Computational prediction of 3D crutch-assisted walking patterns is a challenging problem that could be applied to study different biomechanical aspects of crutch walking in virtual subjects, to assist physiotherapists to choose the optimal crutch walking pattern for a specific subject, and to help in the design and control of exoskeletons, when crutches are needed for balance. The aim of this work is to generate a method to predict three-dimensional crutch-assisted walking motions following different patterns without tracking any experimental data. To reach this goal, we collected gait data from a healthy subject performing a four-point non-alternating crutch walking pattern, and developed a 3D torque-driven full-body model of the subject including the crutches and foot- and crutch-ground contact models. First, we developed a predictive (i.e., no tracking of experimental data) optimal control problem formulation to predict crutch walking cycles following the same pattern as the experimental data collected, using different cost functions. To reduce errors with respect to reference data, a cost function combining minimization terms of angular momentum, mechanical power, joint jerk and torque change was chosen. Then, the problem formulation was adapted to handle different foot- and crutch-ground conditions to make it capable of predicting three new crutch walking patterns, one of them at different speeds. A key aspect of our algorithm is that having ground reactions as additional controls allows one to define phases inside the cycle without the need of formulating a multiple-phase problem, thus facilitating the definition of different crutch walking patterns.

3D拐杖辅助行走模式的计算预测是一个具有挑战性的问题，可以用于研究虚拟受试者中拐杖行走的不同生物力学方面，以帮助物理治疗师为特定受试者选择最佳的拐杖行走模式，并帮助设计需要平衡拐杖时控制外骨骼。这项工作的目的是要产生一种方法来预测遵循不同模式的三维拐杖辅助步行运动而无需跟踪任何实验数据。为了达到这个目标，我们收集了来自健康受试者的步态数据，该受试者进行了四点非交替式拐杖行走模式，并开发了3D扭矩驱动的受试者全身模型，包括拐杖以及脚和拐杖与地面的接触楷模。首先，我们制定了一个预测（即 无需跟踪实验数据）最优控制问题的表述，使用不同的成本函数，按照与收集的实验数据相同的模式预测拐杖的行走周期。为了减少相对于参考数据的误差，选择了一种将角动量，机械功率，关节跳动和扭矩变化的最小化条件组合在一起的成本函数。然后，将问题表述调整为适应不同的脚和拐杖着地情况，使其能够预测三种新的拐杖行走模式，其中一种以不同的速度行驶。我们算法的一个关键方面是，将地面反应作为附加控件，使人们可以在循环内定义相，而无需提出多相问题，从而有助于定义不同的拐杖行走方式。