A Learning Quasi-stiffness Control Framework of a Powered Trans-femoral Prosthesis for Adaptive Speed and Incline Walking

TL;DR

This work tackles the challenge of generalizing impedance-based control for powered transfemoral prostheses across variable walking tasks. It introduces a task-adaptive, tuning-free quasi-stiffness framework that integrates a Gaussian Process Regression model for predicting task-target features and Kernel Movement Primitives for reconstructing task-specific torque-angle relationships, which are then used to configure a quasi-stiffness controller. The approach enables autonomous adaptation to different speeds and inclines without manual impedance tuning and achieves biomimetic joint kinematics and kinetics that compete with or surpass a finite-state machine impedance controller benchmark. Experimental results on a transfemoral amputee demonstrate accurate target feature prediction, reliable torque-angle reconstruction, and improved gait symmetry, indicating potential for daily-life task variation. The framework advances practical deployment by reducing tuning burden and supporting continuous task variation.

Abstract

Impedance-based control represents a prevalent strategy in the powered trans femoral prostheses because of its ability to reproduce natural walking. However, most existing studies have developed impedance-based prosthesis controllers for specific tasks, while creating a task-adaptive controller for variable-task walking continues to be a significant challenge. This article proposes a task-adaptive quasi-stiffness control framework for powered prostheses that generalizes across various walking tasks, including the torque-angle relationship reconstruction part and the quasi-stiffness controller design part. A Gaussian Process Regression model is introduced to predict the target features of the human joints angle and torque in a new task. Subsequently, a Kernel Movement Primitives is employed to reconstruct the torque-angle relationship of the new task from multiple human reference trajectories and estimated target features. Based on the torque-angle relationship of the new task, a quasi-stiffness control approach is designed for a powered prosthesis. Finally, the proposed framework is validated through practical examples, including varying speeds and inclines walking tasks. Notably, the proposed framework not only aligns with but frequently surpasses the performance of a benchmark finite state machine impedance controller without necessitating manual impedance tuning and has the potential to expand to variable walking tasks in daily life for the trans-femoral amputees.

Figures (13)

• Figure 1: Overview of the proposed learning quasi-stiffness control framework. (a) Task estimation as input for learning the new torque-angle relationship. $T(v,\gamma)$ denotes the task parameter (where $v$ denotes the walking speed, $\gamma$ represents the terrain parameters). (b) Diagram of GPR-based target features prediction. Typically, the lower limb joints' angle and torque trajectories in one gait cycle have local maximum and minimum, which can be selected as target features to represent the kinematic and kinetic of the joint in one specific task li2021toward. The blue dots ($\theta_i^\kappa$, where $\theta_i^\kappa$ denotes the $\kappa$ features of the $i$-th reference) represent the target features from human reference trajectories, and the purple dots indicate the predicted target features (${\Gamma _{via}} = \{ \theta _q^{via},\tau _q^{via}\} _{\kappa = 1}^K,$ where $K$ represents the number of target features) of a new task. (c) KMP-based torque-angle relationship reconstruction. The left figure represents the reference torque-relationship retrieved by GMM/GMR and the right figure denotes the reconstructed torque-angle relationship $R(\theta, \tau)$ by the KMP. (d) Quasi-stiffness estimation from the reconstructed torque-angle relationship. Each dashed line represents a linear regression of each part of the relationship. The slope of the linear regression function denotes the quasi-stiffness. The intersection point of the regression equation with the x-axis represents the equilibrium angle. (e) Applying the quasi-stiffness control on a powered transfemoral prosthesis.
• Figure 2: Finite state machine (FSM) of the quasi-stiffness control strategy. Similar to standard impedance control, the quasi-stiffness control strategy also divides the gait cycle into four phases. Stance extension begins when the measured moment $M_y$ reaches the threshold $M_y^{se}$. Once the measured vertical ground reaction force $F_z$ is less than a threshold $F_z^{to}$, which means toe-off happens, the stance extension state switches to the swing flexion state. When the knee angle $q_k$ reaches the swing extension threshold $q_k^{se}$, the swing extension state starts. Finally, the FSM start backs at stance flexion state when the $F_z$ is greater than $F_z^{hs}$ (heel strike happens).
• Figure 3: Powered transfemoral prosthesis used in this study: CAD version with key components (left) and the real manufactured version (right).
• Figure 4: RMSE of the GPR model in the target feature estimation.
• Figure 5: Experimental results of the KMP-based torque-angle relationship reconstruction. (a) Torque-angle relationship reproduces from human reference trajectories, where the blue curves denote the torque-angle relationships of human reference trajectories and the yellow curve (shadow regions denote variance) represents the reference torque-angle relationship retrieved by GMM-GMR. (b) Torque-angle relationship with target features is reconstructed by KMP, where the blue curves denote the torque-angle relationships of different walking speeds from human reference trajectories. The yellow dashed curve represents the torque-angle relationship passing through the target features and reconstructed by KMP at a new walking speed.