Foot–ground contact models play an important role in the accuracy of predictive human gait simulations, and there is a need for a computationally-efficient dynamic contact model for predictive and evaluative studies. In this research, we generated symbolic dynamic equations for a 2D torque-driven 11-DOF human model with a 3D ellipsoidal volumetric foot–ground contact model. The main goal was to increase the prediction accuracy and decrease the computation time for human gait analyses compared to the previous studies that used numerical formulations and point foot–ground contact models.A data-tracking optimization was developed to identify the contact parameters of the human gait model using two optimization approaches: trajectory optimization and optimal control. The first approach is developed with a global search algorithm based on inverse dynamics. In this algorithm, a local optimizer is repeatedly run from multiple potential start points to select the best start point while satisfying the constraints and reaching the lowest cost function value. The second approach is developed using direct collocation based on implicit dynamics. In this method, the optimization problem is solved using a variable-order adaptive orthogonal collocation method along with sparse nonlinear programming.Optimal control was superior to trajectory optimization for identifying a large number of parameters; the simulated torques and ground reaction forces from the optimal control correlated better with the experimental data. For the optimal control, the root-mean-square errors of the resultant torques, tangential and normal ground reaction forces were 0.48 (N.m), 14.07 (N), and 26.44 (N), respectively. However, for the trajectory optimization, these errors were 15.19 (N.m), 36.51 (N), and 234.57 (N). Thus, the optimized contact model from the optimal control, which was developed symbolically and based on volumetric contact equations, is a suitable foot–ground contact model for predictive human gait simulations. Additionally, we demonstrated that optimal control could be used to predict the motion and torque for the metatarsal joints, which are not easily measurable in practice.

中文翻译：

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直接搭配最优控制与轨迹优化的椭圆形脚-地面接触模型参数识别比较

脚地接触模型在预测人类步态模拟的准确性中起着重要作用，因此需要一种计算效率高的动态接触模型来进行预测和评估研究。在这项研究中，我们为2D扭矩驱动的11自由度人体模型和3D椭圆形体积足-地面接触模型生成了符号动力学方程。与先前的使用数值公式和点脚-地面接触模型的研究相比，主要目的是提高人体步态分析的预测准确度并减少计算时间。使用两种优化方法的步态模型：轨迹优化和最优控制。第一种方法是使用基于逆动力学的全局搜索算法开发的。在该算法中，从多个可能的起点重复运行局部优化器，以在满足约束条件并达到最低成本函数值的同时选择最佳起点。第二种方法是使用基于隐式动力学的直接配置开发的。该方法采用变阶自适应正交配置方法和稀疏非线性规划方法解决了优化问题。在识别大量参数方面，最优控制优于轨迹优化。最佳控制下的模拟扭矩和地面反作用力与实验数据的相关性更好。为了达到最佳控制效果，合成转矩的均方根误差 切向和法向地面反作用力分别为0.48（Nm），14.07（N）和26.44（N）。但是，对于轨迹优化，这些误差分别为15.19（Nm），36.51（N）和234.57（N）。因此，从最佳控制中获得的最佳接触模型是基于体积接触方程式进行象征性开发的，是用于预测人体步态模拟的合适的脚地接触模型。此外，我们证明了最佳控制可用于预测the关节的运动和扭矩，这在实践中不易测量。它是基于体积接触方程式进行象征性开发的，是用于预测人类步态模拟的合适的脚地接触模型。此外，我们证明了最佳控制可用于预测the骨关节的运动和扭矩，这在实践中不易测量。它是基于体积接触方程式进行象征性开发的，是用于预测人类步态模拟的合适的脚地接触模型。此外，我们证明了最佳控制可用于预测the关节的运动和扭矩，这在实践中不易测量。