Mohammad Rastgaar

Stochastic Estimation of the Multi-Variable Mechanical Impedance of the Human Ankle With Active Muscles

This article compares stochastic estimates of multi-variable human ankle mechanical impedance when ankle muscles were fully relaxed, actively generating ankle torque or co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Muscle activation levels were monitored electromyographically and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when it was worn by a human subject, the difference between these functions providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in both DP and IE directions.Copyright

Quantitative Characterization of Steady-State Ankle Impedance With Muscle Activation

Characterization of multi-variable ankle mechanical impedance is crucial to understanding how the ankle supports lower-extremity function during interaction with the environment. This paper reports quantification of steady-state ankle impedance when muscles were active. Vector field approximation of repetitive measurements of the torque-angle relation in two degrees of freedom (inversion/eversion and dorsiflexion/plantarflexion) enabled assessment of spring-like and non-spring-like components. Experimental results of eight human subjects showed direction-dependent ankle impedance with greater magnitude than when muscles were relaxed. In addition, vector field analysis demonstrated a non-spring-like behavior when muscles were active, although this phenomenon was subtle in the unimpaired young subjects we studied.

Orthogonal Eigenstructure Control with Non-collocated Actuators and Sensors

An orthogonal eigenstructure control method with collocated actuators and sensors was recently developed by the authors. In this paper the application of the method is extended beyond the collocation of the actuators and sensors, including the cases that different numbers of actuators and sensors are used. Orthogonal eigenstructure control is an output feedback control for multi-input multi-output linear systems. This method uses singular value decomposition to find the matrix that spans the null space of the closed-loop eigenvectors. This method regenerates the open-loop system while simultaneously determines a set of eigenvectors that are orthogonal to the open-loop eigenvectors. This method does not attempt to place the eigenvalues of the closed-loop system, nor does it require defining a set of closed-loop eigenvectors. The closed-loop eigenvectors will be within the achievable eigenvector set and the closed-loop poles will be consistent with them. As a result, no extra constraints have been imposed to the system trying to place the closed-loop poles at certain locations such that excessive force in actuators is prevented. Since there are usually some limitations on the location of the actuators and sensors, collocation of actuators and sensors is not always possible. Also, some systems might not have equal number of actuators and sensors. The proposed method in this paper is based on adding virtual actuators and sensors to the closed-loop system in order to extend the application of the orthogonal eigenstructure control to the systems with non-collocated actuators and sensors as well as the systems with different numbers of actuators and sensors.

Ankle mechanics during sidestep cutting implicates need for 2-degrees of freedom powered ankle-foot prostheses

The ankle joint of currently available powered prostheses is capable of controlling one degree of freedom (DOF), focusing on improved mobility in the sagittal plane. To increase agility, the requirements of turning in prosthesis design need to be considered. Ankle kinematics and kinetics were studied during sidestep cutting and straight walking. There were no significant differences between the ankle sagittal plane mechanics when comparing sidestep cutting and straight walking; however, significant differences were observed in ankle frontal plane mechanics. During straight walking, the inversion-eversion (IE) angles were smaller than with sidestep cutting. The ankle that initiated the sidestep cutting showed progressively increasing inversion from 2 to 13 degrees while the following contralateral step showed progressively decreasing inversion from 8 to -4 degrees during normal walking speed. The changes in IE kinematics were the most significant during sidestep cutting compared with straight walking. The IE moments of the step that initiated the sidestep cutting were always in eversion, acting as a braking moment opposing the inverting motion. This suggests that an ankle-foot prosthesis with active DOFs in the sagittal and frontal planes will increase the agility of gait for patients with limb loss.

Control of a 2-DOF powered ankle-foot mechanism

This paper describes a finite state machine to control an ankle-foot prosthesis with two degrees of freedom (DOF) in the sagittal and frontal planes. Strain gauges were installed in the foot to provide ground reaction torques feedback for impedance and admittance controllers to be used at heel-strike and push-off of the gait, respectively. The quasi-static stiffness of the ankle with the active control was measured showing a near linear relationship between the torque feedback gain and the stiffness of the ankle. The performance of the finite state machine and controllers were also evaluated using a custom-made circular treadmill and the results were compared to the results of the prosthesis using position controller and inactive controllers. The results showed that the impedance/admittance controller was capable of tracking the desired input trajectory while decreasing the required torque at the ankle joint.

Ankle Angles During Step Turn and Straight Walk: Implications for the Design of a Steerable Ankle-Foot Prosthetic Robot

This article compares the three-dimensional angles of the ankle during step turn and straight walking. We used an infrared camera system (Qualisys Oqus ®) to track the trajectories and angles of the foot and leg at different stages of the gait. The range of motion (ROM) of the ankle during stance periods was estimated for both straight step and step turn. The duration of combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The ROM in Inversion/Eversion (IE) increased during turning while Medial/Lateral (ML) rotation decreased and Dorsiflexion/Plantarflexion (DP) changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk (−9.68° of dorsiflexion) and progressively showed less plantarflexion (1.37° at toe off). In IE, the ankle showed increased inversion leaning the body toward the inside of the turn (angles from 5.90° to 13.61°). ML rotation initiated with an increased medial rotation of 5.68° relative to the straight walk transitioning to 12.06° of increased lateral rotation at the toe off. A novel tendon driven transtibial ankle-foot prosthetic robot with active controls in DP and IE directions was fabricated. It is shown that the robot was capable of mimicking the recorded angles of the human ankle in both straight walk and step turn.Copyright

Stochastic Estimation of Multi-Variable Human Ankle Mechanical Impedance

This article presents preliminary stochastic estimates of the multi-variable human ankle mechanical impedance. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Time histories of the torques in Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions and the associated angles of the ankle were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot and when the Anklebot was worn by a human subject. The difference between these impedance functions provided an estimate of the mechanical impedance of the ankle. High coherence was observed over a frequency range up to 30 Hz, indicating that this procedure yielded an accurate measure of ankle mechanical impedance in DP and IE directions.Copyright

Multi-directional Dynamic Mechanical Impedance of the Human Ankle; A Key to Anthropomorphism in Lower Extremity Assistive Robots

The mechanical impedance of the human ankle plays a central role in lower-extremity functions requiring physical interaction with the environment. Recent efforts in the design of lower-extremity assistive robots have focused on the sagittal plane; however, the human ankle functions in both sagittal and frontal planes. While prior work has addressed ankle mechanical impedance in single degrees of freedom, here we report on a method to estimate multi-variable human ankle mechanical impedance and especially the coupling between degrees of freedom. A wearable therapeutic robot was employed to apply torque perturbations simultaneously in the sagittal and frontal planes and record the resulting ankle motions. Standard stochastic system identification procedures were adapted to compensate for the robot dynamics and derive a linear time-invariant estimate of mechanical impedance.

Design and Evaluation of a 2-DOF Instrumented Platform for Estimation of the Ankle Mechanical Impedance in the Sagittal and Frontal Planes

This paper describes the fabrication and initial evaluation of a vibrating platform with two degrees of freedom (DOF) to estimate the human ankles mechanical impedance in two DOFs; namely dorsiflexion-plantarflexion (DP) and inversion-eversion (IE). The device consists of an actuation and a force plate module. The actuation module generates torque perturbations up to 168 N·m in DP and 26 N·m in IE in the force plate module using Bowden cables. This provides a low-profile system that can be installed in a walkway. The frame of the force plate module rotates in two DOFs, applying torque perturbations to the human ankle in DP and IE. The ankles rotations are measured using a motion capture camera system. The analytical and numerical approaches for estimation of the ankles torques, rotations, and impedances are presented. A system validation using a mockup was conducted to verify the systems ability to estimate the impedance of a physical system in two DOFs. The developed system was capable of identifying the mockups physical properties up to 15 Hz. The mockups impedance magnitude at 0.9 Hz using a stochastic identification method was shown to be within 1.68% and 0.54% of the mockups stiffness in DP and IE, respectively.

Orthogonal Eigenstructure Control for Vibration Suppression

Orthogonal eigenstructure control is a novel active control method for vibration suppression in multi-input multi-output linear systems. This method is based on finding an output feedback control gain matrix in such a way that the closed-loop eigenvectors are almost orthogonal to the open-loop ones. Singular value decomposition is used to find the matrix, which spans the null space of the closed-loop eigenvectors. This matrix has a unique property that has been used in this new method. This unique property, which has been proved here, can be used to regenerate the open-loop system by finding a coefficient vector, which leads to a zero gain matrix. Also several vectors, which are orthogonal to the open-loop eigenvectors, can be found simultaneously. The proposed method does not need any trial and error procedure and eliminates not only the need to specify any location or area for the closed-loop eigenvalues but also the requirements of defining the desired eigenvectors. This method determines a set of limited number of closed-loop systems. Also, the elimination of the extra constraints on the locations of the closed-loop poles prevents the excessive force in actuators.