Phase-Variable Control of a Powered Knee-Ankle Prosthesis over Continuously Varying Speeds and Inclines

Abstract

Most controllers for lower-limb robotic prostheses require individually tuned parameter sets for every combination of speed and incline that the device is designed for. Because ambulation occurs over a continuum of speeds and inclines, this design paradigm requires tuning of a potentially prohibitively large number of parameters. This limitation motivates an alternative control framework that enables walking over a range of speeds and inclines while requiring only a limited number of tunable parameters. In this work, we present the implementation of a continuously varying kinematic controller on a custom powered knee-ankle prosthesis. The controller uses a phase variable derived from the residual thigh angle, along with real-time estimates of ground inclination and walking speed, to compute the appropriate knee and ankle joint angles from a continuous model of able-bodied kinematic data. We modify an existing phase variable architecture to allow for changes in speeds and inclines, quantify the closed-loop accuracy of the speed and incline estimation algorithms for various references, and experimentally validate the controller by observing that it replicates kinematic trends seen in able-bodied gait as speed and incline vary.

Fig. 1.

A block diagram of the proposed control architecture. A phase estimate s and task estimate χ feed a kinematic model that produces desired knee and ankle reference angles ${\theta }_{\text{k}}^{\text{d}}$ and ${\theta }_{\text{a}}^{\text{d}}$. A position controller commands knee and ankle joint torques τ_k and τ_a, which interact with the user/prosthesis system to produce thigh, knee, and ankle angles θ_th, θ_k, θ_a, and ground contact forces F_xyz and moments M_xyz.

Fig. 2.

A photo of the experimental setup, including the custom powered knee-ankle prosthesis attached to the able-bodied subject with a bypass adapter. The load cell x, y, and z coordinate axes are indicated by the red, blue, and green arrows, respectively.

Fig. 3.

The initial (left) and minimum (middle) expected thigh angles produced by the adaptive phase variable parameter algorithm as functions of incline for 1.0 m/s walking. The parameter trends align with observations of able-bodied walking, where ${\theta }_{\text{th}}^0$ increases with incline and ${\theta }_{\text{th}}^{\text{min}}$ remains relatively constant for the range of inclines tested. The average phase variable trajectory with respect to normalized stride time T₀ (right), with shading representing one standard deviation, shows that modulating these parameters results in a consistent phase calculation that is independent of incline.

Fig. 4.

The mean knee and ankle joint angles produced by the prosthesis during the steady-state trials (solid) plotted against the ideal joint angles (dashed) for varying tasks as functions of normalized stride time T₀. The shaded regions represent one standard deviation on either side of the mean. The changes in kinematics in response to changes in task show trends that resemble trends seen in able-bodied gait. Differences between kinematics are the net result of phase and task estimate errors, and imperfect position control, and user gait individuality.

Fig. 5.

The RMSE observed in the task estimates during all steady-state walking trials as functions of speed and incline. The average errors over all 18 minutes of steady-state test data were 0.91 deg for the incline estimator and 0.041 m/s for the speed estimator.

Fig. 6.

Normal distributions representing the task estimate errors for different inclines (top) and walking speeds (bottom). The distributions were fit using all 18 minutes of steady-state walking data.

Fig. 7.

Example ramp responses of the task estimators during the transient task trials. The left plot shows an incline ramp from 0.0° to 6.0° at 1.0 m/s and the right plot shows a speed ramp from 1.3 to 1.0 m/s at 0.0 deg. These trials indicate that the task estimators can track task ramps in real-time with an accuracy that is similar to steady-state. Note that the piecewise-continuous nature of these plots is due to the estimates updating only once per stride.

Fig. 8.

The step responses of the task estimators during two discontinuous task trials, demonstrating a reasonable response time and robustness to discontinuous changes in task. The left plot shows an instantaneous incline increase from 0.0 deg to 6.0 deg and the right plot shows an instantaneous decrease in walking speed from 1.0 m/s to 0.7 m/s.