Nonholonomic Virtual Constraints for Control of Powered Prostheses Across Walking Speeds

This article presents a method to design a nonholonomic virtual constraint (NHVC) controller that produces multiple distinct stance-phase trajectories for corresponding walking speeds. NHVCs encode velocity-dependent joint trajectories via momenta conjugate to the unactuated degree(s) of freedom (DOFs) of the system. We recently introduced a method for designing NHVCs that allow for stable bipedal robotic walking across variable terrain slopes. This work extends the notion of NHVCs for application to variable-cadence powered prostheses. Using the segmental conjugate momentum for the prosthesis, an optimization problem is used to design a single stance-phase NHVC for three distinct walking speed trajectories (slow, normal, and fast). This stance-phase controller is implemented with a holonomic swing phase controller on a powered knee–ankle prosthesis, and experiments are conducted with an non-disabled user walking in steady and nonsteady velocity conditions. The control scheme is capable of representing: 1) multiple, task-dependent reference trajectories and 2) walking gait variance due to both temporal and kinematic changes in user motion.