A Phase-Invariant Linear Torque-Angle-Velocity Relation Hidden in Human Walking Data

Human walking is a sequential composition of gait cycles. Each gait cycle can be divided into four motion phases separated by heel strike and toe off. A classical conjecture in the control of lower limb assistive devices, state-of-the-art prostheses, and exoskeletons, is that each motion phase requires a different controller, such that adequate control of locomotion requires at least four distinct controllers. In this paper, we show that the joint torque versus joint angle and velocity relation hidden in the normal human walking data can be remarkably well represented with a single linear controller. In particular, based on the analysis of seven healthy subjects, we show that a one phase 20 +/- 5% sparse linear relation between the joint torques, angles and velocities explains 96.1 +/- 0.4% (mean +/- sem) of the normal human walking data (sparsity defines the percentage of zero control parameters). This result is comparable to what can be achieved using a significantly more complex four-phase non-sparse linear controller which explains 98.7 +/- 0.2% of the walking data, and is significantly better than a one-phase fully sparsified linear controller that could only explain 11.9 +/- 0.2% of the same data. Based on these results, we posit that the proposed phase-invariant sparse linear controller provides one of the simplest representations that can adequately explain the joint torque, angle and velocity relation present in the human walking data. The resulting control structure may be useful in developing simple yet competent phase-invariant controllers for next-generation prostheses and exoskeleton devices used for human assistance and augmentation.