% of the nominal walking torque), showing its intrinsic stability. Finally, no clear benefit of the acceleration-dependent field with respect to a simpler position-dependent field is visible regarding the reduction of metabolic cost. This last result illustrates the challenge of designing sound assistive strategies for complex tasks like walking.

Pre-Impact Detection Algorithm to Identify Tripping Events Using Wearable Sensors

“…This result was expected since it reflects the behavior of the AOs to better track signals with a lower frequency content. In fact, the AOs behave like low-pass filters with zero delay [32]. Noticeably, the frequency content of the shank orientation was lower than that of the foot (Figure 7); thus, the AOs can more accurately track the kinematics of the proximal body segments during steady locomotion.…”

Development of a hierarchical control strategy for a soft knee exoskeleton based on wearable multi-sensor system

“…Similarly, an adaptive oscillator-based estimation method was developed to predict cyclical/periodic trajectory during walking assistance. 42 In Kamalia et al, 43 a trajectory generator was designed to predict the time-normalized sit-to-stand trajectory based on a previously collected database of sample trajectories. Compared with the above methods, the trajectory generator in our research can modulate the desired trajectory in real-time according to the gait variation and motion intention of human.…”

Current developments of robotic hip exoskeleton toward sensing, decision, and actuation: A review

“…Given the cycle feature of gait analysis, AO is a natural way of modeling or generating periodic behavior (Buchli et al, 2004;Ronsse et al, 2011a;Yan et al, 2017;Xue et al, 2019). Ronsse et al (2011bRonsse et al ( , 2012 first applied AO to estimate the user's intended movement while performing a cyclical motion task such as walking. As shown in Figure 5b, Lenzi et al (2013) proposed an assistive controller which can compute the current stride percent by combining the left foot heel strike detection with the gait cycle estimated through an adaptive frequency oscillator.…”

“…Ronsse et al ( 2011b , 2012 ) first applied AO to estimate the user’s intended movement while performing a cyclical motion task such as walking. As shown in Figure 5b , Lenzi et al ( 2013 ) proposed an assistive controller which can compute the current stride percent by combining the left foot heel strike detection with the gait cycle estimated through an adaptive frequency oscillator.…”