Prosthetic leg control in the nullspace of human interaction

Abstract

Recent work has extended the control method of virtual constraints, originally developed for autonomous walking robots, to powered prosthetic legs for lower-limb amputees. Virtual constraints define desired joint patterns as functions of a mechanical phasing variable, which are typically enforced by torque control laws that linearize the output dynamics associated with the virtual constraints. However, the output dynamics of a powered prosthetic leg generally depend on the human interaction forces, which must be measured and canceled by the feedback linearizing control law. This feedback requires expensive multi-axis load cells, and actively canceling the interaction forces may minimize the human's influence over the prosthesis. To address these limitations, this paper proposes a method for projecting virtual constraints into the nullspace of the human interaction terms in the output dynamics. The projected virtual constraints naturally render the output dynamics invariant with respect to the human interaction forces, which instead enter into the internal dynamics of the partially linearized prosthetic system. This method is illustrated with simulations of a transfemoral amputee model walking with a powered knee-ankle prosthesis that is controlled via virtual constraints with and without the proposed projection.

Continuous instinct control for powered knee-ankle prostheses

“…A prosthesis based on HZD control assumes that the bipedal model is in contact with the ground on only one leg stance [8,9,10], i.e the gait stance period and the swing period respectively account for 50% of gait cycle. However, the human actual movement is 60% in the stance period and 40% in the swing period.…”

Hybrid Nonlinear Disturbance Observer Design for Underactuated Bipedal Robots

“…Existence of disturbances in unknown environments is a pervasive challenge in HZD-based control of autonomous bipedal robots [9]. Furthermore, in the context of rehabilitation robotics, persistent human inputs might act as disturbances on the wearable robot HZD-based control scheme [10]. These disturbances can deteriorate the performance of the robot motion control systems and even adversely affect their stability.…”

Automatic tuning of virtual constraint-based control algorithms for powered knee-ankle prostheses

“…This section presents the human-prosthesis biped dynamical model from [13], [20], the necessary preliminaries from virtual constraint-based control, and the standard ESC architecture used in the paper. The planar model of a transfemoral amputee consists of seven leg segments and a point mass at the hip, as shown in Fig.…”

“…Following [13], [20], we model bipedal locomotion as a hybrid dynamical system. During the phases of walking, the state is governed by one second-order differential equation during the prosthetic swing phase and another second-order differential equation during the prosthetic stance phase.…”

“…The transitions between these two phases are governed by two impact maps, which correspond to instantaneous changes in the joint velocities. In particular, the human-prosthesis biped dynamics are given by (see [12], [13], [20], [21] for further details) $$\begin{array}{ccc}rightright{M}_{\mathrm{e}}{\ddot{q}}_{\mathrm{e}}+C_{\mathrm{e}}{\dot{q}}_{\mathrm{e}}+G_{\mathrm{e}}+E_P^T{\lambda }_{\mathrm{P}}=B_{\mathrm{e}}{u}_{\mathrm{e}},& right\text{if}& right{p}_{\mathrm{H}}false(q_{\mathrm{e}}false)>0\\ right\left(q_{\mathrm{e}}^{+},{{\dot{q}}_{\mathrm{normale}}}^{+}\right)={\Delta }_{\mathrm{H}}\left(q_{\mathrm{e}}^{-},{{\dot{q}}_{\mathrm{normale}}}^{-}\right),& right\text{if}& right{p}_{\mathrm{H}}false(q_{\mathrm{e}}false)=0\\ right{M}_{\mathrm{e}}{\ddot{q}}_{\mathrm{e}}+C_{\mathrm{e}}{\dot{q}}_{\mathrm{e}}+G_{\mathrm{e}}+E_H^T{\lambda }_{\mathrm{H}}=B_{\mathrm{e}}{u}_{\mathrm{e}},& right\text{if}& right{p}_{\mathrm{P}}false(q_{\mathrm{e}}false)>0\\ right\left(q_{\mathrm{e}}^{+},{{\dot{q}}_{\mathrm{normale}}}^{+}\right)={\Delta }_{\mathrm{P}}\left(q_{\mathrm{e}}^{-},{{\dot{q}}_{\mathrm{normale}}}^{-}\right),& right\text{if}& right{p}_{\mathrm{P}}false(q_{\mathrm{e}}false)=0\end{array}$$ where the subscripts P and H are associated with the prosthesis and the human, respectively. Also, the vector $E_{}^{}$…”