In this study, we present and evaluate a novel method to estimate multi-joint leg impedance, using a robotic gait training device. The method is based on multi-input-multi-output system identification techniques and is designed for continuous torque perturbations at the hip and knee joint simultaneously. Eight elderly subjects (age 67-82) performed relax and position tasks in three different leg orientations. Multi-joint impedance was estimated nonparametrically and was subsequently modeled in terms of inertia and (inter)joint stiffness and damping. The results indicate that all stiffness and damping parameters were significantly higher during the position task compared to the relax task. The majority of the stiffness and damping parameters were not significantly affected by leg orientation. The results also emphasize the importance of considering the visco-elastic coupling between joints when modeling multi-joint dynamics. Measuring joint stiffness with the same device that is used for robotic gait training allows convenient testing of joint properties in conjunction with the robotic gait training protocol. These measures might serve as a good basis for quantitative assessment and follow up of patients with abnormal joint stiffness due to neurological disorders, and may reveal how changes in these joint properties affect their gait function.

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.