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. 2018 Jun;34(3):686-701.
doi: 10.1109/TRO.2018.2794536. Epub 2018 Feb 27.

Continuous-Phase Control of a Powered Knee-Ankle Prosthesis: Amputee Experiments Across Speeds and Inclines

David Quintero  1   2 , Dario J Villarreal  3 , Daniel J Lambert  4 , Susan Kapp  5 , Robert D Gregg  1   2
Affiliations

Continuous-Phase Control of a Powered Knee-Ankle Prosthesis: Amputee Experiments Across Speeds and Inclines

David Quintero et al. IEEE Trans Robot. 2018 Jun.

Abstract

Control systems for powered prosthetic legs typically divide the gait cycle into several periods with distinct controllers, resulting in dozens of control parameters that must be tuned across users and activities. To address this challenge, this paper presents a control approach that unifies the gait cycle of a powered knee-ankle prosthesis using a continuous, user-synchronized sense of phase. Virtual constraints characterize the desired periodic joint trajectories as functions of a phase variable across the entire stride. The phase variable is computed from residual thigh motion, giving the amputee control over the timing of the prosthetic joint patterns. This continuous sense of phase enabled three transfemoral amputee subjects to walk at speeds from 0.67 to 1.21 m/s and slopes from -2.5 to +9.0 deg. Virtual constraints based on task-specific kinematics facilitated normative adjustments in joint work across walking speeds. A fixed set of control gains generalized across these activities and users, which minimized the configuration time of the prosthesis.

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Figures

Fig. 1
Fig. 1
The UT Dallas powered knee-ankle prosthesis: CAD rendering and key components (left) and manufactured version (right). A timing belt connects each motor to a linear ball screw, which converts rotary motion to translational motion that drives a lever arm to produce a joint torque.
Fig. 2
Fig. 2
The control architecture for the prosthesis comprises an outer and inner loop. The outer loop computes the desired joint torques (Eq. 2) needed to enforce the virtual constraints (Eq. 5) based on the mechanical phase variable (Eq. 7). The desired knee torque τdk is converted to current commands for the knee motor driver ( ukA) using an inverse model of the knee actuator. The current commands for the ankle motor driver ( uaA) are computed by an inner loop (Eq. 10) that provides closed-loop torque control with a friction compensator.
Fig. 3
Fig. 3
Phase plane of the thigh angle ϕ(t) vs. its integral Φ(t) during prosthetic leg experiments (Section IV). The phase plane has been scaled by z and shifted by (γ, Γ) to achieve a circular orbit across the stride, which improves the linearity of the phase variable ϑ(t).
Fig. 4
Fig. 4
Photo of transfemoral amputee subject wearing the powered knee-ankle prosthesis. The IMU sensor is mounted on the pylon between the residual limb socket and the prosthetic knee joint (in the sagittal plane).
Fig. 5
Fig. 5
Phase portrait of the prosthetic leg (measured joint angular positions vs. velocities) over 20 consecutive strides of steady-state, level-ground walking at the comfortable speed (about 2.0 mph) for amputee subjects TF01 (left), TF02 (center), and TF03 (right), compared with averaged able-bodied data (AB) [5]. Note that the prosthetic joints follow similar orbits to the able-bodied data.
Fig. 6
Fig. 6
Powered prosthesis joint kinematics/kinetics for TF01 level-ground walking at 2.0 mph, averaged over 20 consecutive strides with ±1 standard deviation shown by shaded regions. The commanded (Cmd) and measured (2.0 mph) joint angles are shown over normalized time (a–b) and over the phase variable (c–d). The estimated joint torques (e–f) and powers (g–h) are normalized by subject mass and compared with averaged able-bodied data (AB) over the phase variable [5]. The knee torque is estimated with the measured motor current and the knee actuator model, and the ankle torque is estimated with the measured linear force and ankle kinematic model (Fig. 2). The phase variable over time (i) is strictly monotonic and nearly linear, where the most variance occurs during early and mid stance. Box plots of mechanical work per stride (j) show the median (red line), 25th percentile (bottom of box), 75th percentile (top of box), distribution bounds (black whiskers), and outliers (red plus markers). Ankle work is positive, knee work is negative, and total work is near zero as expected from able-bodied walking [5].
Fig. 7
Fig. 7
Powered prosthesis joint kinematics/kinetics for TF02 level-ground walking at multiple speeds with slow, normal, and fast kinematics, averaged over 15–20 consecutive strides. The measured joint angles over phase (a–b) demonstrate that faster speeds produce a larger range of motion. The estimated joint torques (c–d) and powers (e–f) are normalized by subject mass and plotted over phase, demonstrating more torque and power at faster speeds. The phase variable over time (g) is monotonic with a steeper slope (i.e., shorter time duration) for faster speeds. Box plots of mechanical work per stride (h) show the median (red line), 25th percentile (bottom of box), 75th percentile (top of box), distribution bounds (black whiskers), and outliers (red plus markers) for each speed condition. Ankle work and total work increase with walking speed as expected [5].
Fig. 8
Fig. 8
Powered prosthesis joint kinematics/kinetics for TF02 level-ground walking at multiple speeds with fixed normal-speed kinematics, averaged over 15–20 consecutive strides. The measured joint angles (a–b), normalized joint torques (c–d), and normalized joint powers (e–f) are more appropriate for slow and normal speeds than the fastest speed. The phase variable over time (g) adapts appropriately with all speeds, having a steeper slope (i.e., shorter time duration) for faster speeds. Box plots of mechanical work per stride (h) show the median (red line), 25th percentile (bottom of box), 75th percentile (top of box), distribution bounds (black whiskers), and outliers (red plus markers) for each speed condition. Ankle work and total work are appropriate for slow and normal walking but insufficient for the fastest speed [5].
Fig. 9
Fig. 9
Powered prosthesis joint kinematics/kinetics for TF02 walking on multiple ground slopes at 2.0 mph with slope-specific kinematics, averaged over 10–20 consecutive strides. The measured joint angles over phase (a–b) exhibit more stance ankle dorsiflexion and stance knee flexion/extension for steeper inclines. The estimated joint torques (c–d) and powers (e–f) are normalized by subject mass and plotted over phase. The phase variable over time (g) has a consistent, linear trajectory across ground slopes (i.e., similar time durations). Box plots of mechanical work per stride (h) show the median (red line), 25th percentile (bottom of box), 75th percentile (top of box), distribution bounds (black whiskers), and outliers (red plus markers) for each slope condition.
Fig. 10
Fig. 10
Powered prosthesis joint kinematics/kinetics for TF03 walking on 7.5 deg incline at 2.0 mph, averaged over 9 consecutive strides with ±1 standard deviation shown by shaded regions. The commanded (Cmd) and measured (7.5 deg) joint angles are shown over normalized time (a–b) and over the phase variable (c–d). The commanded signals have some variance at the end of the stride due to the use of a rate limiter as a safety feature. The estimated joint torques (e–f) and powers (g–h) are normalized by subject mass and shown over the phase variable. The phase variable over time (i) is strictly monotonic and nearly linear. Box plots of mechanical work per stride (j) show the median (red line), 25th percentile (bottom of box), 75th percentile (top of box), distribution bounds (black whiskers), and outliers (red plus markers).
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References

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