An Optimal Control-Based Digital Computational Framework for Predicting the Entire Cycle Sit-to-Stand Motion in Unilateral Transtibial Amputees

Abstract

Sit-to-stand movement is the prerequisite for other lower limb movements and determines the independent living ability of lower limb amputees. Although optimal control theory enables human motion prediction without experimental data, existing studies on sit-to-stand prediction for lower limb amputees have neither focused on transtibial amputees nor considered buttocks-seat contact. To address these limitations, this study aims to develop an optimal control-based digital computational framework for predicting the entire cycle sit-to-stand movement of transtibial amputees while analysing the biomechanical effect of prosthesis stiffness changes. The motion prediction was formulated as an optimal control problem, where the system dynamic constraints were incorporated into a biomechanical model of the unilateral transtibial amputee and the smooth Hunt-Crossley contact force model. To overcome the challenge of difficult to satisfy static equilibrium constraints at the initial and final time points of motion, a novel “free-fall method” inspired by natural motion was proposed to determine the vertical translation and pitch angle of the human model. Combining the above innovative methods with the numerically efficient direct collocation method, a digital computational framework for predicting the entire cycle sit-to-stand motion of unilateral transtibial amputees was established. After being validated by experimental data, the proposed framework was then used to analyse the effect of changes in prosthetic stiffness on the biomechanical behaviour of amputees. The predicted lower limb joint angles, ground reaction forces, and seat reaction force successfully capture key experimental features. Furthermore, the effects of changes in prosthetic stiffness on dynamic behaviour were revealed, fully demonstrating the unique advantage of predictive simulation that does not require experimental data. Our approach has great potential in multiple fields such as the design of prostheses and rehabilitation strategies, as well as motion planning for humanoid robots.