Analysis of Continuously Varying Kinematics for Prosthetic Leg Control Applications

Abstract

Powered prosthetic legs can improve the quality of life for people with transfemoral amputations by providing net positive work at the knee and ankle, reducing the effort required from the wearer, and making more tasks possible. However, the controllers for these devices use finite state machines that limit their use to a small set of pre-defined tasks that require many hours of tuning for each user. In previous work, we demonstrated that a continuous parameterization of joint kinematics over walking speeds and inclines provides more accurate predictions of reference kinematics for control than a finite state machine. However, our previous work did not account for measurement errors in gait phase, walking speed, and ground incline, nor subject-specific differences in reference kinematics, which occur in practice. In this work, we conduct a pilot experiment to characterize the accuracy of speed and incline measurements using sensors onboard our prototype prosthetic leg and simulate phase measurements on ten able-bodied subjects using archived motion capture data. Our analysis shows that given demonstrated accuracy for speed, incline, and phase estimation, a continuous parameterization provides statistically significantly better predictions of knee and ankle kinematics than a comparable finite state machine, but both methods' primary source of predictive error is subject deviation from average kinematics.

Fig. 1.

Definitions of subject coordinates: the angles of the thigh (θ_th) and foot (θ_f) segments are defined relative to the world frame, and the knee (θ_k) and ankle (θ_a) angles are defined in the frame of the proximal limb segment. All angles are zero when the subject is standing upright.

Fig. 2.

Parameterization by phase variable (φ, solid lines) vs. percent gait (PG, dashed lines) for three example tasks: walking at 1 m/s on a −10° (blue), 0° (red), and +10° (green) incline. Trajectories represent across-subject averages. The phase variable plot (top) shows both φ and PG scaled from 0 to 100% on the vertical axis.

Fig. 3.

Histogram showing the inner 99% of phase errors in the simulation.

Fig. 4.

Histograms and normal distribution approximation of all errors encountered in the task measurement pilot experiment. The frequency count of the incline graph (bottom) is lower than the speed graph (top) due to the number of trials eliminated for saturating the foot IMU gyroscope.

Fig. 5.

Violin plots comparing total error to the expected error due to all five major error factors. For visibility, only the inner 97% of errors are plotted for Phase, Subject, and Total. Subject is the largest error source by far.

Fig. 6.

The SPM t-value indicating which method creates statistically significantly less error for the gait cycle of the knee (top) or ankle (bottom). The colored bars across y = 0 indicate which method has statistically lower error in that region of the gait cycle, as determined by an SPM two-tailed t-test. 62% gait is highlighted to show the expected end of the stance period.